Neural Error Mitigation of Near-Term Quantum Simulations

R., Bennewitz, Elizabeth; Hopfmueller, Florian; Kulchytskyy, Bohdan; Carrasquilla, Juan; Ronagh, Pooya

doi:10.48550/arxiv.2105.08086

Cited by 5 publications

(6 citation statements)

References 46 publications

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“…Our work also clearly indicates that the current gener-ation of Rydberg atom arrays can produce data of high value to physicists, even at measurement rates which may be too low to be informationally complete for a full tomographic reconstruction of the quantum state. This strategy can be combined with the recent observation that Hamiltonian-driven optimization can also be used to mitigate errors in noisy experiments [44]. This suggests that the current generation of quantum hardware is on the cusp of bringing transformative improvement to the understanding of challenging quantum many-body systems, by providing data to enhance variational simulation strategies for any state that can be prepared by an experimental quantum simulator.…”

Section: (B) Inset)mentioning

confidence: 99%

“…In this work, we leverage these unique features of neural network wavefunctions to explore the effect of combined data-and Hamiltonian-driven learning [44]. Beginning with a randomly initialized recurrent neural network (RNN) [18], we first optimize network parameters using a limited amount of simulated [12,14,45] Rydberg occupation data drawn from a two-dimensional array in the vicinity of a quantum phase transition.…”

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confidence: 99%

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Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays

Czischek,

Moss,

Radzihovsky

et al. 2022

Preprint

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Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. Due to long experimental preparation times, obtaining projective measurement data can be relatively slow for large arrays, which poses a challenge for state reconstruction methods such as tomography. Today, novel groundstate wavefunction ansätze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate how pretraining modern RNNs on even small amounts of data significantly reduces the convergence time for a subsequent variational optimization of the wavefunction. This suggests that essentially any amount of measurements obtained from a state prepared in an experimental quantum simulator could provide significant value for neural-network-based VMC strategies.

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Section: (B) Inset)mentioning

confidence: 99%

mentioning

confidence: 99%

Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays

Czischek,

Moss,

Radzihovsky

et al. 2022

Preprint

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“…Two observations are in order. On the one hand, it would seem cautious to expect that standard ML techniques will not be able by themselves to compensate for hardware noise, unless specifically designed for this purpose [73][74][75] : as a result, a minimal well posed target is to show trainability of an MLP up to an overall model error -with respect to noiseless exact values -matching as close as possible the characteristic inaccuracy induced by noise on the training points. On the other hand, one should also keep in mind that fast technological advancements, possibly in combination with error mitigation techniques 64,[76][77][78][79][80][81][82][83][84] , will progressively reduce the impact of hardware noise.…”

Section: Hardware Noisementioning

confidence: 99%

Extending the reach of quantum computing for materials science with machine learning potentials

Schuhmacher¹,

Mazzola²,

Tacchino³

et al. 2022

Preprint

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Solving electronic structure problems represents a promising field of application for quantum computers. Currently, much effort has been spent in devising and optimizing quantum algorithms for quantum chemistry problems featuring up to hundreds of electrons. While quantum algorithms can in principle outperform their classical equivalents, the polynomially scaling runtime, with the number of constituents, can still prevent quantum simulations of large scale systems. We propose a strategy to extend the scope of quantum computational methods to large scale simulations using a machine learning potential, trained on quantum simulation data. The challenge of applying machine learning potentials in today's quantum setting arises from the several sources of noise affecting the quantum computations of electronic energies and forces. We investigate the trainability of a machine learning potential selecting various sources of noise: statistical, optimization and hardware noise. Finally, we construct the first machine learning potential from data computed on actual IBM Quantum processors for a hydrogen molecule. This already would allow us to perform arbitrarily long and stable molecular dynamics simulations, outperforming all current quantum approaches to molecular dynamics and structure optimization.

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“…The remarkable success of variational states in the description of quantum spin systems unfortunately does not have a parallel in correlated systems of fermions, however. It is known, for example, that the natural mean-field analogue of direct-product states, the so-called Slater determinant (SD) states, fail to even qualitatively describe the thermodynamic limit of Fermi-Hubbard type Hamiltonians 3 and the development of systematically improvable neural-network-based trial wave functions is currently an active field of research both in second quantization [6][7][8] , and first quantization [9][10][11][12][13][14][15] . In the latter approach, the wave function amplitudes must be anti-symmetric functions of the particle configurations, while being able to capture correlations beyond the singleparticle Slater determinants.…”

Section: Introductionmentioning

confidence: 99%

Fermionic Wave Functions from Neural-Network Constrained Hidden States

Moreno,

Carleo,

Georges

et al. 2021

Preprint

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We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving 'hidden' additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint which is optimized, together with the single-particle orbitals, using a neural network parametrization. This construction draws inspiration from the success of hidden particle representations 1 but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proven to be universal. We apply this construction to the ground state properties of the Hubbard model on the square lattice, achieving levels of accuracy which are competitive with and in some cases superior to state-of-the-art computational methods.

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Neural Error Mitigation of Near-Term Quantum Simulations

Cited by 5 publications

References 46 publications

Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays

Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays

Extending the reach of quantum computing for materials science with machine learning potentials

Fermionic Wave Functions from Neural-Network Constrained Hidden States

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