Efficient evaluation of quantum observables using entangled measurements

Hamamura, Ikko; Imamichi, Takashi

doi:10.1038/s41534-020-0284-2

Cited by 81 publications

(105 citation statements)

References 58 publications

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“…A, we show it implements a symmetric informationally-complete measurement (SIC POVM) on a qubit, a.k.a., the tetrahedron measurement [32]. Finally, we note that recent work [33] has also suggested to use Bell-measurements in the context of RDMs reconstruction. However, there the use of Bellmeasurements was done on pairs of system qubits.…”

Section: Qubitsmentioning

confidence: 81%

Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning

Zhang

Kalev

Mruczkiewicz

et al. 2020

Quantum

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We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an n-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on ⌈log3⁡(2n+1)⌉ qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than log3⁡(2n) qubits on average. We apply it to the problem of learning k-fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that one can determine individual elements of all k-fermion RDMs in parallel, to precision ϵ, by repeating a single quantum circuit for ≲(2n+1)kϵ−2 times. This result is based on a method we develop here that allows one to determine individual elements of all k-qubit RDMs in parallel, to precision ϵ, by repeating a single quantum circuit for ≲3kϵ−2 times, independent of the system size. This improves over existing schemes for determining qubit RDMs.

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Section: Qubitsmentioning

confidence: 81%

Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning

Zhang

Kalev

Mruczkiewicz

et al. 2020

Quantum

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“…The costs and errors owing to the measurements can be reduced using simultaneous measurements and/or other techniques. Such techniques have been actively developed [65][66][67][68][69][70][71][72][73][74][75], and they can be used to alleviate the problems caused by measuring 1 and 2RDMs. In practice, OO-VQE repeatedly performs the VQE and the orbital optimization until convergence.…”

Section: Orbital Optimized Unitary Coupled Cluster Doublesmentioning

confidence: 99%

Orbital optimized unitary coupled cluster theory for quantum computer

Mizukami

Mitarai

Nakagawa³

et al. 2020

Phys. Rev. Research

110

106

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We propose an orbital optimized method for unitary coupled cluster theory (OO-UCC) within the variational quantum eigensolver (VQE) framework for quantum computers. OO-UCC variationally determines the coupled cluster amplitudes and also molecular orbital coefficients. Owing to its fully variational nature, first-order properties are readily available. This feature allows the optimization of molecular structures in VQE without solving any additional equations. Furthermore, the method requires smaller active space and shallower quantum circuits than UCC to achieve the same accuracy. We present numerical examples of OO-UCC using quantum simulators, which include the geometry optimization of water and ammonia molecules using analytical first derivatives of the VQE.

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“…Commutation is not transitive, and as such, there may be many different solutions to grouping operators together. To find a good solution, we use the largest-degree-first coloring (LDFC) algorithm (for a good summary of the LDFC algorithm, see the Supplemental Material in [46]), whereby groups are composed starting from one of the operators which have the highest number of commuting operators. The results we obtained are summarized in Table I.…”

Section: Entanglement Witness Testsmentioning

confidence: 99%

Qudits for witnessing quantum-gravity-induced entanglement of masses under decoherence

et al. 2021

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Recently, a theoretical and an experimental protocol known as quantum-gravity-induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses, each placed in a superposition of two locations. If after eliminating all nongravitational interactions between them the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e., graviton. In this paper we explore extensions of the QGEM experiment to multidimensional quantum objects and examine a range of different experiment geometries, in order to determine which would generate entanglement faster. We conclude that when a sufficiently high decoherence rate is introduced, multicomponent superpositions can outperform the two-qubit setup. With low decoherence however, and given a maximum distance x between any two spatial states of a superposition, a set of two qubits placed in spatial superposition parallel to one another will outperform all other models given realistic experimental parameters. This is further verified with an experiment simulation, showing that O( 103 ) measurements are required to reject the no-entanglement hypothesis with a parallel-qubit setup without decoherence at a 99.9% confidence level. The number of measurements increases when decoherence is introduced. When the decoherence rate reaches 0.125 Hz, six-dimensional qudits are required as the two-qubit system entanglement cannot be witnessed anymore. However, in this case, O(10 6 ) measurements will be required. One can group the witness operators to measure in order to reduce the number of measurements (up to tenfold). However, this may be challenging to implement experimentally.

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Efficient evaluation of quantum observables using entangled measurements

Cited by 81 publications

References 58 publications

Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning

Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning

Orbital optimized unitary coupled cluster theory for quantum computer

Qudits for witnessing quantum-gravity-induced entanglement of masses under decoherence

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