Variational Quantum Fidelity Estimation

Cerezo, M.; Poremba, Alexander; Cincio, Łukasz; Coles, Patrick J.

doi:10.22331/q-2020-03-26-248

Cited by 136 publications

(126 citation statements)

References 36 publications

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“…The most famous VHQCA is the variational quantum eigensolver (VQE) [8], where the cost function is the energy for some Hamiltonian and hence the goal is to prepare the ground state. VHQCAs have been proposed for many other applications [9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

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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“…were prepared on a quantum computer) it is known that their Hilbert-Schmidt distance is efficiently computable (logarithmic in matrix dimension) on a quantum computer [7,8]. Because of the latter, the Hilbert-Schmidt distance is employed as a cost function in recent variational hybrid quantum-classical algorithms [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…2. The Hilbert-Schmidt distance is often employed as a cost function in variational hybrid quantumclassical algorithms (often with the low-rank assumption already made) [9][10][11][12], since it can be efficiently computed on a quantum computer. Because of our bound, minimizing the cost in these algorithms implies that one is also minimizing a function of the trace distance.…”

Section: Introductionmentioning

confidence: 99%

Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states

2019

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The trace distance between two quantum states, ρ and σ, is an operationally meaningful quantity in quantum information theory. However, in general it is difficult to compute, involving the diagonalization of ρ − σ. In contrast, the Hilbert-Schmidt distance can be computed without diagonalization, although it is less operationally significant. Here, we relate the trace distance and the Hilbert-Schmidt distance with a bound that is particularly strong when either ρ or σ is low rank. Our bound is stronger than the bound one could obtain via the norm equivalence of the Frobenius and trace norms. We also consider bounds that are useful not only for low-rank states but also for low-entropy states. Our results have relevance to quantum information theory, quantum algorithms design, and quantum complexity theory.

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“…Moreover, it was pointed out that Barren plateaus may further slow down the convergence of the heuristic Ansatz with the increase of the dimensionality of the system. 74 , 75 However, there is still no clear evidence that Barren plateaus will play an important role when using the UVCC Ansatz , since physically motivated reductions of the number of variational parameters can be applied, at the cost of reducing the accuracy of the calculation. 54 , 55 , 76 – 79 Additionally, the convergence rate when working with the UVCC Ansatz for larger, strongly anharmonic molecules may be improved by initializing the VQE parameters with a more accurate guess.…”

Section: Resultsmentioning

confidence: 99%