Variational Quantum-Neural Hybrid Eigensolver

Zhang, Shixin; Wan, Zhou‐Quan; Lee, Chee‐Kong; Hsieh, Chang‐Yu; Zhang, Shengyu; Yao, Hong

doi:10.1103/physrevlett.128.120502

Cited by 31 publications

(9 citation statements)

References 61 publications

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“…Here, we describe our approach to construct the re-entangling circuit M (τ) as in eq , carried out as a virtual Heisenberg circuit in the spirit of refs , , . We first start by taking a closer look at folding typical circuit building blocks, not necessarily Clifford, in a generator formalism before introducing a procedure to build M (τ).…”

Section: Methodsmentioning

confidence: 99%

Partitioning Quantum Chemistry Simulations with Clifford Circuits

Schleich

Boen

Cincio

et al. 2023

J. Chem. Theory Comput.

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Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near term. In this work, we investigate the limits of their classical and near-classical treatment while staying within the framework of quantum circuits and the variational quantum eigensolver. To this end, we consider naive and physically motivated, classically efficient product ansatz for the parametrized wavefunction adapting the separable-pair ansatz form. We combine it with post-treatment to account for interactions between subsystems originating from this ansatz. The classical treatment is given by another quantum circuit that has support between the enforced subsystems and is folded into the Hamiltonian. To avoid an exponential increase in the number of Hamiltonian terms, the entangling operations are constructed from purely Clifford or near-Clifford circuits. While Clifford circuits can be simulated efficiently classically, they are not universal. In order to account for missing expressibility, near-Clifford circuits with only few, selected non-Clifford gates are employed. The exact circuit structure to achieve this objective is molecule-dependent and is constructed using simulated annealing and genetic algorithms. We demonstrate our approach on a set of molecules of interest and investigate the extent of our methodology’s reach.

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Section: Methodsmentioning

confidence: 99%

Partitioning Quantum Chemistry Simulations with Clifford Circuits

Schleich

Boen

Cincio

et al. 2023

J. Chem. Theory Comput.

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“…As an approach combining the advantages from both VQE and neural variational Monte Carlo (VMC), [42][43][44][45][46][47][48] this new setup offers a stateof-the-art approximation on the ground state energy for various quantum spin systems and quantum molecules with a provable bound on the efficiency for the computational complexity. [38]…”

Section: Vqnhe Setupmentioning

confidence: 99%

“…Variational quantum-neural hybrid eigensolver (VQNHE) is a powerful VQA approach incorporating the strength of a neural network as a nonunitary postprocessing module efficiently. [38] Recently, the idea of adding a non-unitary processing module to the variational quantum eigensolver [7][8][9][10][11][12] has become popular. However, unlike all previous proposals, VQNHE not only enhances the expressive power of the VQAs but also entails just a polynomial scaling of computational resource overhead.…”

Section: Introductionmentioning

confidence: 99%

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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“…The tensor network engine underlying the simulation of quantum circuits is built on top of various machine learning frameworks with an abstraction layer in between that unifies different backends. At the application layer, TensorCircuit also includes various advanced quantum algorithms based on our latest research [45][46][47][48][49]. The overall software architecture is shown in Figure 3.…”

Section: B Tensor Network Enginementioning

confidence: 99%

TensorCircuit: a Quantum Software Framework for the NISQ Era

Zhang¹,

Allcock²,

Wan³

et al. 2022

Preprint

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TensorCircuit is an open source quantum circuit simulator based on tensor network contraction, designed for speed, flexibility and code efficiency. Written purely in Python, and built on top of industry-standard machine learning frameworks, TensorCircuit supports automatic differentiation, just-in-time compilation, vectorized parallelism and hardware acceleration. These features allow TensorCircuit to simulate larger and more complex quantum circuits than existing simulators, and are especially suited to variational algorithms based on parameterized quantum circuits. TensorCircuit enables orders of magnitude speedup for various quantum simulation tasks compared to other common quantum software, and can simulate up to 600 qubits with moderate circuit depth and low-dimensional connectivity. With its time and space efficiency, flexible and extensible architecture and compact, user-friendly API, TensorCircuit has been built to facilitate the design, simulation and analysis of quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era.

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Variational Quantum-Neural Hybrid Eigensolver

Cited by 31 publications

References 61 publications

Partitioning Quantum Chemistry Simulations with Clifford Circuits

Partitioning Quantum Chemistry Simulations with Clifford Circuits

Variational Quantum‐Neural Hybrid Error Mitigation

TensorCircuit: a Quantum Software Framework for the NISQ Era

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