A Tale of Game Theory: Metastable Peace

Introduction

A non-equilibrium system is like an inverted pendulum; it will not stay upright on its own. 

It requires:

1. Kahn Safety: Ensuring no player ever believes they have “First Strike Stability” (the ability to win without being destroyed).
2. Schelling Safety: Creating “Focal Points” for a new 3-way distribution of the hundreds of resources so no one feels the need to “Burn Bridges.”
3. Jervis Safety: Aggressive “De-escalation Signaling” to ensure that a defensive move by one isn’t seen as an existential threat by the other.

Kahn’s escalation ladder framework

Herman Kahn’s escalation ladder, introduced in his book On Escalation: Metaphors and Scenarios, is a seminal framework in strategic studies and game theory. It models the progression of a conflict from a minor disagreement to a full-scale "spasm" nuclear war.

As a computer scientist, you might view this as a state-transition model, where each rung represents a discrete state with increasing costs (negative payoffs) and decreasing reversibility.

Kahn identified 44 rungs, grouped into several distinct thresholds or "thresholds of no return." The ladder is designed to help strategists understand "escalation dominance"—the ability to increase the stakes to a level where the opponent cannot match the move and is forced to de-escalate or surrender.

Key Theoretical Concepts

1. Escalation Dominance: A player has escalation dominance if they can move to a higher rung where they have a relative advantage, while the opponent suffers more or lacks the capability to respond at that level. This forces the opponent to choose between a "disadvantageous peace" or an "unacceptable war."
2. The "Stability-Instability Paradox": Kahn’s framework suggests that stability at the highest rungs (fear of nuclear spasm) might actually encourage instability at the lower rungs (conventional skirmishes), as players believe the other side is too rational to escalate to the top of the ladder.
3. Bargaining through Risk: Kahn viewed escalation not as an accident, but as a negotiation process. Each rung is a "message." By climbing the ladder, a player is manipulating the "probability of disaster" to influence the opponent's cost-benefit analysis.

Schelling’s The Strategy of Conflict

Thomas Schelling’s "The Strategy of Conflict" fundamentally reoriented game theory from a purely mathematical exercise into a tool for analyzing social interaction and international relations. While Kahn focused on the structural rungs of escalation, Schelling focused on the psychological and informational dynamics of bargaining.

For a computer scientist, Schelling’s work can be viewed as the study of coordination protocols and constraint-based optimization in environments where communication is noisy or untrusted.

Key Concepts

A. Focal Points (Schelling Points)

Schelling observed that in the absence of communication, players can still coordinate their behavior by converging on a "focal point"—a solution that seems natural, special, or relevant to both.

*   Mechanism: Coordination is achieved through shared cultural or logical salience rather than explicit negotiation.

*   Example: If told to meet someone in New York City on a specific day without a time or location, most people choose "Noon at Grand Central Station."

B. The Threat that Leaves Something to Chance

Unlike Kahn’s linear ladder, Schelling viewed escalation as a "slippery slope." He argued that a threat is often most effective when it is not a 100% certainty, but rather a move that creates a probabilistic risk of a disaster that neither side can fully control.

*   Brinkmanship: This is the strategy of deliberately letting the situation get somewhat out of hand, forcing the opponent to back down to avoid the shared risk of a "fall."

Treatment of Signaling

In Schelling’s framework, talk is "cheap" unless it is backed by action or cost. Effective signaling requires Costly Signaling.

*   Signals as Information: A signal must change the receiver's belief about the sender's payoffs or future intentions.

*   The "Tripwire" Signal: Placing a small number of troops (e.g., in West Berlin during the Cold War) serves no tactical purpose in a full-scale invasion. However, it serves as a powerful signal because their deaths would *automatically* force a larger response, making the commitment to defend the territory credible.

The Strategy of Commitment

Schelling’s most counterintuitive insight was that weakness can be strength. In a bargaining situation, your power is often inversely proportional to your freedom of maneuver. If you can prove you cannot back down, the burden of avoiding a collision shifts entirely to your opponent.

A. The "Burning Bridges" Tactic

To make a commitment credible, a player must voluntarily and visibly destroy their own options for retreat. 

*   Logic: By removing the "Exit" node from your own decision tree, you force the opponent to choose between "Yield" or "Mutual Destruction." Since the opponent knows you have no choice but to stay the course, they are incentivized to yield.

B. Delegation and Automicity

Commitment is strengthened by removing human agency. 

*   The "Doomsday Machine": If a response is programmed to be automatic (an "if-then" statement triggered by an opponent's move), the threat becomes perfectly credible because the "threatener" no longer has the power to change their mind at the last second.

Schelling informs our treatment of signaling and commitment by highlighting that strategic behavior is the art of manipulating expectations. 

1.  Signaling is about overcoming the "cheap talk" problem through irreversible or costly actions.

2.  Commitment is about the paradox of choice: you gain bargaining power by constraining your future self, essentially "binding your hands" to make your threats or promises mathematically certain to the opponent.

Perception and misperception

Robert Jervis’s Perception and Misperception in International Politics introduced cognitive psychology to the game-theoretic models of international relations. While Kahn and Schelling assumed "rational actors" processing information correctly, Jervis demonstrated that **systematic cognitive biases** often cause leaders to misread signals, leading to unintended escalation or missed opportunities for cooperation.

From Computer Science, Jervis’s work can be viewed as an analysis of signal processing errors and noisy channel communication where the "receiver" has a biased prior that filters all incoming data.

The Core Thesis: The "Psychological Model"

Jervis argues that it is not the objective reality that determines a state's behavior, but the perceptions of reality held by decision-makers. He identifies several "cognitive shortcuts" that lead to sub-optimal outcomes.

A. The Impact of Pre-existing Beliefs (Bayesian Updating Failures)

Decision-makers are not good Bayesians. Instead of updating their beliefs based on new evidence, they engage in assimilation:

• New information is interpreted in a way that fits existing theories or "schemas."
• Evidence that contradicts a belief is often dismissed as "noise" or a "deception," while ambiguous evidence is seen as confirming the prior.

B. The "Common Deterrence" vs. "Spiral" Models

Jervis identified two primary frameworks through which leaders view conflict, and argued that choosing the wrong one is catastrophic:

1. The Deterrence Model: Assumes the opponent is an aggressor. The solution is to show strength (climb Kahn’s ladder). If you are wrong, you provoke the opponent unnecessarily.
2. The Spiral Model: Assumes the opponent is motivated by fear. The solution is to offer concessions to build trust. If you are wrong, you embolden a true aggressor (Appeasement).

Key Cognitive Biases in Signaling

Jervis identifies several specific "perceptual traps" that complicate the signaling theories of Schelling:

A. The Deterrence Bias (The "Sinister Attribution" Error)

States tend to see their own actions as a response to the environment (reactive), but view the opponent's actions as a reflection of their innate character or aggressive "programming" (dispositional). This is the Fundamental Attribution Error applied to geopolitics.

B. The Illusion of Transparency

Decision-makers often believe their own signals are clear and unambiguous. They assume that because they know they are peaceful, the opponent must also know it. When the opponent reacts defensively, the first state perceives this as unprovoked aggression rather than a fearful response to a misunderstood signal.

