Quantum Advantage from Sequential-Transformation Contextuality

Mansfield, Shane; Kashefi, Elham

doi:10.1103/physrevlett.121.230401

Cited by 50 publications

(59 citation statements)

References 66 publications

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“…Prior measures of contextuality include the contextual fraction (CF) (in [51,60,68,69]), relative entropy of contextuality (REC), mutual information of contextuality (MIC), and contextual cost (CC) (all in [58]), and rank of contextuality (RC) [63]. In a strict sense our contextual p-distance is a complementary measure to CF and CC, both of which measure the fraction of an empirical model that must be strongly contextual.…”

Section: Appendix B: Measurement Contextsmentioning

confidence: 99%

“…A natural next step is to develop measures that quantify contextuality based on our criterion. We suggest two simple measures at the end of Section II, and discuss more general measures in Appendix C, as well as their relations with prior measures, which include the contextual fraction [51,60,68,69], relative entropy of contextuality, mutual information of contextuality, contextual cost (all in [58]), and rank of contextuality [63].…”

Section: Introductionmentioning

confidence: 99%

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Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Love

2019

Phys. Rev. Lett.

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Contextuality is an indicator of non-classicality, and a resource for various quantum procedures. In this paper, we use contextuality to evaluate the variational quantum eigensolver (VQE), one of the most promising tools for near-term quantum simulation. We present an efficiently computable test to determine whether or not the objective function for a VQE procedure is contextual. We apply this test to evaluate the contextuality of experimental implementations of VQE, and determine that several, but not all, fail this test of quantumness.

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Section: Appendix B: Measurement Contextsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Love

2019

Phys. Rev. Lett.

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“…Many features of quantum theory have been proposed as the origin of this supposed quantum computational power: entanglement, superposition, and exponential scaling of Hilbert spaces to name a few. Recently, contextuality has been investigated in a variety of scenarios as a potential resource for quantum computation [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Contextuality can be thought of as the impossibility of assigning pre-determined outcomes to all potential measurements of a quantum system, independent of their measurement context [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Contextuality as a resource for measurement-based quantum computation beyond qubits

Frembs¹,

Roberts²,

Bartlett³

2018

New J. Phys.

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Contextuality-the obstruction to describing quantum mechanics in a classical statistical way-has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate nonlinear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality-the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits, which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for stateindependent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation (MBC) that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality, which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit MBC are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.

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“…Ref. [52] recently introduced a new notion of contextuality for sequences of transformations. Therein, the authors noted that the constant-depth quantum circuits of [51] are sequential-transformation contextual.…”

Section: Sequential Contextualitymentioning

confidence: 99%

Phase-space-simulation method for quantum computation with magic states on qubits

et al. 2020

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We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides amplitude estimation. The simulation cost is then proportional to a robustness measure squared. For all quantum states, this robustness is smaller than or equal to robustness of magic.

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Quantum Advantage from Sequential-Transformation Contextuality

Cited by 50 publications

References 66 publications

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers

Contextuality as a resource for measurement-based quantum computation beyond qubits

Phase-space-simulation method for quantum computation with magic states on qubits

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