Learning the quantum algorithm for state overlap

Cincio, Łukasz; Subaşı, Yiğit; Sornborger, Andrew; Coles, Patrick J.

doi:10.1088/1367-2630/aae94a

Cited by 266 publications

(264 citation statements)

References 36 publications

(74 reference statements)

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“…Clearly, error mitigation techniques will be necessary to make use of NISQ devices. Several promising error mitigation strategies have recently emerged, including zero-noise extrapolation [2], quasi-probability decomposition [2], post-selection [3,4], noise-aware compiling [5], and machine learning for circuit-depth compression [6]. Let us consider two other strategies for error mitigation in what follows.…”

Section: Introductionmentioning

confidence: 99%

Noise resilience of variational quantum compiling

et al. 2020

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Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the costevaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

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Section: Introductionmentioning

confidence: 99%

Noise resilience of variational quantum compiling

et al. 2020

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“…One might think by looking at eq. (4) that B (e) λmm ′ can be easily calculated by preparing the qubit representations of |Ψ N +1 λ and |Ψ (e) m ≡ a † m |Ψ N gs , between which the inner product is calculated using the SWAP test or its versions [40,44,45] with phase factors. Such an approach is, however, difficult in fact.…”

Section: Circuits For Diagonal Componentsmentioning

confidence: 99%

Construction of Green's functions on a quantum computer: Quasiparticle spectra of molecules

Kosugi

Matsushita

2020

Phys. Rev. A

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We propose a scheme for the construction of one-particle Green's function (GF) of an interacting electronic system via statistical sampling on a quantum computer. Although the non-unitarity of creation and annihilation operators for the electronic spin orbitals prevents us from preparing specific states selectively, probabilistic state preparation is demonstrated to be possible for the qubits. We provide quantum circuits equipped with at most two ancillary qubits for obtaining all the components of GF. We perform simulations of such construction of GFs for LiH and H2O molecules based on the unitary coupled-cluster (UCC) method to demonstrate the validity of our scheme by comparing the spectra exact within UCC and those from full configuration interaction calculations. We also examine the accuracy of sampling method by exploiting the Galitskii-Migdal formula, which gives the total energy only from the GF.

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“…with confidence level bounded by c. The last inequality in equation (15) was obtained using M=1+1/ò2/ ò, and | ( )| ( ) p   F k 2 j -see appendix A. Equations (11) and (15) imply the desired condition of equation (2).…”

Section: Solution To the Qeep From The Tsmentioning

confidence: 99%

Quantum eigenvalue estimation via time series analysis

Somma

2019

New J. Phys.

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We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ò, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ò.

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Learning the quantum algorithm for state overlap

Cited by 266 publications

References 36 publications

Noise resilience of variational quantum compiling

Noise resilience of variational quantum compiling

Construction of Green's functions on a quantum computer: Quasiparticle spectra of molecules

Quantum eigenvalue estimation via time series analysis

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