C. Centralization Bias

Observers tend to see the behavior of another state as more centralized and coordinated than it actually is. In reality, a "signal" might be the result of internal bureaucratic infighting or an accidental move by a local commander, but the receiver interprets it as a deliberate, high-level strategic "move."

Misperception in Commitment

Jervis challenges Schelling’s idea of "Burning Bridges." He notes that for a commitment to work, the opponent must perceive that the bridge is burned.

• If the opponent misses the signal due to cognitive "noise," the player has effectively committed themselves to a disastrous course of action that fails to deter.
• Over-reliance on "Salami Slicing": An opponent may misperceive a major commitment as a series of small, unconnected events, leading them to accidentally cross a "red line" they didn't realize existed.

Jervis’s work serves as a "debugging" manual for game theory. He suggests that to understand conflict, one must perform "Cognitive Mapping" of the opponent:

1. Identify their historical analogies: (e.g., Is the leader thinking about Munich 1938 or Vietnam 1965?)
2. Account for "Noise": Recognize that your own signals are likely being distorted by the opponent's internal politics.
3. Empathy as a Tool: Not as a moral virtue, but as a strategic necessity to see the world through the opponent's biased lens to predict their "irrational" moves.

Game with three players

To analyze a game with three main actors (Great Powers or "Oligarchs") and hundreds of limited resources (territories, frequencies, or compute nodes), we can synthesize Kahn, Schelling, and Jervis into a unified framework.

In this scenario, the game is no longer a simple zero-sum duel; it becomes a Coalition-Formation and Resource-Allocation Game with high dimensionality.

1. The Structural Layer: 

Kahn’s Multi-Front EscalationKahn’s ladder provides the State Space for the game. With three players (P1, P2, P3​) and hundreds of resources, escalation is not a single ladder but a Vector of Ladders.

Micro-Escalation: Instead of one "big" war, players can escalate on specific rungs for specific resources (e.g., P1​ and P2 are at Rung 15 regarding Resource A, but at Rung 2 regarding Resource B).

Threshold Management: With hundreds of resources, the "Nuclear Taboo" is replaced by "Systemic Stability Thresholds." If P1 seizes too many resources too quickly, they risk hitting a threshold that triggers a P2+P3 alliance.

Resource Saliency: Not all resources are equal. Kahn’s rungs help categorize which resources are "Counterforce" (strategic assets) vs. "Countervalue" (civilian/economic assets).

2. The Tactical Layer: 

Schelling’s Commitment and Coordination: Schelling provides the Transition Functions between states. In a 3-player game, the primary challenge is Triangular Bargaining.

Focal Points for Partitioning: With hundreds of resources, players cannot negotiate for each one individually. They will naturally gravitate toward "Schelling Points" for division (e.g., geographic boundaries, 33/33/33 splits, or historical ownership).

The "Burning Bridges" of Alliances: In a 3-player game, P1​ can gain leverage by "binding" themselves to P2. By making a public, irreversible commitment to defend P2​’s resources, P1 forces P3​ to back down or face a two-on-one conflict.

Salami Slicing at Scale: With hundreds of resources, a player can engage in "Salami Slicing"—taking one resource at a time. Each slice is too small to justify the opponent's jump up Kahn’s ladder, but the cumulative effect is a total takeover.

3. The Cognitive Layer: Jervis’s Signal Filtering

Jervis explains the Information Asymmetry and Noise in the system. As the number of resources and players increases, the probability of "Signal Overload" and "Misperception" grows exponentially.​​​​​​If P1 takes a resource from P2, P3 may misperceive this as a signal of P1’s global aggression, even if P1 intended it as a local correction. Jervis warns that P3 might "pre-emptively escalate" based on this misperception.​​​​

Attribution Errors in Resource Grabs: If P1 is losing resources to "market forces" or internal decay, P1 is likely to perceive this as a coordinated "shadow attack" by P2 and P3 (Centralization Bias).

The Spiral of Fear: In a 3-player resource game, any move to secure a resource for "defensive" reasons (to ensure P1​ has enough) is perceived by P2​ and P3​ as an "offensive" move to deprive them. This creates a Security Dilemma across hundreds of fronts.

A Unified Analytical Framework

To model this, we can define a Strategic State Vector for the system:

S={Ri,j, Ei,k, Ci,j}

Where:

Ri,j: The allocation of resource i to player j.

Ei,k​: The Kahn-level escalation state between players for resource k.

Ci,j: The Schelling-style commitment/alliance strength between players i and j.

The Simulation Logic:

Optimization (Schelling): Players attempt to maximize their R (resources) by creating C (commitments) that deter others. They look for Focal Points to minimize the cost of coordination.

Escalation (Kahn): If a player feels they are being "Salami Sliced," they jump to a higher E (rung) on a high-value resource to signal resolve.

The Error Term (Jervis): We introduce a "Perceptual Filter" Φ. Player j does not see S directly; they see Φj(S). If Φj perceives a defensive move as offensive, the player triggers an escalation E that the "Rational Model" would not predict.

Summary for the 3-Player, Multi-Resource Game:

• Use Kahn to define the "Cost of Conflict" at different intensities.
• Use Schelling to define how players "Lock In" their gains and form 2-vs-1 coalitions via credible signals.
• Use Jervis to audit the system for "Feedback Loops." In a 3-player game with many resources, the most likely cause of a "Spasm War" is not a rational calculation of resource value, but a misperceived signal where one player thinks the others have formed a secret coalition to eliminate them.

Strategic Advice: In this complex game, the winner is usually the player who successfully manages Jervis-style perceptions to keep the other two players from coordinating (Schelling) against them, while maintaining Escalation Dominance (Kahn) in the few resources that are truly "Focal."

Power Transition

To integrate Organski and Kugler’s Power Transition Theory (PTT) into the Kahn-Schelling-Jervis framework, we must shift from a static game to a dynamic, non-equilibrium system.

In PTT, the "winner" isn't necessarily the strongest player, but the one who manages the differential growth rates of the three actors. From CS, this is essentially a control theory problem where the "Rising Power" ($P_{rise}$) attempts to overtake the "Dominant Power" ($P_{dom}$)  before the system hits a terminal state (Kahn’s Rung 44).

 

1. The PTT Logic: The "Zone of Transition"

Organski and Kugler argue that war is most likely when a dissatisfied rising challenger approaches parity (80%–120% of the leader's power).

2. Explicit Reasoning: The Three-Actor Dynamics

In a three-player game ($P_{dom}$, $P_{rise}$, and $P_{dec}$—the declining power), the Power Transition creates specific strategic pressures:

A. The Preventive War Logic (Kahn + PTT)

The Dominant Power ($P_{dom}$) sees their lead shrinking.

• Reasoning: $P_{dom}$ calculates that it is cheaper to fight a "Limited Nuclear War" (Kahn Rungs 21-25) now while they still have escalation dominance, rather than waiting until $P_{rise}$ achieves parity.
• The Goal: Use a "demonstration of force" to break the $P_{rise}$ growth trajectory or force a resource-sharing agreement that favors the status quo.

