Coherence dynamics in Simon's quantum algorithm
Linlin Ye, Zhaoqi Wu, Shao-Ming Fei
Abstract
Quantum coherence plays a pivotal role in quantum algorithms. We study the coherence dynamics of the evolved states in Simon's quantum algorithm based on Tsallis relative entropy and norm. We prove that the coherences of the first register and the second register both rely on the dimension of the state spaces of the qubit systems, and increase with the increase of . We show that the oracle operator does not change the coherence. Moreover, we study the coherence dynamics in the Simon's quantum algorithm and prove that in overall the coherence is in production when and in depletion when .
AI Impact Assessments
(3 models)Scientific Impact Assessment: "Coherence dynamics in Simon's quantum algorithm"
1. Core Contribution
This paper analyzes the quantum coherence dynamics of evolved states throughout Simon's quantum algorithm, using two coherence quantifiers: the Tsallis relative α entropy and the l_{1,p} norm. The main claims are:
The paper follows a template established by prior works studying coherence dynamics in other quantum algorithms (e.g., Grover's algorithm, Deutsch-Jozsa), now applied to Simon's algorithm.
2. Methodological Rigor
The mathematical derivations are straightforward calculations. The authors compute density matrices at each step of Simon's algorithm (after Hadamard, after oracle, after second Hadamard) and plug them into known coherence formulas. The proofs are direct substitutions — for instance, Theorem 1 simply evaluates the Tsallis coherence measure on the uniform superposition state ρ_H = (1/2^n) Σ_{x,y} |x⟩⟨y|, which is a standard pure state with well-known properties.
Several concerns arise regarding rigor:
3. Potential Impact
The practical and theoretical impact of this work is limited:
4. Timeliness & Relevance
The study of quantum resources (coherence, entanglement) in quantum algorithms is a legitimate research direction, but this particular paper arrives relatively late in the cycle. Similar analyses for Grover's algorithm, Deutsch-Jozsa, and Bernstein-Vazirani have been published years ago (refs [38-40]). The extension to Simon's algorithm, while filling a gap, does not introduce new methodology or conceptual advances.
The coherence measures used (Tsallis relative α entropy, l_{1,p} norm) are known quantities, and the paper does not leverage any special properties of these measures that would be unavailable with simpler measures like relative entropy of coherence or l_1 norm.
5. Strengths & Limitations
Strengths:
Limitations:
Overall Assessment
This paper represents a routine application of existing coherence measures to track coherence through the steps of Simon's quantum algorithm. While mathematically correct, the results are largely unsurprising and lack the depth needed to advance our understanding of the role of coherence in quantum computation. The paper does not establish any operational connection between coherence and algorithmic performance, making the analysis primarily descriptive. The contribution is incremental and of limited impact.
Generated Apr 20, 2026
Comparison History (54)
Paper 1 likely has higher impact due to broader scope and cross-field relevance: it links geometric quantum mechanics, symplectic/topological structures, entanglement dynamics, and concrete spin models (XXZ, all-range Ising) with applications to quantum speed limits/brachistochrone problems—topics relevant to quantum information, condensed matter, and quantum control. Paper 2 is narrower (Simon’s algorithm) and focuses on coherence measures with results that appear incremental and possibly limited in applicability, though timely for resource-theory analyses. Overall breadth and potential applications favor Paper 1.
Paper 2 presents a more novel theoretical contribution by addressing the fundamental problem of superposition in the Bohm-Madelung formulation, revealing how linear spectral structure re-emerges from intrinsically nonlinear equations through a hierarchical separation and Fourier-Bessel representation. This bridges nonlinear quantum hydrodynamics with standard interference phenomena, potentially impacting quantum foundations, mathematical physics, and applications in optics/interferometry. Paper 1 applies existing coherence measures to a well-known algorithm (Simon's), yielding incremental results about coherence scaling with dimension, which is less novel and has narrower impact.
Paper 1 is more likely to have higher scientific impact due to its novelty (first quantum-hardware implementation targeting time-domain Maxwell equations with sign/direction reconstruction), stronger real-world application potential (computational electromagnetics, scattering, boundary conditions), and broader cross-disciplinary reach (quantum algorithms + numerical PDEs + EM engineering). It also demonstrates methodological rigor via concrete circuit mapping and hardware results on an IonQ QPU with benchmarks. Paper 2 provides a mainly theoretical coherence analysis of Simon’s algorithm with limited practical implications and narrower impact.
