Noise-induced barren plateaus in variational quantum algorithms

Wang, Samson; Fontana, Enrico; Cerezo, M.; Sharma, Kunal; Sone, Akira; Cincio, Łukasz; Coles, Patrick J.

doi:10.1038/s41467-021-27045-6

Cited by 354 publications

(269 citation statements)

References 78 publications

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“…In order to solve (18), we multiply both sides with the Hermitian conjugate to obtain a recursion relation involving only the upper triangular matrices G k , i.e.…”

Section: From Aba To Abc a Detailed Methodsmentioning

confidence: 99%

Algebraic Bethe Circuits

Sopena,

Gordon,

García-Martín

et al. 2022

Preprint

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“…In order to solve (18), we multiply both sides with the Hermitian conjugate to obtain a recursion relation involving only the upper triangular matrices G k , i.e.…”

Section: From Aba To Abc a Detailed Methodsmentioning

confidence: 99%

Algebraic Bethe Circuits

Sopena,

Gordon,

García-Martín

et al. 2022

Preprint

View full text Add to dashboard Cite

“…These are shallow enough circuits which have been simulated exactly in a classical computer. Hence, we cannot attribute the effect to vanishing gradients or barren plateaus [53,54], but to an intrinsic limitation of the algorithm.…”

Section: Entangling Layer Structurementioning

confidence: 99%

Quantum variational optimization: The role of entanglement and problem hardness

Díez-Valle,

Porras,

García-Ripoll

2021

Preprint

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Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this manuscript we study systematically the role of entanglement, the structure of the variational quantum circuit, and the structure of the optimization problem, in the success and efficiency of these algorithms. For that purpose, our study focuses on the Variational Quantum Quantum Eigensolver (VQE) algorithm, as applied to Quadratic Unconstrained Binary Optimization (QUBO) problems on random graphs with tunable density. Our numerical results indicate an advantage in adapting the distribution of entangling gates to the problem's topology, specially for problems defined on low-dimensional graphs. Furthermore, we find evidence that applying CVaR type cost functions improves the optimization, increasing the probability of overlap with the optimal solutions. However, these techniques also improve the performance of ansatz based on product states (no entanglement), suggesting a new classical optimization method based on these could outperform existing NISQ architectures in certain regimes. Finally, our study also reveals a correlation between the hardness of a problem and the Hamming distance between the ground-and first-excited state, an idea that can be used to engineer benchmarks and understand the performance bottlenecks of optimization methods.

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“…The algorithm prepares both the ground state and the correction vector for different frequency points using circuits representing a variational ansatz. The approach of parameterized quantum circuits has been widely used for the practical simulation of both ground and excited states in recent years [12,[18][19][20][21][22][23][24][25], although the scalability of the optimization problem for the gate parameters is a source of debate in the literature [81][82][83]. This is expected to be compounded by the condition number of the H (z, j) operator generally being larger than that of its parent Hamiltonian used to simulate the ground state.…”

Section: E Perspectivementioning

confidence: 99%

A variational quantum eigensolver for dynamic correlation functions

Chen,

Nusspickel,

Tilly

et al. 2021

Preprint

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Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parameterized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parameterization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground state VQE. We apply the method to compute the single-particle Green's function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.

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Noise-induced barren plateaus in variational quantum algorithms

Cited by 354 publications

References 78 publications

Algebraic Bethe Circuits

Algebraic Bethe Circuits

Quantum variational optimization: The role of entanglement and problem hardness

A variational quantum eigensolver for dynamic correlation functions

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