B. The Challenger's "Salami Slicing" (Schelling + PTT)

The Rising Power ($P_{rise}$) knows they will be stronger tomorrow.

• Reasoning: Their optimal strategy is to avoid high-rung Kahn escalations until they reach parity. They use Schelling’s "Salami Slicing" to pick off the hundreds of limited resources one by one.
• The Commitment Problem: $P_{rise}$ cannot credibly commit (Schelling) to not revise the rules once they become #1. This "Insecurity Dilemma" makes $P_{dom}$ paranoid.

C. The Kingmaker Strategy (Jervis + PTT)

The Declining Power ($P_{dec}$) or the "Third Player" holds the balance.

• Reasoning: $P_{dec}$ knows they cannot win alone. They must signal (Schelling) a coalition with either $P_{dom}$ or $P_{rise}$.
• The Perceptual Trap (Jervis): $P_{dom}$ might misperceive $P_{dec}$'s neutrality as a secret alliance with $P_{rise}$. This misperception can trigger a "Pre-emptive Spasm" (Kahn Rung 44) because $P_{dom}$ feels "encircled."

3. Combining the Frameworks for the "Winner"

If a player’s goal is to maintain Kahn’s Escalation Dominance during a power transition, their reasoning follows these three scenarios:

Scenario 1: The "Hegemonic Squeeze" (Winner = $P_{dom}$)

To win, $P_{dom}$ must use Jervis’s insights to prevent a $P_{rise}+P_{dec}$ alliance.

• Action: $P_{dom}$ offers $P_{dec}$ a disproportionate share of the "hundreds of resources" to keep them satisfied.
• Escalation: $P_{dom}$ then uses Kahn’s Rungs to "draw a line in the sand" against $P_{rise}$ early. Because $P_{dom}$ still has superior tech/resources, they win the "Game of Chicken" (Schelling) because $P_{rise}$ isn't ready for a high-intensity conflict yet.

Scenario 2: The "Overtake by Stealth" (Winner = $P_{rise}$)

To win, $P_{rise}$ must manage Schelling’s focal points to keep the conflict "sub-threshold."

• Action: $P_{rise}$ frames every resource grab as "restoring historical norms" or "market competition" (Jervis-style framing) to avoid triggering $P_{dom}$’s preventive war instinct.
• Escalation: They only climb Kahn's ladder once their $dP\mathrm{/}dt$ has brought them to 110% of $P_{dom}$'s power. At that point, they possess Escalation Dominance by default.

Scenario 3: The "Spiral of Misperception" (Winner = None/System Failure)

This is the Thucydides Trap analyzed through Jervis.

• Reasoning: $P_{dom}$ sees $P_{rise}$’s growth as a threat. $P_{rise}$ sees $P_{dom}$’s military exercises as a prelude to an attack.
• Result: Both players climb Kahn’s ladder simultaneously, thinking they are "signaling resolve" (Schelling), but because of Jervis’s Illusion of Transparency, both sides believe they are being "defensive" while the other is "offensive." The transition ends in a Rung 44 "Spasm War."

Then, in a 3-player resource game, the "Winner" is the one who synchronizes their position on Kahn's ladder with their location in the PTT Zone of Transition.

• If you are rising, you stay at the bottom of the ladder and use Schelling-style coordination.
• If you are declining, you must use Jervis-style manipulation to force the other two into a conflict, or use Kahn-style escalation early while you still have the "Legacy Hardware" to win.

Is it possible to avoid a conflict?

In a dynamic, non-equilibrium system with three actors and shifting power levels (PTT), avoiding a "spasm" conflict (Kahn’s Rung 44) requires engineering the system to prevent the "Pre-emptive War" logic of the decliner and the "Salami Slicing" logic of the riser from intersecting.

From a systems and game-theoretic perspective, there are four primary "safety protocols" to keep such a system stable.

1. Transparency Protocols: Reducing the "Jervis Noise"

The greatest threat to a non-equilibrium system is Signal Distortion. If $P_{dom}$ perceives $P_{rise}$’s natural economic growth as a deliberate military "move," they may escalate prematurely.

• Verification Mechanisms: Implement high-fidelity, automated monitoring of the "hundreds of resources." If resource allocation is transparent (e.g., a shared ledger or "Open Skies" for compute/data), players cannot "Salami Slice" in secret.
• The "Hotline" (Direct Communication): Schelling argued that for a signal to be effective, it must be understood. Safety requires a "Low-Latency Metadata Channel" between actors to explain why a move was made, preventing the Centralization Bias (assuming every move is a top-down attack).

2. The "Golden Bridge": Schelling’s Exit Strategy

Sun Tzu and Schelling both emphasize that a trapped opponent is the most dangerous. If $P_{dom}$ (the declining power) feels their total elimination is inevitable, their rational move is a Kahn-style "Spasm" strike while they still have some hardware.

• Institutional Enmeshment: Create a "Focal Point" where $P_{dom}$ retains a prestigious, protected status even as their relative power drops.
• Side-Payments: Use the "hundreds of resources" to compensate the decliner. If $P_{dom}$ loses relative power but gains absolute resources, the incentive for a preventive war (Kahn) drops.

3. Interdependence: Raising the "Cost of Departure"

In a non-equilibrium system, safety is maintained if the payoff for "Defect" (War) is lower than the payoff for "Stay in the System" (Peace), even for the loser.

• Resource Entanglement: If the resources are "intertwined" (e.g., $P_1$ owns the raw materials, $P_2$ owns the processing, $P_3$ owns the distribution), a climb up Kahn’s ladder destroys the attacker’s own assets.
• The "Hostage" Strategy (Schelling): In ancient times, kings exchanged children. In a modern resource game, this means "Cross-Investment." If $P_{rise}$ has 30% of its assets located within $P_{dom}$’s territory, $P_{rise}$ cannot escalate without committing "Economic Suicide."

4. Managing the "Zone of Transition" (PTT Safety)

Organski and Kugler noted that the "danger zone" is the Parity Window (80%–120% power). Safety can be engineered by modifying the Velocity of Transition ($dP\mathrm{/}dt$):

• Damping the Growth Curve: If $P_{rise}$ grows at 10% per year, $P_{dom}$ panics. If $P_{rise}$ grows at 2% per year, $P_{dom}$ has time to psychologically and structurally adapt (reducing Jervis-style misperception).
• The "Third Player" as a Stabilizer: $P_{dec}$ (the third actor) can act as a Feedback Controller. By consistently siding with the "weaker" of the two giants, the third player keeps the system in a state of "Stagnant Parity," preventing anyone from reaching the threshold of Escalation Dominance.

Then: Is it possible to avoid conflict?

Yes, but it requires "Active Stabilizing Feedback."

Conflict is avoided when the Information Entropy of the system is low (everyone knows what the others are doing) and the Coupling is high (everyone's survival depends on the system's integrity). If you can keep the "Perceived Payoff" of the status quo higher than the "Maximum Potential Payoff" of a Kahn-style escalation, the system remains in a metastable peace.

