arXiv subjects

Jeongrak Son

Publications and source records attributed to Jeongrak Son.

16 recordsLinked to original sources

arXiv2026

Gaussian time-translation covariant operations: structure, implementation, and thermodynamics

Time-translation symmetry strongly constrains physical dynamics, yet systematic characterization for continuous-variable systems lags behind its discrete-variable counterpart. We close this gap by providing a rigorous classification of Gaussian quantum operations that are covariant under time translations, termed Gaussian covariant operations. We show that several key results known for discrete-variable covariant operations break down in the Gaussian optical setting: discrepancies arise in physical and thermodynamic implementation, in the extensivity of asymmetry, and in catalytic advantages. Our results provide comprehensive mathematical and operational toolkits for Gaussian covariant operations, including a peculiar pair of asymmetry measures that are completely non-extensive. Our findings also reveal surprising consequences of the interplay among symmetry, Gaussianity, and thermodynamic constraints, suggesting that real-world scenarios with multiple constraints have a rich structure not accessible from examining individual constraints separately.

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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.

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arXiv2026

Quantum Qomrades: Catalysts in Resource Theories and Memories in Dynamic Programming

Quantum information theory explores the limits of manipulating quantum states. While auxiliary systems often enhance information processing, a systematic explanation for their power has been lacking. This thesis addresses this gap by investigating the underlying sources of strength in using auxiliary systems. We then apply these insights to practical problems in quantum computing and devise an algorithmic paradigm leveraging auxiliary systems. The first part examines catalysts -- auxiliary systems that remain unaltered -- and identifies three advantages: a memory effect, the ability to fine-tune catalyst states, and their role as seed states for resource distribution. The second part presents a strategy for solving recursive problems in quantum algorithms by employing auxiliary states as memories, achieving an exponential reduction in circuit depth at the cost of increased width. The findings in this thesis would facilitate future research into fundamental problems like resource interconversion and practical ones like optimal quantum circuit synthesis.

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arXiv2026

Manipulating heterogeneous quantum resources over a network

Quantum information processing relies on a variety of resources, including entanglement, coherence, non-Gaussianity, and magic. In realistic settings, protocols run on networks of parties with heterogeneous local resource constraints, so different resources coexist and interact. Yet, resource theories have mostly treated each resource in isolation, and a general theory for manipulation in such distributed settings has been lacking. We develop a unified framework for composite quantum resource theories that describes distributed networks of locally constrained parties. We formulate natural axioms a composite theory should satisfy to respect the local structure, and from these axioms derive fundamental bounds on resource manipulation that hold universally, independent of the particular network characteristics. We apply our results to central operational tasks, including resource conversion and assisted distillation, and introduce new methods to construct new resource monotones from this setup. Our framework further reveals previously unexplored phenomena in the remote certification of quantum resources. Together, these results establish foundational laws for distributed quantum resource manipulation across diverse physical platforms.

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arXiv2026

Grover's algorithm is an approximation of imaginary-time evolution

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This ITE formulation provides a unified perspective on Grover's algorithm, its variants and extensions to widely used quantum subroutines including amplitude amplification and oblivious amplitude amplification. Specifically, the framework explains the choice of angles in the original Grover's algorithm and $π/3$-algorithm. It also motivates a new $π/2$-algorithm, for cases a modest failure probability is acceptable, that converges faster than the $π/3$-algorithm without overshooting. Our analysis further provides a link between ITE and quantum signal processing, which yields a new implementation of the fixed-point quantum search algorithm. Moreover, the ITE formulation can systematically reproduce widely-used subroutines in modern quantum algorithms, such as (oblivious) amplitude amplification. These results collectively establish a deeper understanding of Grover's algorithm and suggest a potential role for thermodynamics and geometry in quantum algorithm design.

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arXiv2026

Catalytic channels are the only noise-robust catalytic processes

Catalysis refers to the possibility of enabling otherwise inaccessible quantum state transitions by supplying an auxiliary system, provided that the auxiliary is returned to its initial state at the end of the protocol. We show that previous studies on catalysis are largely impractical, because even small errors in the system's initial state can irreversibly degrade the catalyst. To overcome this limitation, we introduce robust catalytic transformations and explore the fundamental extent of their capabilities. We demonstrate that robust catalysis is closely tied to the property of resource broadcasting. In particular, in completely resource non-generating theories, robust catalysis is possible if and only if resource broadcasting is possible. We develop a no-go theorem under a set of general axioms, demonstrating that robust catalysis is unattainable for a broad class of quantum resource theories. However, surprisingly, we also identify thermodynamical scenarios where maximal robust catalytic advantage can be achieved. Our approach clarifies the practical prospects of catalytic advantage for a wide range of quantum resources, including entanglement, coherence, thermodynamics, magic, and imaginarity.

