Pre-optimizing variational quantum eigensolvers with tensor networks

• URL: http://arxiv.org/abs/2310.12965v1
• Date: Thu, 19 Oct 2023 17:57:58 GMT
• Title: Pre-optimizing variational quantum eigensolvers with tensor networks
• Authors: Abid Khan, Bryan K. Clark, Norm M. Tubman
• Abstract summary: We present and benchmark an approach where we find good starting parameters for parameterized quantum circuits by simulating VQE. We apply this approach to the 1D and 2D Fermi-Hubbard model with system sizes that use up to 32 qubits. In 2D, the parameters that VTNE finds have significantly lower energy than their starting configurations, and we show that starting VQE from these parameters requires non-trivially fewer operations to come down to a given energy.
• Score: 1.4512477254432858
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The variational quantum eigensolver (VQE) is a promising algorithm for demonstrating quantum advantage in the noisy intermediate-scale quantum (NISQ) era. However, optimizing VQE from random initial starting parameters is challenging due to a variety of issues including barren plateaus, optimization in the presence of noise, and slow convergence. While simulating quantum circuits classically is generically difficult, classical computing methods have been developed extensively, and powerful tools now exist to approximately simulate quantum circuits. This opens up various strategies that limit the amount of optimization that needs to be performed on quantum hardware. Here we present and benchmark an approach where we find good starting parameters for parameterized quantum circuits by classically simulating VQE by approximating the parameterized quantum circuit (PQC) as a matrix product state (MPS) with a limited bond dimension. Calling this approach the variational tensor network eigensolver (VTNE), we apply it to the 1D and 2D Fermi-Hubbard model with system sizes that use up to 32 qubits. We find that in 1D, VTNE can find parameters for PQC whose energy error is within 0.5% relative to the ground state. In 2D, the parameters that VTNE finds have significantly lower energy than their starting configurations, and we show that starting VQE from these parameters requires non-trivially fewer operations to come down to a given energy. The higher the bond dimension we use in VTNE, the less work needs to be done in VQE. By generating classically optimized parameters as the initialization for the quantum circuit one can alleviate many of the challenges that plague VQE on quantum computers.

Related papers

• Large-scale quantum annealing simulation with tensor networks and belief propagation [0.0]
  We show that quantum annealing for 3-regular graphs can be classically simulated even at scales of 1000 qubits and 5000000qubit gates. For non-degenerate instances, the unique solution can be read out from the final reduced single-qubit states. For degenerate problems, such as MaxCut, we introduce an approximate measurement simulation algorithm for graph tensor-network states.
  arXiv  Detail & Related papers  (2024-09-18T18:00:08Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Quantum Circuit Optimization through Iteratively Pre-Conditioned Gradient Descent [0.4915744683251151]
  iteratively preconditioned gradient descent (IPG) for optimizing quantum circuits and demonstrate performance speedups for state preparation and implementation of quantum algorithmics. We show an improvement in fidelity by a factor of $104$ for preparing a 4-qubit W state and a maximally entangled 5-qubit GHZ state compared to other commonly used classicals tuning the same ansatz. We also show gains for optimizing a unitary for a quantum Fourier transform using IPG, and report results of running such optimized circuits on IonQ's quantum processing unit (QPU)
  arXiv  Detail & Related papers  (2023-09-18T17:30:03Z)
• 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)
• Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis [42.275148861039895]
  Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy processors. gate noise due to imperfections and decoherence affects the gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits. QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently small.
  arXiv  Detail & Related papers  (2022-09-23T10:48:04Z)
• Improving the Accuracy of Variational Quantum Eigensolvers With Fewer Qubits Using Orbital Optimization [5.266892492931388]
  Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited to small molecules using minimal basis sets. We propose incorporating an orbital optimization scheme into quantum eigensolvers wherein a parameterized partial unitary transformation is applied to the basis functions set.
  arXiv  Detail & Related papers  (2022-08-30T17:50:23Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Optimal training of variational quantum algorithms without barren plateaus [0.0]
  Variational quantum algorithms (VQAs) promise efficient use of near-term quantum computers. We show how to optimally train a VQA for learning quantum states. We propose the application of Gaussian kernels for quantum machine learning.
  arXiv  Detail & Related papers  (2021-04-29T17:54:59Z)
• FLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuits [105.54048699217668]
  We propose a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.
  arXiv  Detail & Related papers  (2021-03-15T17:38:33Z)
• Improving the variational quantum eigensolver using variational adiabatic quantum computing [0.0]
  variational quantumsampling (VAQC) is a hybrid quantum-classical algorithm for finding a Hamiltonian minimum eigenvalue of a quantum circuit. We show that VAQC can provide more accurate solutions than "plain" VQE, for the evaluation.
  arXiv  Detail & Related papers  (2021-02-04T20:25:50Z)
• 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.