Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

@article{Zhang2020ShallowcircuitVQ,
  title={Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations},
  author={Feng Zhang and Niladri Gomes and Noah F. Berthusen and Peter P. Orth and Caizhuang Wang and Kai‐Ming Ho and Yongxin Yao},
  journal={Physical Review Research},
  year={2020}
}
Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all… 

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References

SHOWING 1-10 OF 41 REFERENCES

Progress towards practical quantum variational algorithms

The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

The application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz is studied and an analytical method to compute the energy gradient is proposed that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients.

Symmetry Configuration Mapping for Representing Quantum Systems on Quantum Computers.

This work proposes to construct customized mappings tailored to the considered quantum mechanical systems, and takes advantage of existing symmetry, which is build into the mappings a priori to obtain optimal compactness.

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

The experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms is demonstrated, determining the ground-state energy for molecules of increasing size, up to BeH2.

The Bravyi-Kitaev transformation for quantum computation of electronic structure.

An alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev, is developed that reduces the simulation cost to O(log n) qubit operations for one fermionic operation and demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure.

Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure

Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Efficient Ansätze on a Quantum Processor

A hardware-efficient variant of ADAPT-VQE that drastically reduces circuit depths using an operator pool that is guaranteed to contain the operators necessary to construct exact ans\"atze and shows that the minimal pool size that achieves this scales linearly with the number of qubits.

An adaptive variational algorithm for exact molecular simulations on a quantum computer

A new variational hybrid quantum-classical algorithm which allows the system being simulated to determine its own optimal state, and highlights the potential of the adaptive algorithm for exact simulations with present-day and near-term quantum hardware.

Gutzwiller hybrid quantum-classical computing approach for correlated materials

Rapid progress in noisy intermediate-scale quantum (NISQ) computing technology has led to the development of novel resource-efficient hybrid quantum-classical algorithms, such as the variational

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