References

1. Herman Kahn. On Escalation: Metaphors and Scenarios. Praeger, New York, 1965. Archive.org: https://archive.org/details/onescalationmeta0000kahn 

2. Thomas C. Schelling. The Strategy of Conflict. Harvard University Press, Cambridge, MA, 1960. Archive.org: https://archive.org/details/strategyofconfli00sche 

3. Thomas C. Schelling. Arms and Influence. Yale University Press, New Haven, CT, 1966 - 2008. Archive.org: https://archive.org/details/armsinfluence0000sche 

4. Robert Jervis. Perception and Misperception in International Politics. Princeton University Press, Princeton, NJ, 1976. Archive.org: https://archive.org/details/perceptionmisper0000jerv/page/n9/mode/2up 

5. A. F. K. Organski and Jacek Kugler. The War Ledger. University of Chicago Press, Chicago, 1980. 

GitHub:  

https://juanjosearanda.github.io/metastable/Metastable_Peace_Infographic.html 

https://juanjosearanda.github.io/metastable/Interactive_Metastable_Peace_Framework.html

The Silicon Paradox: 5 Surprising Takeaways on the Future of Sustainable AI

 

Introduction

In 1987, the United Nations’ Brundtland Report established a definition of sustainability that remains our global North Star: development that "meets the needs of the present without compromising the ability of future generations to meet their own needs." As we approach 2026, this generational promise faces a pivotal trial in the silicon processor. This era represents a significant pivot point where the "1987 Promise" meets the "2026 Processor"—a confrontation between our desire for infinite digital acceleration and the physical reality of planetary boundaries.

Artificial Intelligence orchestrates a profound dilemma. It is simultaneously positioned as a potential savior for the planet—capable of optimizing decarbonization and predicting climate shifts with unprecedented precision—and a resource-intensive behemoth whose energy requirements now rival those of entire nations. To navigate this "Silicon Paradox," we must transition from mere hype to a sophisticated analysis of the interplay between technical innovation and moral philosophy.

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1. The Enabler-Inhibitor Duality (The 134/59 Split)

The impact of AI on global governance is not a simple net positive; rather, it presents a significant challenge for stakeholders attempting to reconcile digital speed with ecological health. According to research synthesized by Bolón-Canedo et al. in Neurocomputing, AI acts as an enabler for 134 targets of the UN Sustainable Development Goals (SDGs), yet simultaneously serves as an inhibitor for 59 others.

While the European Parliament estimates that AI could reduce global greenhouse gas emissions by 1.5% to 4% by 2030, the immediate costs are staggering. Training a single GPT-4 model necessitates between 51,772 and 62,319 MWh—energy equivalent to the annual consumption of 5,000 U.S. homes. Crucially, the environmental cost is not a one-time event; the "inference" phase (ongoing usage) is even more demanding. For example, GPT-3 was accessed 590 million times in a single month, consuming energy equivalent to 175,000 people. At a granular level, a single ChatGPT query consumes energy equivalent to running a 5W LED bulb for 1 hour and 20 minutes.

As Ernst & Young (EY) notes in the inaugural article of their SustAInable series:

"Sustainability considerations of the impacts of technology are embedded throughout the AI lifecycle to promote physical, social, economic, and planetary well-being."

2. The "Thirsty" Nature of Virtual Intelligence

While discourse often centers on carbon, the "hidden footprint" of AI is heavily liquid. To move toward true transparency, organizations must adopt specific metrics like WUE (Water Usage Effectiveness) and CUE (Carbon Usage Effectiveness).

Data centers require immense cooling to prevent hardware degradation. A mid-sized facility can consume up to 1.1 million liters of water daily. This resource strain begins upstream: the manufacturing of a single microchip requires 8,328 liters of "ultra-pure" water. By 2027, global AI demand is projected to necessitate the extraction of up to 6 billion cubic meters of water. This heavy liquid footprint poses a direct threat to regional water security in already stressed areas, revealing that "the cloud" is anchored in very real, very finite terrestrial resources.

3. The 4Ms of Efficiency: A Blueprint for Mitigation

Despite rising resource costs, research from Google and UC Berkeley (Patterson et al., IEEE Computer, July 2022) suggests the carbon footprint of machine learning (ML) will plateau and then shrink. This depends on the "4Ms"—a set of multiplicative factors that, when co-optimized, can reduce energy use by 100x and CO2 emissions by 1000x:

1. Model: Switching from inefficient architectures like the standard Transformer to more advanced ones like "Primer" can yield a 4x efficiency gain.
2. Machine: Transitioning from general GPUs (like the NVIDIA P100) to specialized hardware (like TPUv4) offers a 14x improvement.
3. Mechanization: Optimizing the Power Usage Effectiveness (PUE) of data centers—moving from the global average to elite facility standards—provides a 1.4x gain.
4. Map: Relocating compute tasks to regions with carbon-free energy (e.g., Google’s Oklahoma data center) can reduce the carbon footprint by 9x.

When these factors are multiplied (4 x 14 x 1.4 x 9), the compounded efficiency allows the field to realize AI's potential while maintaining a manageable energy profile.

4. Babel vs. Jerusalem: The Ethical Dimension

In the Encyclical Magnifica Humanitas, Pope Leo XIV provides a philosophical critique of the "Technocratic Paradigm." This paradigm reduces the "mystery of the person" to mere performance metrics and data outputs, challenging our inherent Ontological Dignity—a value that exists regardless of productivity or efficiency. He uses two biblical metaphors to describe our path:

• The Syndrome of Babel: The idolatry of profit and uniformity that sacrifices the weak for efficiency, seeking a "single language" of data that homogenizes human experience.
• The Way of Nehemiah: A vision of technology as a tool for community-led reconstruction (Jerusalem). This aligns with the Logic of Subsidiarity, which argues that technology should empower local communities to be protagonists of their own development rather than being absorbed by centralized, opaque digital powers.

Pope Leo XIV challenges us to choose:

"The magnificent humanity that God has created seizes today a choice for the collective heart: raising a new tower of Babel or building the city where God and humanity dwell together."

5. The "Green-In" vs. "Green-By" Regulation Gap

Strategists must distinguish between Green-in AI (optimizing the models themselves) and Green-by AI (using AI to solve external environmental issues). Current regulations like the EU AI Act and CSRD are essential but face a significant "Scope 3" hurdle. If cloud compute is treated as a "purchased service," businesses must factor those emissions into their value chain reporting.

Furthermore, measurement tools like CarbonTracker and CodeCarbon often underestimate impact because they lack access to internal hardware utilization data. A potential solution lies in the "AI Regulatory Sandbox" proposed in the EU AI Act, which provides a controlled environment for testing eco-friendly AI innovations. Until standardization is achieved, the industry remains in a grey area of self-reporting and estimated impacts.

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Conclusion: A Choice for the Collective Heart

Technology is never neutral; it takes the face of those who design, fund, and regulate it. AI can be an accelerant for environmental collapse or a catalyst for planetary healing. As we refine our digital tools, we must ensure they serve the human spirit and the home we share.

The ultimate question for the digital age is not whether AI will advance, but toward what end: Are we using AI to enhance our humanity and heal our home, or are we simply building faster machines to accelerate our exit from it?

