arXiv subjects

Mile Gu

Publications and source records attributed to Mile Gu.

At least 19 recordsLinked to original sources

arXiv2026

How much randomness in a quantum process can be explained using memory?

For a stochastic process describing observations of a dynamical system, complexity science provides systematic methods to decompose the information produced into true irreducible randomness, and that which corresponds to structure superficially disguised as random but can in fact be learned and predicted. Such methods then equip vital tools for prediction, control and inference of the system's internal structure. However, quantum analogs remain underdeveloped due to the inherent complications of invasive measurements and quantum correlations. By harnessing the Choi state representation of process tensors which encode multi-time input-output relations, we formulate a convergent measure of irreducible randomness in stationary quantum stochastic processes. This directly enables a measure of temporal correlations which lower bounds the memory resources required to replicate the process via a recurrent quantum circuit.

quant-ph↗

arXiv2026

Single-shot online sequence classification with unbounded quantum memory advantage

An agent monitors a complex environment, receiving one observation at each time step and eventually deciding how to label the resulting sequence. Does the sequence indicate an anomaly, and if so, of what type? Does it signal market instability, and to what degree? This is the setting of online multi-class classification: the input arrives sequentially, the full history is never available at once, and the agent must retain any past information relevant to the eventual decision. As the environment becomes more complex, the memory needed to track this information can grow rapidly without bound. Here, we introduce families of such multi-class classification games and show that any exact classical agent requires memory that grows without bound, whereas exact quantum agents can solve all tasks in the family with bounded memory. This separation is sharp: any classical agent using less than the required memory, under suitable input distributions, performs arbitrarily close to random guessing. Moreover, our quantum constructions are provably memory minimal, allowing us to derive the exact classical and quantum memory complexities to perform such tasks. In doing so, we establish an unbounded separation between classical and quantum memory cost for online multi-class classification.

quant-ph↗

arXiv2026

An Irreducible Quantum Advantage in Aligning World Models with Reality

World models provide digital simulacra of the true world, allowing agents to be trained and tested before costly real-world deployment. At each time step, they receive an action and generate an observation and reward matching the statistics of the true world. In complex environments where present outcomes depend on events far in the past, this requires memory. One might expect that, by increasing memory, we can always build a model accurately enough to align the optimal agent policies of the real and virtual worlds. We show that this is false for classical world models, even when the true world itself is classical. We construct true worlds for which every finite classical model fails along the same possible trajectory: it either loses the ability to distinguish actions when the true world clearly prefers one, or repeatedly assigns the highest expected reward to suboptimal actions. Its expected-reward estimates also retain a nonvanishing average error. In contrast, each such true world admits a quantum world model using a single qutrit that reproduces it exactly: its reward estimates and preferred actions always match those of the true world, ensuring that the optimal policies of the real and virtual worlds remain perfectly aligned.

quant-ph↗

arXiv2026

Time-ordered free energy in correlated quantum systems: An agentic approach

How much work can an agent extract from a temporal sequence of quantum states when it can only operate online under causal constraints---deciding which energy extraction method to use with knowledge of what it has observed before? Here, we study this problem in the context of quantum state sequences that are potentially non-Markovian---generated by some underlying hidden Markov machine that the agent cannot observe. Using techniques from dynamic programming and computational mechanics, we present a method to identify the provably optimal agent strategy, with time complexity that scales linearly with sequence length. This motivates us to introduce the maximum work such agents can extract---time-ordered free energy(TOFE)---as a fundamental measure of free energy available in a temporally correlated quantum system subject to causal considerations.

