Compact quantum circuits from one-way quantum computation

Silva, Raphael Dias da; Galvão, Ernesto F.

doi:10.1103/physreva.88.012319

Cited by 7 publications

(11 citation statements)

References 20 publications

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“…[19] and is also an extended version of the method proposed in Ref. [12]. We have divided an open graph with gflow into layers, and transformed each layer into an open graph with flow followed by a sequence of CNOTgates.…”

Section: Discussionmentioning

confidence: 99%

“…constructed inductively by Eqs. (7), (8), (9), (12) and (11) a matching gflow of (G, I, O), and denote it by…”

Section: Lemma Iii1 Let (G I O) Be An Open Graph With Gflow With mentioning

confidence: 99%

“…To date, there are three methods to translate a measurement pattern into a compact quantum circuit proposed by [9,11,12]. In [9], a translation method called the star pattern transformation (SPT) applicable to measurement patterns on the graph states with flow is presented.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the trade-off between spatial and temporal resources for measurement-based quantum computation

2015

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In measurement-based quantum computation (MBQC), elementary quantum operations can be more parallelized than the quantum circuit model by employing a larger Hilbert space of graph states used as the resource. Thus MBQC can be regarded as a method of quantum computation where the temporal resource described by the depth of quantum operations can be reduced compared to the quantum circuit model by using the extra spatial resource described by graph states. To analyze the trade-off relationship of the spatial and temporal resources, we consider a method to obtain quantum circuit decompositions of general unitary transformations represented by MBQC on graph states with a certain underlying geometry called generalized flow. We present a method to translate any MBQC with generalized flow into quantum circuits without extra spatial resource. We also show an explicit way to unravel acausal gates that appear in the quantum circuit decomposition derived by a translation method presented in [V. Danos and E. Kashefi, Phys. Rev. A 74, 052310 (2006)] and that represent an effect of the reduction of the temporal resource in MBQC. Finally, by considering a way to deterministically simulate these acausal gates, we investigate a general framework to analyze the trade-off between the spacial and temporal resources for quantum computation.

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Section: Discussionmentioning

confidence: 99%

“…constructed inductively by Eqs. (7), (8), (9), (12) and (11) a matching gflow of (G, I, O), and denote it by…”

Section: Lemma Iii1 Let (G I O) Be An Open Graph With Gflow With mentioning

confidence: 99%

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Analysis of the trade-off between spatial and temporal resources for measurement-based quantum computation

2015

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“…Local processes can also be used to translate a pattern into a circuit. This is used, for example, to verify that the pattern represents the desired operation [15,17,20,24,45]. Conversely, a translation of a circuit into a pattern can be used to implement known algorithms in the one-way model, or it can be combined with a translation back to a circuit to trade depth against width, to parallelise Clifford operations, or to reduce the number of T gates [8,16,32].…”

Section: Introductionmentioning

confidence: 99%

There and back again: A circuit extraction tale

Backens

Miller-Bakewell

Felice

et al. 2021

Quantum

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Translations between the quantum circuit model and the measurement-based one-way model are useful for verification and optimisation of quantum computations. They make crucial use of a property known as gflow. While gflow is defined for one-way computations allowing measurements in three different planes of the Bloch sphere, most research so far has focused on computations containing only measurements in the XY-plane. Here, we give the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes and having gflow. The algorithm is efficient and the resulting circuits do not contain ancillae. One-way computations are represented using the ZX-calculus, hence the algorithm also represents the most general known procedure for extracting circuits from ZX-diagrams. In developing this algorithm, we generalise several concepts and results previously known for computations containing only XY-plane measurements. We bring together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus. These rules are used to simplify measurement patterns by reducing the number of qubits while preserving both the semantics and the existence of gflow. The results can be applied to circuit optimisation by translating circuits to patterns and back again.

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“…It can solve Simon's Problem -a black box period-finding problem which has an exponential gap between the classical and quantum runtime [6] . It can realize the compact quantum circuits from one-way quantum computation [7] . One-way quantum computing requires qubits to be initialized in a highly-entangled cluster state, and performs single qubit measurements on its corresponding qubits.…”

Section: Introductionmentioning

confidence: 99%