Paper 1 offers a practical, analytical framework for designing and optimizing superconducting single-photon detectors. Its findings have immediate, broad applications in quantum communication, astronomy, and applied physics, as the design concepts can be extended to other detectors like MKIDs and TESs. Paper 2, while theoretically rigorous, focuses narrowly on the coherence dynamics of a specific quantum algorithm, making its potential real-world impact and breadth of application significantly smaller than the hardware advancements proposed in Paper 1.
Paper 1 presents the first quantum-hardware implementation of a Hamiltonian simulation algorithm for Maxwell's equations, combining novelty (Schrödingerisation-based approach, relative-phase sign reconstruction) with significant practical applications in computational electromagnetics. It demonstrates results on real quantum hardware (IonQ QPU) and extends to scattering problems. Paper 2 provides a mathematical analysis of coherence dynamics in Simon's algorithm, which, while rigorous, addresses a well-studied algorithm with limited practical relevance and narrower impact. Paper 1's bridging of quantum computing with electromagnetic simulation opens broader interdisciplinary research directions.
Paper 2 has higher potential impact due to strong real-world applicability (improving SSPD absorptance/design), methodological rigor (analytical derivations validated against simulations), and broader cross-field relevance (extends to MKIDs and TES detectors, useful for quantum optics/communication, astronomy, and sensing). Its impedance-matching design principle is timely and actionable for device engineering. Paper 1 provides a coherence-resource analysis of Simon’s algorithm with limited immediate application; results appear more incremental and niche within quantum algorithm characterization.
Paper 2 addresses quantum batteries under realistic open-system conditions (finite temperature, dissipation), which is a rapidly growing field with clear practical applications in quantum technologies. It combines analytical and numerical approaches in a systematic framework, offering broader utility. Paper 1 analyzes coherence dynamics in a well-known algorithm (Simon's) using specific coherence measures, which is more incremental and narrower in scope, primarily contributing to quantum information theory without significant algorithmic or practical advancement.
Paper 1 addresses fundamental questions in quantum foundations and quantum information theory, offering novel operational characterizations for entanglement and beyond-quantum states in Bell scenarios. Its broad implications for noise robustness and optimal witnessing provide greater potential impact across the field compared to Paper 2, which focuses more narrowly on the coherence dynamics of a specific quantum algorithm.
Paper 1 is more likely to have higher impact: it introduces a novel tensor-network (MPS/TT) sampling heuristic for discrete quantum optimal control, targets a practical bottleneck (gradient-free search in high-dimensional nonconvex landscapes), and demonstrates performance across multiple benchmark tasks including open systems—suggesting broader applicability to quantum computing/control engineering. Paper 2 provides analytical observations about coherence measures in Simon’s algorithm, but it is narrower in scope, largely interpretive (coherence bookkeeping), and less directly tied to improved algorithms or implementations, limiting real-world and cross-field impact.
Paper 1 addresses the practically important problem of quantum battery performance under realistic conditions (thermal effects, dissipation), combining analytical and numerical approaches in a systematic framework. This has broader impact due to connections to quantum thermodynamics, open quantum systems, and Floquet engineering, with clear relevance to near-term quantum devices. Paper 2 provides a more narrow analysis of coherence dynamics in Simon's algorithm using specific coherence measures, which, while technically sound, has limited novelty and practical relevance since Simon's algorithm is primarily of theoretical interest and the results are relatively incremental.
Paper 1 offers a foundational theoretical framework for analyzing device-dependent correlation sets, entanglement witnesses, and beyond-quantum states, which has broad implications across quantum information theory and foundations. Paper 2 is more narrowly focused on the coherence dynamics of a specific algorithm (Simon's), limiting its generalizability and broader impact compared to the fundamental results presented in Paper 1.