quant-ph↗

arXiv2026

Quantum Circuit Fragments and Link Products in Continuous Variables

Quantum circuits are often drawn as complete processes, with fixed inputs and outputs. In many quantum-information tasks, however, the natural object is only a fragment of such a circuit: an unknown source of non-Markovian noise to be probed, a subroutine to be inserted into a larger algorithm, or an agent implementing an adaptive strategy. In finite dimensions, the link product provides a systematic means to analyze how such circuit fragments interact and compose. Here, we develop the corresponding framework for continuous-variable systems. We introduce continuous-variable circuit fragments and associated link products that stitch such fragments together into larger processes. We show that the formalism simplifies substantially in the Gaussian regime, where link products can be evaluated efficiently using covariance-matrix representations. We use the formalism to construct non-Markovian processes and adaptive agent-environment interactions from modular components. This extends the quantum-comb toolkit to continuous variables, providing systematic methods for adaptive sensing, non-Markovian noise mitigation, and higher-order quantum circuit design.

quant-ph↗

arXiv2026

Quantum enhanced rare event discovery and sampling

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

quant-ph↗

arXiv2026

Photonic-Implemented Efficient Deep Quantum Neural Network via Virtual-Driven Hilbert Space Expansion

The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a compelling avenue, offering exceptional computational power enhancements, with inherent programmability and scalability of integrated architectures. A critical challenge, however, is implementing the fundamental non-unitary and nonlinear activation function of QNNs within a linear quantum photonic system. Existing strategies, such as the adding ancillary qubits and measurement-based feedback or forward are constrained by high qubit resource costs, overhead devices, and poor cascadability. Here, we propose a novel deep photonic QNN with an expanded computational Hilbert space via input replication and mode expansion, which enables the realization of effective non-unitary and nonlinear activation on a linear programmable quantum photonic chip. This approach eliminates the need for physical ancillary qubits, measurement-induced qubit consumption and the measurement device burden, thereby significantly reduce resource costs. The fabricated chip integrates four high-quality entanglement sources and a programmable high-dimensional interferometric network, enabling a two-hidden-layer QNN that exhibits dimension-enhanced expressivity over the existing QNN architectures. We demonstrate its capabilities across diverse tasks, including nonlinear classification, image generation, and quantum Gibbs state preparation. This work establishes a scalable and efficient architecture toward practical quantum deep learning systems capable of tackling problems beyond the reach of classical computation.

quant-ph↗

arXiv2026

Theory of Quantum Imaginary-Time Mpemba Effect

Quantum imaginary-time evolution (QITE) is a fundamental framework for preparing ground and thermal states, yet its computational cost scales significantly with the evolution duration $τ$. Reducing this duration is critical for practical quantum advantage. Here, we establish a unified theoretical framework for the Mpemba effect in QITE -- a counterintuitive phenomenon where a state initially farther from the ground state relaxes to it faster than one initially closer. We derive a remarkably simple necessary and sufficient condition for the occurrence of this effect, showing it is uniquely determined by the population ratios of excited states to the ground state. For practical state preparation, we introduce a rigorous sufficient condition for the finite-time Mpemba effect, ensuring the crossing occurs before reaching a prescribed proximity threshold. Furthermore, we unveil unique dynamical features, including a multiple-crossing phenomenon in multi-level systems and simultaneous intersections for collinear initial states. Our results provide criteria for identifying favorable initial states in QITE and offer deep insights into the speed limit of quantum state preparation.

quant-ph↗

arXiv2026

Reinforcement learning for quantum processes with memory

In reinforcement learning, an agent interacts sequentially with an environment to maximize a reward, receiving only partial, probabilistic feedback. This creates a fundamental exploration-exploitation trade-off: the agent must explore to learn the hidden dynamics while exploiting this knowledge to maximize its target objective. While extensively studied classically, applying this framework to quantum systems requires dealing with hidden quantum states that evolve via unknown dynamics. We formalize this problem via a framework where the environment maintains a hidden quantum memory evolving via unknown quantum channels, and the agent intervenes sequentially using quantum instruments. For this setting, we adapt an optimistic maximum-likelihood estimation algorithm. We extend the analysis to continuous action spaces, allowing us to model general positive operator-valued measures (POVMs). By controlling the propagation of estimation errors through quantum channels and instruments, we prove that the cumulative regret of our strategy scales as $\widetilde{\mathcal{O}}(\sqrt{K})$ over $K$ episodes. Furthermore, via a reduction to the multi-armed quantum bandit problem, we establish information-theoretic lower bounds demonstrating that this sublinear scaling is strictly optimal up to polylogarithmic factors. As a physical application, we consider state-agnostic work extraction. When extracting free energy from a sequence of non-i.i.d. quantum states correlated by a hidden memory, any lack of knowledge about the source leads to thermodynamic dissipation. In our setting, the mathematical regret exactly quantifies this cumulative dissipation. Using our adaptive algorithm, the agent uses past energy outcomes to improve its extraction protocol on the fly, achieving sublinear cumulative dissipation, and, consequently, an asymptotically zero dissipation rate.