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arXiv2025

Double-bracket algorithm for quantum signal processing without post-selection

Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic protocols for implementing QSP rely on post-selection. This can impose prohibitive costs for tasks when amplitude amplification cannot sufficiently improve the success probability. For example, in the context of ground-state preparation, this occurs when using a too poor initial state. In this work, we introduce a new formula for implementing QSP transformations of Hermitian matrices, which requires neither auxiliary qubits nor post-selection. Rather, using approximation to the exact unitary synthesis, we leverage the theory of the double-bracket quantum algorithms to provide a new quantum algorithm for QSP, termed Double-Bracket QSP (DB-QSP). The algorithm requires the energy and energetic variance of the state to be measured at each step and has a recursive structure, which leads to circuit depths that can grow super exponentially with the degree of the polynomial. With these strengths and caveats in mind, DB-QSP should be viewed as complementing the established QSP toolkit. In particular, DB-QSP can deterministically implement low-degree polynomials to "warm start" QSP methods involving post-selection.

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arXiv2025

Double-bracket quantum algorithms for high-fidelity ground state preparation

Ground state preparation is a central application for quantum computers but remains challenging in practice. In this work, we quantitatively investigate the performance and gate counts of double-bracket quantum algorithms (DBQAs) for ground state preparation. We propose a practical strategy in which DBQAs refine initial state preparation circuits, and we compile them for Heisenberg chains using controlled-Z and single-qubit gates. Warm-started DBQAs consistently improve both the energy and ground-state fidelity relative to the initial states provided by variational ansätze, indicating that DBQAs offer an effective unitary synthesis method. To demonstrate compatibility with near-term hardware, we executed a proof-of-concept example on IBM devices. With error mitigation, we observed a statistically significant improvement over the corresponding warm-start circuit. Furthermore, numerical emulations for the same system size indicate that executing DBQAs on Quantinuum's hardware could achieve similar cost-function gains without requiring error mitigation. These findings suggest that DBQAs are a promising approach for enhancing ground-state approximations on near-term quantum devices.

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arXiv2025

Thermal operations from informational equilibrium

Thermal operations are quantum channels that have taken a prominent role in deriving fundamental thermodynamic limitations in quantum systems. We show that these channels are uniquely characterized by a purely quantum information theoretic property: They admit a dilation into a unitary process that leaves the environment invariant when applied to the equilibrium state. In other words, they are the only channels that preserve equilibrium between system and environment. Extending this perspective, we explore an information theoretic idealization of heat bath behavior, by considering channels where the environment remains locally invariant for every initial state of the system. These are known as catalytic channels. We show that catalytic channels provide a refined hierarchy of Gibbs-preserving maps for fully-degenerate Hamiltonians, and are closely related to dual unitary quantum circuits.

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arXiv2025

Double-bracket quantum algorithms for quantum imaginary-time evolution

Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to ground-state preparation that aim to replicate cooling processes via imaginary-time evolution. However, synthesizing quantum circuits that efficiently implement imaginary-time evolution is itself difficult, with prior proposals generally adopting heuristic variational approaches or using deep block encodings. Here, we use the insight that quantum imaginary-time evolution is a solution of Brockett's double-bracket flow and synthesize circuits that implement double-bracket flows coherently on the quantum computer. We prove that our Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) algorithm inherits the cooling guarantees of imaginary-time evolution. Concretely, each step is guaranteed to i) decrease the energy of an initial approximate ground-state by an amount proportion to the energy fluctuations of the initial state and ii) increase the fidelity with the ground-state. We provide gate counts for DB-QITE through numerical simulations in Qrisp which demonstrate scenarios where DB-QITE outperforms quantum phase estimation. Thus DB-QITE provides a means to systematically improve the approximation of a ground-state using shallow circuits.

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arXiv2025

Quantum Dynamic Programming

We introduce a quantum extension of dynamic programming, a fundamental computational method that efficiently solves recursive problems using memory. Our innovation lies in showing how to coherently generate recursion step unitaries by using memorized intermediate quantum states. Quantum dynamic programming achieves an exponential reduction in circuit depth for a broad class of fixed-point quantum recursions, though this comes at the cost of increased circuit width. Interestingly, the trade-off becomes more favourable when the initial state is pure. By hybridizing our approach with a conventional memoryless one, we can flexibly balance circuit depth and width to optimize performance on quantum devices with fixed hardware constraints. Finally, we showcase applications of quantum dynamic programming to several quantum recursions, including a variant of Grover's search, quantum imaginary-time evolution, and a new protocol for obliviously preparing a quantum state in its Schmidt basis.