Paper 1 is more likely to have higher impact due to a novel, algorithmic contribution: introducing tensor-network (MPS/TT) sampling as a gradient-free heuristic for discrete quantum optimal control, with benchmarking across multiple control tasks (including open systems) and direct relevance to near-term quantum hardware. Its applications (pulse design, gate/state preparation) are broad and timely, and the method could transfer to other high-dimensional discrete optimization problems. Paper 2 offers a more limited, mainly analytical study of coherence measures within a single established algorithm (Simon), with narrower practical and cross-field impact.
Paper 2 addresses Device-Independent Quantum Key Distribution (DIQKD), a highly relevant field with significant real-world applications in secure communications. By evaluating noise impact and error correction, it tackles practical barriers in quantum cryptography. Paper 1 offers a theoretical analysis of coherence in Simon's algorithm, which, while mathematically rigorous, is narrower in scope and lacks the immediate practical applicability and broader interdisciplinary impact of Paper 2.
Paper 1 addresses a fundamental mathematical question about the convergence and reliability of HEOM truncations, a widely used method in open quantum systems. Proving spectral convergence and absence of spurious modes provides rigorous theoretical guarantees that impact computational practice across chemistry, physics, and materials science. Paper 2 analyzes coherence in Simon's algorithm using specific measures, yielding results that are more descriptive than transformative, with limited practical implications since Simon's algorithm is primarily of theoretical interest. Paper 1's methodological rigor and broader applicability give it higher impact.
Paper 2 investigates quantum coherence dynamics in a specific quantum algorithm, offering actionable insights for the rapidly growing and highly impactful field of quantum computing. Understanding coherence evolution is critical for optimizing quantum algorithms and developing practical quantum technologies. In contrast, Paper 1 re-examines the foundational double-slit experiment within the Heisenberg picture. While conceptually interesting for quantum foundations and pedagogy, it is less likely to drive novel technological applications or widespread advancements across disciplines compared to Paper 2.
Paper 1 has higher impact potential due to its novel, system-level integration of OR decomposition (Lagrangian knapsack subproblems), learning-based dual control, and hardware/noise-aware execution for a real industrial problem (CVRP). It targets a key near-term bottleneck—qubit/gate limits and noisy execution—offering broadly applicable ideas (decomposition + adaptive execution) across hybrid quantum optimization and operations research. Paper 2 provides incremental theoretical analysis of coherence measures in a specific algorithm (Simon), with narrower applicability and less clear practical or cross-field leverage.
Paper 2 introduces a consistent mathematical framework for neutrino oscillations with non-Hermitian dynamics, bridging non-Hermitian quantum mechanics and particle physics. It compares two distinct approaches, identifies limitations of the metric operator method, and reveals non-Markovian behavior—findings with broader implications across quantum foundations, open quantum systems, and neutrino physics. Paper 1 analyzes coherence in a well-known quantum algorithm using existing measures, providing incremental insights without significant novelty or broad applicability beyond quantum information theory.
Paper 1 is more novel and application-oriented, linking measurement backaction/monitoring protocols to controllable generation and characterization of multiphoton entanglement (e.g., N00N states) in realistic cavity–fiber/cavity–qubit platforms. It uses concrete physical models (coupled cavities, Jaynes–Cummings) and multiple entanglement metrics, making it broadly relevant to quantum optics, metrology, and quantum control. Paper 2 mainly analyzes coherence measures within an established algorithm, yielding dimension-scaling observations with limited methodological or practical novelty and narrower cross-field impact.
Paper 1 focuses on quantum coherence in Simon's quantum algorithm, a foundational algorithm in the rapidly advancing field of quantum computing. Understanding these dynamics has direct implications for quantum algorithm design and optimization, offering broader potential real-world applications and interdisciplinary impact. Paper 2, while methodologically rigorous, addresses a highly specialized theoretical problem in condensed matter physics (Bose gases), which likely has a narrower scope of immediate scientific impact.
Paper 1 addresses fundamental corrections to the equation of state of weakly interacting Bose gases beyond the Lee-Huang-Yang framework, revealing nonuniversal finite-range effects. This has broad implications for ultracold atomic physics and many-body quantum theory, connecting to active experimental programs. Paper 2 analyzes coherence dynamics in Simon's algorithm using specific coherence measures, but Simon's algorithm is primarily of pedagogical interest with limited practical application, and the results (coherence depending on dimension N) are somewhat expected, limiting the novelty and broader impact.