Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems

• URL: http://arxiv.org/abs/2205.07097v1
• Date: Sat, 14 May 2022 17:08:18 GMT
• Title: Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• Authors: Takashi Tsuchimochi, Masaki Taii, Taisei Nishimaki, Seiichiro L. Ten-no
• Abstract summary: Current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as variational quantum eigensolver (VQE) In this study, we report the importance of the Hamiltonian symmetry in constructing VQE circuits adaptively. We demonstrate that symmetry-projection can provide a simple yet effective solution to this problem, by keeping the quantum state in the correct symmetry space, to reduce the overall gate operations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum computing is a promising approach to harnessing strong correlation in molecular systems; however, current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as the variational quantum eigensolver (VQE). In this study, we report the importance of the Hamiltonian symmetry in constructing VQE circuits adaptively. This treatment often violates symmetry, thereby deteriorating the convergence of fidelity to the exact solution, and ultimately resulting in deeper circuits. We demonstrate that symmetry-projection can provide a simple yet effective solution to this problem, by keeping the quantum state in the correct symmetry space, to reduce the overall gate operations. The scheme also reveals the significance of preserving symmetry in computing molecular properties, as demonstrated in our illustrative calculations.

Related papers

• Efficient quantum algorithms for testing symmetries of open quantum systems [17.55887357254701]
  In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
  arXiv  Detail & Related papers  (2023-09-05T18:05:26Z)
• Molecular Symmetry in VQE: A Dual Approach for Trapped-Ion Simulations of Benzene [0.2624902795082451]
  Near-term strategies hinge on the use of variational quantum eigensolver (VQE) algorithms combined with a suitable ansatz. We employ several circuit optimization methods tailored for trapped-ion quantum devices to enhance the feasibility of intricate chemical simulations. These methods, when applied to a benzene molecule simulation, enabled the construction of an 8-qubit circuit with 69 two-qubit entangling operations.
  arXiv  Detail & Related papers  (2023-08-01T17:03:10Z)
• Symmetry enhanced variational quantum imaginary time evolution [1.6872254218310017]
  We provide guidance for constructing parameterized quantum circuits according to the locality and symmetries of the Hamiltonian. Our approach can be used to implement the unitary and anti-unitary symmetries of a quantum system. Numerical results confirm that the symmetry-enhanced circuits outperform the frequently-used parametrized circuits in the literature.
  arXiv  Detail & Related papers  (2023-07-25T16:00:34Z)
• Modular Cluster Circuits for the Variational Quantum Eigensolver [0.0]
  In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit. The design was tested on the H2, (H2) and LiH molecules, as well as the finite-size transverse-field Ising model.
  arXiv  Detail & Related papers  (2023-05-08T02:33:33Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Analytical and experimental study of center line miscalibrations in M\o lmer-S\o rensen gates [51.93099889384597]
  We study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate. We compute the gate evolution operator which allows us to obtain relevant key properties. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor.
  arXiv  Detail & Related papers  (2021-12-10T10:56:16Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)
• Symmetry-adapted variational quantum eigensolver [0.7734726150561086]
  We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm. The symmetry-adapted VQE scheme simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry.
  arXiv  Detail & Related papers  (2019-12-31T02:13:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.