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References

• Ernst & Young (EY) Netherlands: "AI and Sustainability: Opportunities, Challenges, and Impact" (SustAInable series, 2024).
• Pope Leo XIV: Encyclical Letter Magnifica Humanitas (May 2026).
• OECD Digital Economy Papers: "Measuring the environmental impacts of artificial intelligence compute and applications." (November 2022)
• Bolón-Canedo, et al.: "A review of green artificial intelligence: Towards a more sustainable future" (Neurocomputing, 2024).
• Earth.Org: "The Green Dilemma: Can AI Fulfil Its Potential Without Harming the Environment?"
• Patterson, et al.: "The Carbon Footprint of Machine Learning Training Will Plateau, Then Shrink" (IEEE Computer, July 2022).
• Sivsa: "¿Cuál es el impacto ambiental de la IA generativa?" (Marzo, 2025)

NOTE

This post was generated using NotebookLM based on the references mentioned. The image was generated by using Gemini Flash 3.5 based on the content of the post.

The Quantum Threat Is Here: 5 Surprising Truths About the Race to Secure Our Data

"Becoming Quantum Safe: Protect Your Business and Mitigate Risks with Post-Quantum Cryptography and Crypto-Agility"

Authors: Jai Singh Arun, Ray Harishankar, and Walid Rjaibi

Foreword by Whitfield Diffie, co- inventor of public key cryptography

Copyright © 2026 by John Wiley & Sons, Inc. All rights reserved, including rights for text and data mining and training of artificial intelligence technologies or similar technologies.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada and the United Kingdom.

ISBNs: 9781394374328 (hardback), 9781394374342 (ePDF), 9781394374335 (ePub)

Introduction

Quantum computing often sounds like a concept pulled from the pages of science fiction—a futuristic technology decades away from impacting our daily lives. While the full potential of quantum machines is still on the horizon, the security threat they pose is not a distant problem. It is an urgent, present-day reality that is quietly undermining the security of our most sensitive information.

This threat operates on a simple, insidious principle known as "harvest now, decrypt later." While the digital locks forged in the last century still hold, adversaries are already pocketing the keys for a future heist. They are capturing and storing vast amounts of encrypted data—from government secrets to corporate intellectual property—with the full expectation of breaking the encryption once a powerful quantum computer is built.

This article cuts through the hype to reveal five surprising truths about the quantum threat and the monumental race to secure our digital world.

1. The Real Threat Isn’t a Decade Away—It’s Already Here

The most immediate danger from quantum computers isn't an active attack; it's a patient data heist known as "Harvest Now, Decrypt Later" (HNDL). This strategy involves adversaries intercepting and storing encrypted data today, knowing that it's only a matter of time before a cryptographically relevant quantum computer (CRQC) can break the codes that protect it.

This makes any data with long-term value immediately vulnerable—think of military secrets, intellectual property, financial records, and sensitive healthcare data that must remain secure for decades. This information is being siphoned off and stockpiled right now. This is a threat with no warning signs; there is neither a way to detect it nor a way to protect data that has already been exfiltrated. While the damage from its decryption won't be felt until a CRQC is available, the vulnerability exists today.

The core of the problem is that our current security infrastructure was built on the assumption that certain mathematical problems were too hard for classical computers to solve. As MIT professor and RSA co-inventor Ron Rivest noted, this creates a fundamental challenge.

“It’s very hard to secure a system that’s been built on the assumption that certain problems are hard, once those problems become easy.”

2. Quantum Computers Aren't "Faster" in the Way You Think

A common misconception is that quantum computers will be universally faster than the classical computers we use today. The reality is far more nuanced. Quantum computers will not replace classical machines for tasks like sending emails or creating spreadsheets. Their power is highly specialized, targeting specific types of complex problems.

The relationship between classical and quantum computing can be broken down into four categories of problems:

• Problems classical computers are best suited for. Simple tasks like multiplication are great examples where classical computers will remain superior.
• Problems classical computers cannot solve but quantum computers can. The factorization of very large integers—the mathematical foundation of most modern public-key encryption—is the prime example. This is the core of the quantum threat.
• Problems classical computers can solve, but quantum computers are much better at. Complex optimization problems, such as optimizing supply chains or financial portfolios, fall into this category.
• Problems that neither classical nor quantum computers can solve.

This distinction is critical. It focuses the quantum threat squarely on the algorithms that form the bedrock of cybersecurity. A CRQC won't make your laptop obsolete, but it will have the specific power to shatter the cryptographic shield that protects global finance, communications, and national security.

3. The "Fix" Isn't a Simple Software Update—It's a Monumental Task

Transitioning our digital world to quantum-safe systems is profoundly complex, far exceeding past upgrades. To put this in perspective, earlier cryptographic transitions, such as moving from Secure Hash Algorithm 1 (SHA-1) to Secure Hash Algorithm 2 (SHA-2), have taken anywhere from 7 to 10 years to complete. Cryptography isn't a single application you can update; it's a foundational utility woven deeply and often invisibly into the fabric of our technology.

The challenges are immense:

• Cryptography is everywhere. It is embedded in countless applications, hardware systems, and infrastructure components developed over decades.
• Organizations lack a complete inventory. Most enterprises do not have a comprehensive map of where and how all forms of cryptography are used across their systems, from web servers to third-party APIs.
• The entire supply chain is affected. The transition requires identifying and updating every single instance of vulnerable cryptography. This extends beyond an organization's own systems to include dependencies on vendors, partners, and the entire software supply chain.

This complexity is precisely why organizations cannot afford to wait. The process of discovery, planning, and migration will take years of meticulous effort. Starting now is a strategic necessity to ensure a secure transition before the threat fully materializes.

4. The Solution Is Being Built in Public—For Friends and Enemies Alike

In previous eras of cryptographic transition, nations and corporations worked in secret. The goal was to develop superior encryption for themselves, hoping their adversaries would fail to keep pace. The systems used by opposing entities were never intended to communicate with one another.

As Whitfield Diffie, co-inventor of public-key cryptography, points out, the internet changed everything. It is a global network "intended for communications between friends and enemies alike." This reality demands a fundamentally different approach to building the next generation of security.

The solution cannot be a secret weapon. It must be a public, global infrastructure upgrade. This is why organizations like the U.S. National Institute of Standards and Technology (NIST) have been leading a transparent, international process to standardize new post-quantum cryptographic (PQC) algorithms. This effort has already culminated in the first suite of official standards—including algorithms like CRYSTALS-Kyber for key exchange and CRYSTALS-Dilithium for digital signatures—which are now ready for implementation. The goal is to create new, open standards that everyone can use and trust, ensuring the interoperability required for a secure global network.

5. The Ultimate Goal Isn't Just a New Lock—It's an Entirely New Kind of Key System

Facing a transition so monumental that it could span a decade, it becomes clear that a one-time fix is strategically insufficient. The true long-term goal, therefore, isn't just to replace today's algorithms but to build systems with "crypto-agility"—ensuring we never face a cryptographic crisis of this scale again.

Crypto-agility is the capability to swap out cryptographic algorithms and protocols without making significant, disruptive changes to a system's core infrastructure. It is about designing our technology so that future cryptographic transitions are simple configuration changes, not massive, multi-year engineering projects.

