Tsallis relative α entropy of coherence dynamics in Grover′s search algorithm

2023/06/09 by Linlin Ye, Zhaoqi Wu, Shao-Ming Fei · 1 voice · 1 citation
Computer Science · Physics and Astronomy · #Algorithm #Coherence (philosophical gambling strategy) #Computer science #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Tsallis entropy #Tsallis statistics #quant-ph

paper · pdf · doi:10.1088/1572-9494/acdce5

openalex publication_date 2023/06/09 · openalex created_date 2023/06/10 · arxiv published 2026/04/15 · arxiv updated 2026/04/16 · openalex updated_date 2026/08/05

Abstract

Abstract Quantum coherence plays a central role in Grover’s search algorithm. We study the Tsallis relative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> entropy of coherence dynamics of the evolved state in Grover’s search algorithm. We prove that the Tsallis relative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> entropy of coherence decreases with the increase of the success probability, and derive the complementarity relations between the coherence and the success probability. We show that the operator coherence of the first <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⨂</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:math> relies on the size of the database <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>N</mml:mi> <mml:mo>,</mml:mo> </mml:math> the success probability and the target states. Moreover, we illustrate the relationships between coherence and entanglement of the superposition state of targets, as well as the production and deletion of coherence in Grover iterations.

Citations

• Towards the coherent control of robust spin qubits in quantum algorithms
• Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation
• Incoherent quantum algorithm dynamics of an open system with near-term devices
• Coherence and complementarity based on modified generalized skew information
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Simulating Quantum Algorithms Using Fidelity and Coherence Time as Principle Models for Error
• Coherence Depletion in Quantum Algorithms
• Quantum Resource Theories
• Witnessing quantum resource conversion within deterministic quantum computation using one pure superconducting qubit
• Family of coherence measures and duality between quantum coherence and path distinguishability
• Of Local Operations and Physical Wires
• Quantum Coherence via Skew Information and Its Polygamy
• Coherence and Entanglement Monogamy in the Discrete Analogue of Analog Grover Search
• Coherence depletion in the Grover quantum search algorithm
• Measuring Coherence with Entanglement Concurrence
• Alternative framework for quantifying coherence
• Measure-Independent Freezing of Quantum Coherence
• Distribution of quantum coherence in multipartite systems
• Robustness of asymmetry and coherence of quantum states
• Irreversible degradation of quantum coherence under relativistic motion
• Coherent control of quantum systems as a resource theory
• Quantum-coherence quantifiers based on the Tsallis relative α-entropies
• Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
• Maximally coherent states and coherence-preserving operations
• Trace-distance measure of coherence
• Converting Coherence to Quantum Correlations
• Quantifying coherence of Gaussian states
• Relating the Resource Theories of Entanglement and Quantum Coherence
• Coherence susceptibility as a probe of quantum phase transitions
• Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm
• Operational Resource Theory of Coherence
• Cohering and de-cohering power of quantum channels
• Quantum coherence in multipartite systems
• Quantifying coherence in infinite-dimensional systems
• Coherence measures and optimal conversion for coherent states
• Conditions for coherence transformations under incoherent operations
• Measuring Quantum Coherence with Entanglement
• Coherence and measurement in quantum thermodynamics
• Frozen Quantum Coherence
• Quantum coherence, time-translation symmetry and thermodynamics
• Low-temperature thermodynamics with quantum coherence
• Quantum coherence and correlations in quantum system
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantifying Coherence
• Vibrations, Quanta and Biology
• Scale invariance of entanglement dynamics in Grover's quantum search algorithm
• Fundamental limitations for quantum and nano thermodynamics
• Quantum coherence in biological systems
• Increasing thermoelectric performance using coherent transport
• Quantum algorithm for solving linear systems of equations
• The quadratic speedup in Grover's search algorithm from the entanglement perspective
• Non-Markovian decoherence in the adiabatic quantum search algorithm
• Fundamental properties of Tsallis relative entropy
• Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification
• Monotonic decrease of the quantum nonadditive divergence by projective measurements
• Entanglement versus relaxation and decoherence in a quantum algorithm for quantum chaos
• On the Power of One Bit of Quantum Information
• Quantum Mechanics helps in searching for a needle in a haystack
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• On the Power of Quantum Computation
• Quantifying quantum coherence based on the generalized α α –z-relative R \acutee e ´ nyi entropy

Cited by

• Coherence dynamics in quantum algorithm for linear systems of equations

Discussions

• Tsallis relative $α$ entropy of coherence dynamics in Grover's search algorithm This article provides a fresh theoretical perspective on one of quantum computing's most famous algorithms by examining [bsky, 0 points, 0 comments]

Related

• Coherence dynamics in Simon's quantum algorithm
• Coherence Fraction in Grover Search Algorithm
• Coherence dynamics in quantum algorithm for linear systems of equations
• Coherence and Entanglement Monogamy in the Discrete Analogue of Analog Grover Search
• Entropic characterization of coherence in quantum evolutions