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arXiv2024

Entanglement generation from athermality

We investigate the thermodynamic constraints on the pivotal task of entanglement generation using out-of-equilibrium states through a model-independent framework with minimal assumptions. We establish a necessary and sufficient condition for a thermal process to generate bipartite qubit entanglement, starting from an initially separable state. Consequently, we identify the set of system states that cannot be entangled, when no external work is invested. In the regime of infinite temperature, we analytically construct this set; while for finite temperature, we provide a simple criterion to verify whether any given initial state is or is not entanglable. Furthermore, we provide an explicit construction of the future thermal cone of entanglement - the set of entangled states that a given separable state can thermodynamically evolve to. We offer a detailed discussion on the properties of this cone, focusing on the interplay between entanglement and its volumetric properties. We conclude with several key remarks on the generation of entanglement beyond two-qubit systems, and discuss its dynamics in the presence of dissipation.

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arXiv2023

A hierarchy of thermal processes collapses under catalysis

Thermal operations are a generic description for allowed state transitions under thermodynamic restrictions. However, the quest for simpler methods to encompass all these processes remains unfulfilled. We resolve this challenge through the catalytic use of thermal baths, which are assumed to be easily accessible. We select two sets of simplified operations: elementary thermal operations and Markovian thermal operations. They are known for their experimental feasibility, but fail to capture the full extent of thermal operations due to their innate Markovianity. We nevertheless demonstrate that this limitation can be overcome when the operations are enhanced by ambient-temperature Gibbs state catalysts. In essence, our result indicates that free states within thermal operations can act as catalysts that provide the necessary non-Markovianity for simpler operations. Furthermore, we prove that when any catalyst can be employed, different thermal processes (thermal operations, elementary thermal operations, and Markovian thermal operations) converge. Notably, our results extend to scenarios involving initial states with coherence in the energy eigenbasis, a notoriously difficult process to characterise.

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arXiv2023

Catalysis in Action via Elementary Thermal Operations

We investigate catalysis in the framework of elementary thermal operations, leveraging the distinct features of such operations to illuminate catalytic dynamics. As groundwork, we establish new technical tools that enhance the computability of state transition rules for elementary thermal operations. Specifically, we provide a complete characterisation of state transitions for a qutrit system and special classes of initial states of arbitrary dimension. By employing these tools in conjunction with numerical methods, we find that by adopting a small catalyst, including just a qubit catalyst, one can significantly enlarge the set of state transitions for a qutrit system. This advancement notably narrows the gap of reachable states between elementary thermal operations and generic thermal operations. Furthermore, we decompose catalytic transitions into time-resolved evolution, which critically enables the tracking of nonequilibrium free energy exchanges between the system and bath. Our results provide evidence for the existence of simple and practicable catalytic advantage in thermodynamics while offering insight into analysing the mechanism of catalytic processes.

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arXiv2022

Charging quantum batteries via Otto machines: The influence of monitoring

The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat and workflows of the machine, the average, and variance of the battery's energy as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During the first charging epoch with an engine, the regular measurements speed up the charging, whereas the gain of ergotropy is more pronounced in the absence of measurements. In a later stage, the engine fails to work as such while it still continues charging the battery that eventually reaches the maximally charged state in the absence of intermediate measurements and a suboptimally charged state for a periodically measured battery. For a refrigerator, the charging of the measured battery also proceeds faster during the first epoch. Only during the second stage when the machine fails to extract heat from the cold bath the influence of the measurements become less pronounced leading to rather similar asymptotic states for the two measurement scenarios.

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arXiv2021

Monitoring quantum Otto engines

Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or heat. For joint work and heat diagnostics, two pointers are needed. These schemes are applied to Otto engines, whose working substance consists of a two-level system. Depending on the engine protocol, the duration of a single cycle may be infinite or finite. Because in the repeated contact scheme, the number of measurements is drastically reduced compared to the repeated measurement scheme, the quantum coherence after and during the contact diagnostics is much better maintained than repeated measurements that destroy any coherence at the end of each stroke. We demonstrate that maximum power, reliability, and efficiency of the engine in the presence of repeated contacts typically outperform these figures of merit of repeated measurements. Due to the improved coherence persistence, heat engines with a finite cycle duration require a larger number of cycles to reach a periodically asymptotic state. Overall, our results document the importance of taking into account the particular nature of diagnostic tools for monitoring and testing purposes but also for feedback control, both in theory and experiment.

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