quant-ph↗

arXiv2026

Learning Quantum-Samplers for Stochastic Processes with Quantum Sequence Models

Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing such circuits from data face immense challenges, given the exponential growth in the size of the associated probability vectors as the desired simulation time horizon increases. Here, we introduce quantum sequence models that leverage a recurrent quantum circuit structure to generate coherent superpositions with circuit complexity that grows linearly with the desired time horizon; together with a recurrent variant of the parameter-shift rule, we train these models from observational data. When benchmarked against baseline quantum Born machines, our constructions exhibit orders-of-magnitude improvements in model accuracy in data-sparse regimes.

quant-ph↗

arXiv2026

Variational Quantum Dimension Reduction for Recurrent Quantum Models

Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large memory spaces, introducing redundancy and limiting scalability. Here, we introduce a \textit{variational quantum dimension reduction} framework that identifies and removes irrelevant memory degrees of freedom while preserving the recurrent dynamics of the target model. Our approach employs two parameterized quantum circuits: a decoupling unitary $V(θ_1)$ that isolates the essential memory subspace; and a compressed recurrent unitary $\tilde{U}(θ_2)$ that reconstructs the dynamics in the reduced space. The optimization is guided by a unified cost function combining decoupling fidelity and dynamical accuracy, evaluated using the \textit{Quantum Fidelity Divergence Rate} (QFDR), a metric that quantifies long-term fidelity per time step. Applied to a cyclic random walk model, our framework achieves up to three orders of magnitude smaller QFDR compared to variational matrix product state truncation, while requiring only trajectory samples rather than explicit state reconstructions. This establishes a scalable, data-driven paradigm for learning minimal recurrent quantum architectures, enabling variational circuit optimization and quantum process compression for near-term quantum devices.

quant-ph↗

arXiv2026

Ideal stochastic process modeling with post-quantum quasiprobabilistic theories

In stochastic modeling, the excess entropy -- the mutual information shared between a process's past and future -- represents the fundamental lower bound of the memory needed to simulate its dynamics. However, this bound cannot be saturated by either classical machines or their enhanced quantum counterparts. Simulating a process fundamentally requires us to store more information in the present than is shared between the past and the future. Here, we consider a generalization of hidden Markov models beyond classical and quantum models, referred to as n-machines, that allow for negative quasiprobabilities. We show that under the collision entropy measure of information, the minimal memory of such models can equal the excess entropy. Our results suggest that negativity can be a useful resource for achieving nonclassical memory advantage.

quant-ph↗

arXiv2026

Classically Spoofing System Linear Cross Entropy Score Benchmarking

In recent years, several experimental groups have claimed demonstrations of ``quantum supremacy'' or computational quantum advantage. A notable first claim by Google Quantum AI revolves around a metric called the Linear Cross Entropy Benchmarking (Linear XEB), which has been used in many quantum supremacy experiments since. The complexity-theoretic hardness of spoofing Linear XEB, however, depends on the Cross-Entropy Quantum Threshold (XQUATH) conjecture put forth by Aaronson and Gunn, which has been disproven for sublinear depth circuits. In the efforts on demonstrating quantum supremacy by quantum Hamiltonian simulation, a similar benchmarking metric called the System Linear Cross Entropy Score (sXES) holds firm in light of the aforementioned negative result due to its fundamental distinction with Linear XEB. Moreover, the complexity-theoretic hardness of spoofing sXES rests on the System Linear Cross-Entropy Quantum Threshold Assumption (sXQUATH), the formal relationship of which to XQUATH is unclear. Despite the promises offered by sXES for future demonstration of quantum supremacy, in this work we show that it can be classically simulated efficiently in certain regimes.

