Coherence Depletion in Quantum Algorithms
arXiv:1808.02222 · doi:10.3390/e21030260
Abstract
Besides the superior efficiency compared to their classical counterparts, quantum algorithms known so far are basically task-dependent, and scarcely any common features are shared between them. In this work, however, we show that the depletion of quantum coherence turns out to be a common phenomenon in these algorithms. For all the quantum algorithms that we investigated including Grover's algorithm, Deutsch-Jozsa algorithm and Shor's algorithm, quantum coherence of the system states reduces to the minimum along with the successful execution of the respective processes. Notably, a similar conclusion cannot be drawn using other quantitative measures such as quantum entanglement. Thus, we expect that coherence depletion as a common feature can be useful for devising new quantum algorithms in the future.
arXiv commentfinal version, title changed; 11 pages, 2 figures, 44 references
References in corpus (30)
- Quantum entanglement
- Quantum algorithm for solving linear systems of equations
- Quantifying Coherence
- Entanglement detection
- Quantum Coherence as a Resource
- Strengths and Weaknesses of Quantum Computing
- Quantum Algorithms Revisited
- Quantum discord and the power of one qubit
- Operational Resource Theory of Coherence
- Measuring Quantum Coherence with Entanglement
- On the Power of One Bit of Quantum Information
- On the role of entanglement in quantum computational speed-up
- Converting Coherence to Quantum Correlations
- Quantum coherence in multipartite systems
- Separable states are more disordered globally than locally
- A mathematical theory of resources
- Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
- Relating the Resource Theories of Entanglement and Quantum Coherence
- (Quantumness in the context of) Resource Theories
- Coherence depletion in the Grover quantum search algorithm
- Operational one-to-one mapping between coherence and entanglement measures
- Deutsch-Jozsa algorithm as a test of quantum computation
- Multipartite entanglement in quantum algorithms
- Universality of Entanglement and Quantum Computation Complexity
- Axiomatic and operational connections between the -norm of coherence and negativity
- The Majorization Arrow in Quantum Algorithm Design
- Entanglement Simulations of Shor's Algorithm
- Entanglement and deterministic quantum computing with one qubit
- Systematic Analysis of Majorization in Quantum Algorithms
- Entangling capacity of global phases and implications for Deutsch-Jozsa algorithm
Cited by in corpus (13)
- On the Role of Coherence in Shor's Algorithm
- Tsallis relative entropy of coherence dynamics in Grover's search algorithm
- Generalized exceptional quantum walk search
- Estimating quantum coherence by noncommutativity of any observable and its incoherent part
- Cohering and decohering power of massive scalar fields under instantaneous interactions
- Coherence dynamics in quantum algorithm for linear systems of equations
- Coherence Fraction in Grover Search Algorithm
- Experimental investigation of quantum uncertainty relations with classical shadows
- All multipartite entanglements are quantum coherences in locally distinguishable bases
- Quantum resources in Harrow-Hassidim-Lloyd algorithm
- Correlation between resource-generating capacities of quantum gates
- Coherence and entanglement dynamics in Shor's algorithm
- The tightness of multipartite coherence from spectrum estimation