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Reichardt, Ben W.; Špalek, Robert

doi:10.4086/toc.2012.v008a013

Cited by 20 publications

(7 citation statements)

References 36 publications

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“…The adversary bound characterizes quantum query complexity up to a constant factor, as shown by Reichardt et al [21,18]. Previously, the adversary bound was used for formula evaluation [23,25], triangle and other subgraph detection [3,17,5], the k-distinctness problem [2], and learning symmetric juntas [4]. This paper demonstrates an application to property testing.…”

Section: Introductionmentioning

confidence: 78%

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Belovs¹,

Blais²

2015

Theory of Comput.

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Section: Introductionmentioning

confidence: 78%

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Belovs¹,

Blais²

2015

Theory of Comput.

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“…Span programs [18] were first introduced to the study of quantum algorithms by Reichardt and Špalek [24]. They have since proven to be immensely important for designing quantum algorithms in the query model.…”

Section: Span Programs and Quantum Query Algorithmsmentioning

confidence: 99%

“…Quantum speed-ups for evaluating formulas like or [15] and the nand-tree [14] spurred interest in better understanding the performance of quantum algorithms for Boolean formulas. This research culminated in the development of span program algorithms [23,24], which can have optimal quantum query complexity for any problem [20]. Using span program algorithms, it was shown that O( √ N ) queries are sufficient for any read-once formula with N inputs [20,22].…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithms for graph connectivity and formula evaluation

Jeffery

Kimmel

2017

Quantum

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We give a new upper bound on the quantum query complexity of deciding st-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation reduces to deciding connectivity on just such a class of graphs. Applying the algorithm for st-connectivity to Boolean formula evaluation problems, we match the O( √ N ) bound on the quantum query complexity of evaluating formulas on N variables, give a quadratic speed-up over the classical query complexity of a certain class of promise Boolean formulas, and show this approach can yield superpolynomial quantum/classical separations. These results indicate that this st-connectivity-based approach may be the "right" way of looking at quantum algorithms for formula evaluation.

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“…One such universal model was suggested by Childs 16 , and describes a single particle performing a quantum walk on a graph [17][18][19][20] . Quantum walk models have been shown to have an advantage over classical random walk, with 21,22 and without [23][24][25][26][27][28][29][30][31][32][33] a black-box. The model opens the door for using well-developed tools in physics for the study of quantum computation, such as scattering and localization.…”

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confidence: 99%

Noisy Quantum Computation Modeled by Quantum Walk: Universality without Ancillas

Feldman¹,

Goldstein²

2021

Preprint

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The universal quantum computation model based on quantum walk by Childs has opened the door for a new way of studying the limitations and advantages of quantum computation, as well as for its intermediate-term simulation. In recent years, the growing interest in noisy intermediatescale quantum computers (NISQ) has lead to intense efforts being directed at understanding the computational advantages of open quantum systems. In this work, we extend the quantum walk model to open noisy systems in order to provide such a tool for the study of NISQ computers. Our method does not use explicit purification, and allows to ignore the environment degrees of freedom and get direct and much more efficient access to the entanglement properties of the system. In our representation, the quantum walk amplitudes represent elements in a density matrix rather than the wavefunction of a pure state. Despite the non-trivial manifestation of the normalization requirement in this setting, we model the application of general unitary gates and nonunitary channels, with an explicit implementation protocol for channels that are commonly used in noise models.

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Cited by 20 publications

References 36 publications

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Quantum algorithms for graph connectivity and formula evaluation

Noisy Quantum Computation Modeled by Quantum Walk: Universality without Ancillas

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