quant-ph↗

arXiv2025

Spatial Incompatibility Witnesses for Quantum Temporal Correlations

We introduce a witness-based framework for certifying quantum temporal correlations via the pseudo-density matrix (PDM) formalism, which is a spatiotemporal generalization of the density matrix. We define spatial incompatibility (SI) as the minimum distance between a PDM and valid density matrices. For trace-norm distance, we show that this reduces to the PDM's negativity, enabling the construction of experimentally accessible SI witnesses. We derive a tight bound on SI for quantum channels and analyze the respective roles of state and channel coherence in witnessing SI. Our approach, unlike the LG framework, exploits measurements that generate coherence through state disturbance. We further show that channels satisfying the LG inequality for incoherent states can still exhibit detectable SI, demonstrating that measurement disturbance enhances the certification of temporal correlations.

quant-ph↗

arXiv2025

Gaussian Atemporality: When Gaussian Quantum Correlations Imply Common Cause

Conventionally, covariances do not distinguish between spatial and temporal correlations. The same covariance matrix could equally describe temporal correlations between observations of the same system at two different times or correlations made on two spatially separated systems that arose from some common cause. Here, we demonstrate Gaussian quantum correlations that are `atemporal', such that the covariances governing their quadrature measurements are unphysical without postulating some common cause. We introduce Gaussian atemporality robustness as a measure of atemporality, illustrating its efficient computability and operational meaning as the maximum noise which can be added without removing this uniquely quantum phenomenon. We illustrate that (i) specific spatiotemporal Gaussian correlations possess an intrinsic arrow of time, such that Gaussian atemporality robustness is zero in one temporal direction and not the other and (ii) that it measures quantum correlations beyond entanglement.

quant-ph↗

arXiv2025

How Quantum Agents Can Change Which Strategies Are More Complex

Whether winning blackjack or navigating busy streets, achieving desired outcomes requires agents to execute adaptive strategies, strategies where actions depend contextually on past events. In complexity science, this motivates memory as an operational quantifier of complexity: given two strategies, the more complex one demands the agent to track more about the past. Here, we show that conclusions about complexity fundamentally depend on whether agents can process and store quantum information. Thus, while classical agents might find Strategy A more complex to execute than Strategy B, quantum agents can reach the opposite conclusion. We derive sufficient conditions for such contradictory conclusions and illustrate the phenomenon across multiple scenarios. As a byproduct, our results yield an information-theoretic lower bound on the minimal memory required by any agent - classical or quantum - to execute a given strategy.

quant-ph↗

arXiv2025

Undecidability in Physics: a Review

The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is to survey this recent development. After a historical introduction, we first explain the necessary results about undecidability in mathematics and computer science. Then we briefly review the first results about undecidability in physics which emerged mostly in the 80s and early 90s. Finally we focus on the most recent contributions, which we divide in two main categories: many body systems and quantum information problems.

math-ph↗

arXiv2025

Quantum state-agnostic work extraction (almost) without dissipation

We investigate work extraction protocols designed to transfer the maximum possible energy to a battery using sequential access to $N$ copies of an unknown pure qubit state. The core challenge is designing interactions to optimally balance two competing goals: charging of the battery optimally using the qubit in hand, and acquiring more information by qubit to improve energy harvesting in subsequent rounds. Here, we leverage exploration-exploitation trade-off in reinforcement learning to develop adaptive strategies achieving energy dissipation that scales only poly-logarithmically in $N$. This represents an exponential improvement over current protocols based on full state tomography.

quant-ph↗