Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians

• URL: http://arxiv.org/abs/2407.10523v2
• Date: Tue, 1 Oct 2024 13:43:30 GMT
• Title: Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Authors: Hao-En Li, Xiang Li, Jia-Cheng Huang, Guang-Ze Zhang, Zhu-Ping Shen, Chen Zhao, Jun Li, Han-Shi Hu,
• Abstract summary: The matrix product state (MPS) ansatz offers a promising approach for finding the ground state of molecular Hamiltonians. We enhance the optimization performance of the QCMPS ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach.
• Score: 11.985673663540688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The matrix product state (MPS) ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS) enables the simulation of chemical systems using a relatively small number of qubits. In this study, we enhance the optimization performance of the QCMPS ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach. Guided by McLachlan's variational principle, the VarQITE method provides analytical metrics and gradients, resulting in improved convergence efficiency and robustness of the QCMPS. We validate these improvements numerically through simulations of $\rm H_2$, $\rm H_4$, and $\rm LiH$ molecules. Additionally, given that VarQITE is applicable to non-Hermitian Hamiltonians, we evaluate its effectiveness in preparing the ground state of transcorrelated (TC) Hamiltonians. This approach yields energy estimates comparable to the complete basis set (CBS) limit while using even fewer qubits. Specifically, we perform simulations of the beryllium atom and $\rm LiH$ molecule using only three qubits, maintaining high fidelity with the CBS ground state energy of these systems. This qubit reduction is achieved through the combined advantages of both the QCMPS ansatz and transcorrelation. Our findings demonstrate the potential practicality of this quantum chemistry algorithm on near-term quantum devices.

Related papers

• Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers [37.69303106863453]
  We propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers. Our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28% and 57% on average.
  arXiv  Detail & Related papers  (2024-06-17T14:10:10Z)
• Simulating electronic structure on bosonic quantum computers [35.884125235274865]
  One of the most promising applications of quantum computing is the simulation of many-fermion problems. We show how an electronic structure Hamiltonian can be transformed into a system of qumodes through qubit-assisted fermion-to-qumode mapping.
  arXiv  Detail & Related papers  (2024-04-16T02:04:11Z)
• Quantum Information Driven Ansatz (QIDA): shallow-depth empirical quantum circuits from Quantum Chemistry [0.0]
  We propose a new approach for constructing variational quantum circuits, leveraging quantum mutual information associated with classical Quantum Chemistry states. The proposed methodology gives rise to highly effective ans"atze, surpassing the standard empirical ladder-entangler ansatz in performance.
  arXiv  Detail & Related papers  (2023-09-26T21:50:02Z)
• 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)
• 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)
• Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers [10.26362298019201]
  We numerically test the method for the hydrogenation reaction of C6H8 and the equilibrium geometry of the C18 molecule, with basis sets up to cc-pVDZ. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices.
  arXiv  Detail & Related papers  (2021-09-16T15:44:38Z)
• Towards a NISQ Algorithm to Simulate Hermitian Matrix Exponentiation [0.0]
  A practical fault-tolerant quantum computer is worth looking forward to as it provides applications that outperform their known classical counterparts. It would take decades to make it happen, exploiting the power of noisy intermediate-scale quantum(NISQ) devices, which already exist, is becoming one of current goals. In this article, a method is reported as simulating a hermitian matrix exponentiation using parametrized quantum circuit.
  arXiv  Detail & Related papers  (2021-05-28T06:37:12Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• 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)

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.