Neural Error Mitigation of Near-Term Quantum Simulations

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

doi:10.1038/s42256-022-00509-0

Cited by 22 publications

(11 citation statements)

References 44 publications

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“…The neural error mitigation scheme proposed in Ref. [37] essentially provides a good initialization for the neural VMC with expensive resource requirements for the state tomography. And the second stage of the scheme in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…And the second stage of the scheme in Ref. [37] is a purely classical VMC training with no input from the PQC. On the contrary, the noisy PQC is always one part of the quantum state generation pipeline in our case.…”

Section: Discussionmentioning

confidence: 99%

“…There are already various proposals for QEM techniques [14][15][16][17][18][19][20][21][22][23][24][25][26][27] and specifically some of the proposals are based DOI: 10.1002/qute.202300147 on the principle of variational optimizations. [28][29][30][31][32][33][34][35][36][37] However, the interplay in terms of variational optimization between VQA and QEM remains largely elusive so far. To pave the way toward more practical quantum advantages, it is natural and urgent to investigate the interplay between VQAs and QEM as well as design VQA-native QEM techniques or QEM baked-in VQAs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Variational Quantum‐Neural Hybrid Error Mitigation

Zhang,

Wan,

Hsieh

et al. 2023

Adv Quantum Tech

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Quantum error mitigation (QEM) is crucial for obtaining reliable results on quantum computers by suppressing quantum noise with moderate resources. It is a key factor for successful and practical quantum algorithm implementations in the noisy intermediate scale quantum (NISQ) era. Since quantum‐classical hybrid algorithms can be executed with moderate and noisy quantum resources, combining QEM with quantum‐classical hybrid schemes is one of the most promising directions toward practical quantum advantages. This work shows how the variational quantum‐neural hybrid eigensolver (VQNHE) algorithm, which seamlessly combines the expressive power of a parameterized quantum circuit with a neural network, is inherently noise resilient with a unique QEM capacity, which is absent in vanilla variational quantum eigensolvers (VQE). The study carefully analyzes and elucidates the asymptotic scaling of this unique QEM capacity in VQNHE from both theoretical and experimental perspectives. Finally, a variational basis transformation is proposed for the Hamiltonian to be measured under the VQNHE framework, yielding a powerful tri‐optimization setup, dubbed as VQNHE++. VQNHE++ can further enhance the quantum‐neural hybrid expressive power and error mitigation capacity.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational Quantum‐Neural Hybrid Error Mitigation

Zhang,

Wan,

Hsieh

et al. 2023

Adv Quantum Tech

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show abstract

“…Therefore, it is advisible and feasible to integrate the molecular orbital optimization into the optimization of NQS, enhancing its numerical flexibility and making it more efficient in finding the optimal ground-state energy in various systems. Furthermore, the exploration of other powerful neural-network architectures ,− or parameter optimization algorithms − warrants further attention, which will shed light on the applications of NQS in chemical systems.…”

Section: Discussionmentioning

confidence: 99%

A Nonstochastic Optimization Algorithm for Neural-Network Quantum States

Li,

Huang,

Zhang

et al. 2023

J. Chem. Theory Comput.

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Neural-network quantum states (NQS) employ artificial neural networks to encode many-body wave functions in a second quantization through variational Monte Carlo (VMC). They have recently been applied to accurately describe electronic wave functions of molecules and have shown the challenges in efficiency compared with traditional quantum chemistry methods. Here, we introduce a general nonstochastic optimization algorithm for NQS in chemical systems, which deterministically generates a selected set of important configurations simultaneously with energy evaluation of NQS. This method bypasses the need for Markov-chain Monte Carlo within the VMC framework, thereby accelerating the entire optimization process. Furthermore, this newly developed nonstochastic optimization algorithm for NQS offers comparable or superior accuracy compared to its stochastic counterpart and ensures more stable convergence. The application of this model to test molecules exhibiting strong electron correlations provides further insight into the performance of NQS in chemical systems and opens avenues for future enhancements.

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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 analog of direct-product states, the so-called Slater determinant (SD) states, fails to even qualitatively describe the thermodynamic limit of Fermi–Hubbard-type Hamiltonians ( 2 ) and the development of systematically improvable neural-network–based trial wave functions is currently an active field of research both in second quantization ( 5 – 7 ) and in first quantization ( 8 – 14 ). In the latter approach, the wave-function amplitudes must be antisymmetric functions of the particle configurations, while being able to capture correlations beyond the single-particle Slater determinants.…”

mentioning

confidence: 99%

Fermionic wave functions from neural-network constrained hidden states

Moreno

Carleo

Georges

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

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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 that is optimized, together with the single-particle orbitals, using a neural network parameterization. This construction draws inspiration from the success of hidden-particle representations 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 proved to be universal. We apply this construction to the ground-state properties of the Hubbard model on the square lattice, achieving levels of accuracy that are competitive with those of state-of-the-art variational methods.

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Neural Error Mitigation of Near-Term Quantum Simulations

Cited by 22 publications

References 44 publications

Variational Quantum‐Neural Hybrid Error Mitigation

Variational Quantum‐Neural Hybrid Error Mitigation

A Nonstochastic Optimization Algorithm for Neural-Network Quantum States

Fermionic wave functions from neural-network constrained hidden states

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