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Science

Quantum Information Processing Without Entanglement

P. L. Knight

Published Jan 21, 2000• 31 citations
Publisher

Abstract

Quantum computers have the potential to significantly reduce the amount of time required for certain computational tasks. It is often assumed that for a quantum computer to be efficient, entanglement between different states is required. Ahn et al . (page [463][1]) show that a single quantum system possessing no entanglement whatsoever can implement the search algorithm in a non-classical and highly effective way. [1]: http://www.sciencemag.org/cgi/content/short/287/5452/463

DOI
10.1126/science.287.5452.441

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Quantum computers have the potential to significantly reduce the amount of time required for certain computational tasks. It is often assumed that for a quantum computer to be efficient, entanglement between different states is required. Ahn et al . (page 463) show that a single quantum system possessing no entanglement whatsoever can implement the search algorithm in a non-classical and highly effective way.
Entanglement is generally accepted as the resource that allows quantum systems to be more efficient in performing classical computation, but the practical utility of entanglement in a variety of quantum information-processing processes is inadequately comprehended. The following paper examines the operational importance, constraints, and trade-offs of entanglement in quantum algorithms, communication protocols, error-correction frameworks and complexity-theoretic settings. Though entanglement (between two or more systems) is a requirement of uniquely quantum behaviours: teleportation, superdense coding, and non-classical correlations, we have found that a larger entanglement does not necessarily improve algorithmic performance. We find through analytical modelling, small-circuit entropy analysis, and comparative analysis of representative use-cases, an optimum entanglement zone, at which performance gains cease to improve with noise, gate infidelity, circuit-depth and hardware decoherence. It has also been found that moderate, noise-resilient entanglement is most useful in algorithmic tasks, structural connectivity is essential in communication tasks, and that quantum error-correction needs highly stable, topology-optimised entangled states rather than maximally entangled states. In addition, resource-theory views indicate conflicts between entanglement entropy, gate cost and classical stimulability thresholds and point to the importance of designing entanglement-efficiently. The paper identifies multiparty entanglement as the bottleneck to scalable quantum advantage, especially with the constraints in NISQ era. Comprehensively, this paper has provided a single analytical framework explaining when, where and how entanglement has real computational benefit. The analysis argues the development of algorithms and hardware in a so-called just-enough entanglement paradigm, to optimise fidelity, limit the effects of noise, and have scalable quantum architectures.
Quantum entanglement, in which the physical properties of particles become correlated, is an essential property of quantum information systems. In their Perspective, [Cory and Havel][1] discuss results reported in the same issue by [ Roos et al .][2] and by [ Leibfried et al .][3] in which trapped ions were put into entangled quantum states. The two complementary studies show that substantial progress is being made in quantum information processing and point to practical applications of entangled states. [1]: http://www.sciencemag.org/cgi/content/full/304/5676/1456 [2]: http://www.sciencemag.org/cgi/content/short/304/5676/1478 [3]: http://www.sciencemag.org/cgi/content/short/304/5676/1476
Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speedups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speedup over classical methods, but that do not require entanglement. These methods rely instead on interference to provide a speedup. Search without entanglement comes at a cost: although they outperform analogous classical devices, the quantum devices that perform the search are not universal quantum computers and require exponentially greater overhead than a quantum computer that operates using entanglement. Quantum search without entanglement is compared to classical search using waves.
Quantum computation is usually performed through optical or magnetic resonance and does not obviously have anything to do with geometry. But, as [Lloyd][1] explains in his Perspective, computation can benefit from geometry. He highlights the report by [ Duan et al .][2], who have found a way to exploit geometry to perform quantum computations more efficiently through sending quantum bits for walks through potential space. [1]: http://www.sciencemag.org/cgi/content/full/292/5522/1669 [2]: http://www.sciencemag.org/cgi/content/short/292/5522/1695