This is the ultimate objective because the quantum threat will not be the last cryptographic challenge we face. By building for crypto-agility, we are future-proofing our digital world. We are creating resilient systems that can adapt quickly to the next vulnerability, whatever it may be. It is a strategic shift from a one-time fix to a state of permanent readiness.

Conclusion

The quantum era is dawning, and while it promises revolutionary advancements, it also casts a long shadow over our digital security. The threat is not a distant hypothetical; it is an active, ongoing risk through "harvest now, decrypt later" attacks. The transition to a quantum-safe world is a monumental undertaking, but a clear, strategic path forward is emerging through public collaboration and a focus on long-term resilience.

The digital world is built on cryptographic promises made decades ago. With quantum computers on the horizon, the critical question every leader must ask is this: Is your organization prepared to make new promises for the future, or will you wait until the old ones are broken?

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A Tale of Vibe Coding by using Google´s Antigravity and Gemini 3.0 Pro

Google released Antigravity, an AI IDE Core. It has options to select among some models: Gemini 3 Pro, Claude Sonnet 4.5,  and GPT-OSS 120B.

For testing purposes, using the default Gemini 3.0 Pro, it was prompted:

<prompt> Generate an app to help teaching how to program quantum computers to undergraduate students by using IBM's Qiskit. </prompt> 

After a few minutes, Antigravity generated the Qiskit Learning App, a Next.js application designed to help students learn quantum computing.

Features Implemented

1. Challenge System

• Challenge List: A home page displaying available challenges.

• Challenge Data: A flexible data structure (lib/challenges.ts) that supports multiple challenges with starter code, solutions, and hints.

• Mock Execution: A simulated Qiskit execution engine (lib/mockExecutor.ts) that validates code logic and returns mock quantum circuit drawings.

2. Interactive Workspace

• Code Editor: Integrated Monaco Editor for a full-featured coding experience.

• Split View: Instructions and Assistant on the left, Code and Output on the right.

• Output Console: Displays execution status, success/failure messages, and ASCII-art circuit diagrams.

3. AI Assistant

• Chat Interface: A built-in chat component (AssistantChat) where students can ask for help.

• Mock Responses: The assistant currently provides predefined hints to guide students.

Verification Results

Build Verification

I ran npm run build to verify the application builds correctly for production.

• Result: Success (Exit code: 0)

• Output:

• ✓ Compiled successfully

• ✓ Linting and checking validity of types    

• ✓ Collecting page data    

• ✓ Generating static pages (4/4)       

• ✓ Finalizing page optimization

Code Quality

• Linting: Resolved all ESLint errors, including unescaped quotes and syntax issues in the mock executor.

• Type Safety: TypeScript checks passed during the build process.

Next Steps

• Real Execution: Replace the mock executor with a backend service (e.g., Python/Flask) running actual Qiskit code.

• More Content: Add more advanced challenges (Teleportation, Grover's Algorithm).

• User Progress: Implement local storage or a database to track completed challenges.

 

Aprendiendo Computación Cuántica

Introducción

La UNESCO declaró 2025 como el "Año  Internacional de la Ciencia y las Tecnologías  Cuánticas". 

Desde finales de 2024 he dedicado parte de mi tiempo al aprendizaje de la Computación Cuántica.

Reconozco que me falta por aprender mucho más de lo que he logrado avanzar, por lo que sigo estudiando con empeño, pensando en aplicaciones realmente factibles en corto plazo, y programando: la única manera que conozco de hacer que las computadoras funcionen para ayudarnos a resolver los problemas que planteamos. 

Resultados obtenidos

En mi proceso de aprendizaje, he obtenido estas credenciales:

1. Microsoft Learn: "Introduction to quantum computing with Azure Quantum" - Training 
2. IBM course: "Quantum Business Foundations" 
3. IBM course: "Practical Introduction to Quantum-Safe Cryptography" 

También he publicado notas sobre el tema:

• A Tale of Programming Languages - The impact of Quantum Computing 
• The Six Fundamental Concepts of Quantum Computing You Must Know
• Crucigrama Física Cuántica. 
• Quantum Computing Advantage 
• What are the most promising industries for quantum advantage applications by 2030? 
• Chile celebra la Semana de las Tecnologías Cuánticas 
• A tale of computers: Quantum AI
• Quantum Approaches to Vehicle Routing Problems: A Review of Recent Advances and Future Directions
• A Tale of Cybernetics

Adicionalmente, participé con mis criterios compartiendo mi visión y experiencias de vida en la Consulta Pública Estrategia Nacional de Tecnologías Cuánticas 2025-2035 en el marco de Chile celebra la Semana de las Tecnologías Cuánticas 

Objetivo

El objetivo de esta nota es divulgar, compartir y, en el plano personal, unificar el acceso a diferentes fuentes de información que has sido revisadas en el camino que estoy recorriendo para aprender Computación Cuántica.

Contenidos que comparto

Al respecto, asistido por NotebookLM, he creado los siguientes cuadernos para el estudio:

• Quantum_IBM_Courses
• IBM_Quantum_Machine_Learning
• Quantum for Cryptography
• Computación Cuántica - Wikipedia
• Computación Cuántica y LLMs
• Quantum_Logistics_Papers
• Quantum Machine Learning (Cuaderno compartido conmigo por otro usuario. Gracias.)

Espero próximamente compartir también un enlace a un repositorio con los códigos en Python 3 que he estado probando.

Conclusión (temporal)  

El aprendizaje es un proceso, y aún estoy comenzando...

A tale of Cybernetics

The first time I read the seminal Norbert Wieners' book "Cybernetics: or Control and Communication in the Animal and the Machine"  I was eleven years old. It was a beautiful challenge that changed my life. Of course, that time I did not understand the mathematics inside the book; but it was the moment to decide studying Computer Sciences.

A few years later, when I was researching for my PhD, I read the book again. Now, after about 30 years later, I am reading the book third time.

Why is this book a MUST READ?

It explores the evolution and implications of Cybernetics, highlighting how the study of information, communication, and control has evolved from a novel field to a fundamental discipline in diverse areas.

Norbert Wiener, in 1948, emphasized the importance of feedback in engineering and biology, and how systems, both artificial and living, operate under shared principles. 

The book also deeps into machine learning and self-organization, examining everything from artificial intelligence in games to the complex physiology of brain waves, and how the new statistical mechanics is just as mechanistic as the old, but with a deeper understanding of time and probability. 

Finally, the text addresses the social dangers of these technologies and the need for an interdisciplinary perspective for their study.

Contents:

PART I ORIGINAL EDITION (1948) <= The one that I have as a printed book, and have read twice.

• Introduction 
• Newtonian and Bergsonian Time 
• Groups and Statistical Mechanics 
• Time Series, Information, and Communication 
• Feedback and Oscillation
• Computing Machines and the Nervous System 
• Gestalt and Universale 
• Cybernetics and Psychopathology 
• Information, Language, and Society 

PART II SUPPLEMENTARY CHAPTERS (1961) <= Additional chapters found in the PDF - Reading.

• On Learning and Self-Reproducing Machines 
• Brain Waves and Self-Organizing Systems 

NOTE: I strongly recommend take your time and read the book. I understand that most of us "do not have enough time", and it would be faster to summarize the book by using your favourite LLM. It is up to you; but if you do so, you will miss the opportunity of  enjoy the pleasure of "letting your imagination fly!".

