Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions

• URL: http://arxiv.org/abs/2411.16915v2
• Date: Mon, 19 May 2025 09:26:11 GMT
• Title: Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions
• Authors: Hamzat A. Akande, Alexandre Perrin, Bruno Senjean, Matthieu Saubanere,
• Abstract summary: We propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for extraction of low-lying energy states.<n>As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.
• Score: 39.58317527488534
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and Quantum Subspace Methods, offer practical solutions but face limitations in circuit depth and measurement overhead. In this article, we propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for the extraction of low-lying energy states. We show that, under certain conditions, our approach leads to a tridiagonal representation similar to that obtained with the Lanczos algorithm. The iterative process allows control over the trade-off between circuit depth, the number of variational parameters, and the number of measurements required to achieve the desired accuracy, making it suitable for current quantum hardware. As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.

Related papers

• Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise [49.97673761305336]
  Noise remains a major obstacle to achieving reliable quantum algorithms.<n>We present a provably noise-resilient training theory and algorithm to enhance the robustness of parameterized quantum circuit classifiers.
  arXiv  Detail & Related papers  (2025-05-24T02:51:34Z)
• Quantum Boltzmann machine learning of ground-state energies [3.187381965457262]
  Esting the ground-state energy of Hamiltonians is a fundamental task for which quantum computers can be helpful. We analyze the performance of quantum Boltzmann machines for this task. Our algorithm estimates the gradient of the energy function efficiently by means of a novel quantum circuit construction.
  arXiv  Detail & Related papers  (2024-10-16T18:22:03Z)
• QAdaPrune: Adaptive Parameter Pruning For Training Variational Quantum Circuits [2.3332157823623403]
  emphQAdaPrune is an adaptive parameter pruning algorithm that automatically determines the threshold and then intelligently prunes the redundant and non-performing parameters. We show that the resulting sparse parameter sets yield quantum circuits that perform comparably to the unpruned quantum circuits.
  arXiv  Detail & Related papers  (2024-08-23T19:57:40Z)
• Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set [3.087342164520494]
  In electronic structure calculations on classical computers, resource reduction has been achieved by using the projector augmented-wave method (PAW) and plane wave basis sets.<n>We develop a unitary variant of the PAW that preserves the orthogonality constraints.<n>We provide the quantum resources for energy estimation of a nitrogen-vacancy defect centre in diamond.
  arXiv  Detail & Related papers  (2024-08-06T12:56:10Z)
• Qubit-efficient quantum combinatorial optimization solver [0.0]
  We develop a qubit-efficient algorithm that overcomes the limitation by mapping a candidate bit solution to an entangled wave function of fewer qubits. This approach could benefit near-term intermediate-scale and future fault-tolerant small-scale quantum devices.
  arXiv  Detail & Related papers  (2024-07-22T11:02:13Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• A circuit-generated quantum subspace algorithm for the variational quantum eigensolver [0.0]
  We propose combining quantum subspace techniques with the variational quantum eigensolver (VQE) In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies.
  arXiv  Detail & Related papers  (2024-04-09T18:00:01Z)
• 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)
• Parallel circuit implementation of variational quantum algorithms [0.0]
  We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution. We apply this specifically to optimization problems, where inherent structures from the problem can be identified. We show that not only can our method address larger problems, but that it is also possible to run full VQA models while training parameters using only one slice.
  arXiv  Detail & Related papers  (2023-04-06T12:52:29Z)
• Efficient estimation of trainability for variational quantum circuits [43.028111013960206]
  We find an efficient method to compute the cost function and its variance for a wide class of variational quantum circuits. This method can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem.
  arXiv  Detail & Related papers  (2023-02-09T14:05:18Z)
• Adiabatic quantum computing with parameterized quantum circuits [0.0]
  We propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device. We compare our proposed algorithm with the Variational Quantum Eigensolver on two classical optimization problems.
  arXiv  Detail & Related papers  (2022-06-09T09:31:57Z)
• Quantum Davidson Algorithm for Excited States [42.666709382892265]
  We introduce the quantum Krylov subspace (QKS) method to address both ground and excited states. By using the residues of eigenstates to expand the Krylov subspace, we formulate a compact subspace that aligns closely with the exact solutions. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems.
  arXiv  Detail & Related papers  (2022-04-22T15:03:03Z)
• 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)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Variational Quantum Algorithms for Steady States of Open Quantum Systems [2.740982822457262]
  We propose a variational quantum algorithm to find the steady state of open quantum systems. The fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification.
  arXiv  Detail & Related papers  (2020-01-08T14:47:36Z)

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.