 

Quantum Approaches to Vehicle Routing Problems: A Review of Recent Advances and Future Directions

DISCLAIMER

This post was generated with the assistance of ChatGPT and NotebookLM. Its content, and redaction are still under human analysis/improvement. Any comment will be welcome. Thanks in advance.

Abstract

The application of quantum computing to vehicle routing problems (VRP) has gained traction as researchers seek novel approaches to tackle combinatorially complex, real-world logistics challenges. This paper surveys recent advancements since 2021, focusing on quantum annealing, gate-based quantum algorithms, and hybrid quantum-classical models. We compare their capabilities in solving different VRP variants, such as those with time windows, heterogeneous fleets, and multi-dimensional constraints. Emphasis is placed on the integration of quantum techniques within practical logistics contexts. We also discuss key challenges, performance metrics, and open problems in current quantum routing research.

1. Introduction

Vehicle Routing Problems (VRPs) represent a central challenge in operations research, with implications for logistics, urban mobility, and supply chains. Traditional algorithms struggle with large, constraint-laden instances due to the NP-hard nature of VRPs. Quantum computing, particularly quantum annealing and hybrid methods, offers a promising alternative. This review synthesizes research since 2021, reflecting the rapid growth and practical experimentation in this domain.

2. Methodologies

2.1 Quantum Annealing

Quantum annealing (QA) relies on minimizing a cost function encoded into a Hamiltonian, enabling optimization over large discrete spaces. D-Wave's Leap Constrained Quadratic Model (CQM) hybrid solver has become a focal point in recent studies. For example, Osaba et al. (2024) developed Q4RPD, a hybrid solver targeting real-world logistics with priority deliveries and multi-dimensional constraints.

Tambunan et al. (2022) extended this by integrating weighted road segments, modeling traffic congestion in the routing process. Weinberg et al. (2022) tackled multi-truck logistics with hybrid methods, demonstrating applicability to supply chain problems.

2.2 Gate-Based Algorithms

Gate-based quantum computing offers alternatives like Quantum Walk Optimization Algorithms (QWOA) and Quantum Approximate Optimization Algorithms (QAOA). A 2021 study introduced QWOA for solving capacitated VRPs with encouraging results on small-scale instances.

Palmieri (2022) proposed a hybrid QAOA-based model with clustering for the Capacitated VRP, showing improved convergence on pre-processed clusters solved with quantum subroutines.

2.3 Hybrid Learning-Quantum Models

Recent works explore integrating classical machine learning with quantum techniques. Abualigah et al. (2024) applied quantum support vector machines (QSVM) to classify optimal routes in small VRPs. While not scalable yet, these methods hint at future AI-quantum synergies.

2.4 Quantum Metaheuristics

A 2024 review introduced hybrid quantum tabu search methods for VRP, showcasing improved solution quality over classical heuristics by leveraging quantum-enhanced diversification.

3. Applications and Benchmarks

3.1 Real-World Scenarios

Q4RPD (Osaba et al., 2024) stands out for its industrial relevance. Applied to real Spanish logistics data, it respects time windows, prioritizes vehicle ownership, and models multi-dimensional truck capacities. It achieves near-parity with Google OR-Tools, validating the model’s practical utility.

Holliday et al. (2025) addressed VRPs with time windows, introducing feasibility-repair heuristics within quantum pipelines, achieving <4% optimality gaps on Solomon benchmarks.

3.2 Toy vs. Scalable Benchmarks

Most quantum studies still use toy-size datasets. Q4RPD and Holliday et al. are notable exceptions, solving 20+ node problems. Scalability remains limited by hardware (qubit count, noise) and model encoding complexity.

4. Challenges and Open Problems

• Scalability: Encoding and solving larger instances remains impractical for pure quantum solutions.

• Constraint handling: Time windows and multi-attribute constraints require flexible encoding strategies.

• Benchmarking: Lack of standard datasets impedes fair performance comparisons.

• Black-box solvers: Proprietary tools (e.g., LeapCQMHybrid) limit transparency and reproducibility.

5. Future Directions

• Heuristic–Quantum Integration: Embedding business preferences as soft constraints or sub-objectives.

• 3D constraints: Extending current models to include bin-packing and volumetric truck capacities.

• Multi-modal logistics: Incorporating air, sea, or rail into routing scenarios.

• Adaptive solvers: Creating systems that auto-tune heuristics and constraint weights based on instance profiles.

• Open frameworks: Developing reproducible, open-source benchmarks and solvers for quantum VRP research.

6. Conclusion

Quantum computing holds considerable promise for solving VRPs, especially via hybrid approaches. As hardware improves and methods mature, quantum-enhanced solvers may become viable for industrial-scale logistics. Current research, while still in early stages, has laid important groundwork—particularly in integrating constraints, business logic, and real-world data into quantum models.

References

1. Osaba, E. et al. (2024). Solving a real-world package delivery routing problem using quantum annealers. Scientific Reports, 14, 24791.

2. Weinberg, S. J. et al. (2022). Supply Chain Logistics with Quantum and Classical Annealing Algorithms. Scientific Reports, 13, 4770.

3. Tambunan, T. D. et al. (2022). Quantum Annealing for Vehicle Routing Problem with Weighted Segment. AIP Conf. Proc., 2906.

4. Palmieri, A. (2022). Quantum Integer Programming for the Capacitated Vehicle Routing Problem. Ph.D. Thesis.

5. Holliday, J. et al. (2025). Advanced Quantum Annealing Approach to Vehicle Routing Problems with Time Windows. arXiv:2503.01234.

6. Abualigah, L. et al. (2024). Solving the Vehicle Routing Problem via Quantum Support Vector Machines. Quantum Machine Learning, 3(1).

7. Mohanty, N., Behera, B.K. & Ferrie, C. Solving the vehicle routing problem via quantum support vector machines. Quantum Mach. Intell. 6, 34 (2024).

8. Frontiers in Physics (2021). Quantum Walk‑Based Vehicle Routing Optimization. Front. Phys., 9, 730856.

9. Hybrid Quantum Tabu Search for VRP (2024). Review Summary, TheMoonlight.io.

10. Quantum Computing in Logistics and SCM (2024). Comprehensive Review, TheMoonlight.io.

APENDIX A

Summary generated by ChatGPT of the paper “Solving a real-world package delivery routing problem using quantum annealers” by Osaba et al., including key achievements, identified drawbacks, and suggested improvements:

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🔍 Summary

✅ Key Achievements

1. Real-World Relevance:

   • The paper introduces Q4RPD, a hybrid quantum-classical algorithm to solve a realistic last-mile delivery routing problem.

   • Unlike traditional Vehicle Routing Problems (VRP), this includes:

     • A heterogeneous fleet (owned and rented trucks),

     • Multi-dimensional capacities (weight and volume),

     • Priority deliveries (time-constrained),

     • Real business preferences (e.g., prioritize owned vehicles, reduce the number of trucks used).

2. Hybrid Quantum-Classical Approach:

   • The algorithm offloads route computation to D-Wave’s Leap Constrained Quadratic Model (CQM) Hybrid Solver, while classical routines manage problem decomposition and business logic.

3. Iterative Sub-Problem Solving:

   • Uses sub-route decomposition (Depot–TP, TP–TP, TP–Depot, full regular routes), enabling scalability and constraint compliance.

4. Benchmark with Six Scenarios:

   • Evaluated with six synthetic instances designed with the logistics partner Ertransit.

   • Q4RPD respected all constraints (capacity, priority, workday length) across the cases.

   • Performance was comparable or superior to Google OR-Tools, especially when priority constraints (TP) were included.

5. Scalability in NISQ Era:

   • Demonstrated capability to solve instances with up to 29 deliveries, which is larger than typical quantum routing benchmarks in current literature.

⚠️ Drawbacks and Limitations

1. Suboptimality due to Heuristics:

   • The pre-routing heuristics (e.g., preference for owned trucks) can limit global optimization potential, sometimes preventing the best solution.

2. Limited Constraint Flexibility:

   • Some preferences (notably P3: minimize number of trucks used) are not consistently enforced, despite being modeled as high-priority preferences.

3. No True End-to-End Quantum Formulation:

   • The actual quantum computation only addresses single-route subproblems, not the full 2DH-PDP optimization.

   • Full end-to-end quantum optimization remains out of reach, reflecting current hardware limitations.

4. Lack of Comparative Full-Classical Baseline:

   • While comparisons are made to classical TSP via Google OR-Tools, a full classical solver that handles all constraints (priority, heterogeneous fleet, 2D capacities) was not implemented as a baseline.

5. Synthetic Data Only:

   • All test instances are synthetic, limiting external generalizability. There's no validation against open, standard logistics datasets.

6. Proprietary Solver Black Box:

   • D-Wave’s LeapCQMHybrid is a proprietary black-box solver, limiting reproducibility and deeper understanding of quantum contributions.

🛠️ Suggested Improvements

1. Transform Preferences into Soft Constraints:

   • Rather than rigid heuristics, preferences like P1–P3 could be integrated into the objective function with penalty weights, allowing optimization flexibility.

2. Implement a Full Classical Baseline:

   • Design a comparable metaheuristic or MILP-based solver that handles the same constraints to better assess quantum advantage.

3. Generalize Dataset and Validation:

   • Incorporate real-world or standardized benchmarks, or release the synthetic generator to ensure better benchmarking by others.

4. Improve Constraint Fulfillment Mechanism:

   • Develop mechanisms to guarantee enforcement of business preferences like minimizing vehicle use (P3), possibly via dynamic preference weighting.

5. Quantum Efficiency Analysis:

   • Include runtime breakdown and a more detailed analysis of quantum vs classical contribution in solving times and quality.

6. Enable Truck Reuse and 3D Capacities:

   • Extend the model to allow multi-route assignments per truck and 3D volume constraints, increasing applicability.

7. Open Solver Source (if possible):

   • Open-source the classical components of Q4RPD for broader adoption and independent benchmarking.

🧠 Conclusion

The Q4RPD framework represents a significant step forward in real-world quantum logistics applications, pushing past toy problems into more practical constraints and objectives. However, to fully realize its potential, the authors (or future researchers) should prioritize:

• More flexible modeling of constraints and preferences,

• A stronger comparative baseline against classical solvers,

• Greater transparency in solver behavior, and

• Expansion of the framework’s generalizability and realism.

APENDIX B

Notable papers since 2021 found using ChatGPT that build on or relate closely to the topic of quantum-based vehicle routing and package-delivery:

\🛰️ Frontiers, 2021

"Quantum Walk‑Based Vehicle Routing Optimisation" demonstrates a gate-based quantum algorithm (QWOA) applied to the Capacitated Vehicle Routing Problem (CVRP). Through simulation on an 8-location instance, it achieves near-optimal results—showing the potential of quantum walks in routing contexts.

🧠 Weinberg et al., 2022

"Supply Chain Logistics with Quantum and Classical Annealing Algorithms" explores a hybrid workflow where multi-truck routing is broken down per truck. Using D-Wave Hybrid and simulated annealing on ~2500-variable QUBO subproblems, the routes feed into a classical simulation showing excellent supply-chain performance .

🚗 Tambunan et al., 2022

"Quantum Annealing for Vehicle Routing Problem with weighted Segment" offers a pure QUBO formulation targeting road congestion by incorporating weighted road segments. Tested on D-Wave hardware, it optimizes multi-vehicle route selection to ease congestion .

📦 Palmieri, 2022–2023 (Ph.D. thesis)

"Quantum Integer Programming for the Capacitated Vehicle Routing Problem" presents a two-phase hybrid: clustering via modularity maximization, then solving TSP subproblems using VQE/QAOA. Benchmarked against Gurobi for small instances .

🕒 Holliday et al., 2025 (arXiv)

"Advanced Quantum Annealing Approach to Vehicle Routing Problems with Time Windows" (Mar 2025) builds directly on the Q4RPD lineage. It uses D-Wave’s CQM hybrid solver and adds a feasibility-repair heuristic to handle time window violations. Achieves ~3.86% optimality gap on Solomon benchmarks .

🧪 Abualigah et al., 2024

"Solving the vehicle routing problem via quantum support vector machines" (June 2024) investigates a hybrid QSVM‑based encoding for small VRP instances (3–4 cities), using VQE-trained classifiers to predict optimal routes.

🔄 Hybrid Quantum Tabu Search, 2024

A promising hybrid metaheuristic combining tabu search with quantum annealing. Though I only found Lit‑Review coverage (April 2024), it specifically targets VRP and shows higher-quality solutions via intelligent search.

📈 2021–2023 Survey: "Quantum Computing in Logistics and SCM"

A comprehensive review published in February 2024 catalogs multiple hybrid and gate-based quantum approaches to VRP, CVRP, and VRP with time windows since 2021.

📊 Summary Table

Year	Approach / Platform	Highlights
2021	QWOA (gate-based)	CVRP on 8 locations (frontiersin.org)
2022	Hybrid D-Wave + classic	Multi-truck routing, 2500-variable models
2022	QUBO with road congestion	Weighted-segment VRP
2022/23	Quantum integer programming (thesis)	Clustering + TSP via VQE/QAOA
2024	QSVM-based for small VRPs	Hybrid ML + quantum classification
2024	Hybrid Quantum Tabu Search	VRP-focused metaheuristic
2025	Advanced CQM hybrid + fix heuristic	VRPTW, ~3.9% gap on benchmarks
2024	Broad logistics/SCM quantum survey	Catalog of recent VRP quantum research

🧭 Takeaways & Potential Gaps

• Techniques range widely: gate-based (QWOA, QSVM), annealing + hybrid splits, heuristic repair methods, and metaheuristics (tabu).

• Most scale only to small/routed subproblems, with few studies addressing real-world-sized, time-windowed, heterogeneous fleet problems.

• Time-window feasibility remains a bottleneck—recent repair heuristics (Holliday et al.) begin to bridge that gap.

• There’s a growing trend of hybridizing quantum with classical algorithms, plus early forays into machine learning enhancements.

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