Quantum annealing with symmetric subspaces

• URL: http://arxiv.org/abs/2209.09575v1
• Date: Tue, 20 Sep 2022 09:44:23 GMT
• Title: Quantum annealing with symmetric subspaces
• Authors: Takashi Imoto, Yuya Seki, Yuichiro Matsuzaki
• Abstract summary: We propose a drive Hamiltonian that preserves the symmetry of the problem Hamiltonian for more efficient Quantum annealing (QA) As non-adiabatic transitions occur only inside the specific subspace, our approach can potentially suppress unwanted non-adiabatic transitions. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a key challenge in QA. The choice of the drive Hamiltonian is known to affect the performance of QA because of the possible suppression of non-adiabatic transitions. Here, we propose the use of a drive Hamiltonian that preserves the symmetry of the problem Hamiltonian for more efficient QA. Owing to our choice of the drive Hamiltonian, the solution is searched in an appropriate symmetric subspace during QA. As non-adiabatic transitions occur only inside the specific subspace, our approach can potentially suppress unwanted non-adiabatic transitions. To evaluate the performance of our scheme, we employ the XY model as the drive Hamiltonian in order to find the ground state of problem Hamiltonians that commute with the total magnetization along the $z$ axis. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.

Related papers

• Hamiltonian-reconstruction distance as a success metric for the Variational Quantum Eigensolver [1.0916270449935084]
  Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can run on near-term quantum hardware. A challenge in VQE is to know how close the algorithm's output solution is to the true ground state, when the true ground state and ground-state energy are unknown. Recent developments in Hamiltonian reconstruction give a metric can be used to assess the quality of a variational solution to a Hamiltonian-eigensolving problem.
  arXiv  Detail & Related papers  (2024-03-18T17:28:06Z)
• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• Catastrophic failure of quantum annealing owing to non-stoquastic Hamiltonian and its avoidance by decoherence [0.0]
  We present examples showing that non-stoquastic Hamiltonians can lead to catastrophic failure of Quantum annealing (QA) In our example, owing to a symmetry, the Hamiltonian is block-diagonalized, and a crossing occurs during the QA, which leads to a complete failure of the ground-state search. Our results provide a deep insight into the fundamental mechanism of QA.
  arXiv  Detail & Related papers  (2022-09-22T13:10:58Z)
• 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)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers [0.0]
  Variational quantum eigensolver (VQE) solves the ground state problem of a given Hamiltonian by finding the parameters of a quantum circuit ansatz. We show that the proposed ansatz finds the ground state in depth significantly shorter than the bare HVA when the target Hamiltonian has symmetry-broken ground states.
  arXiv  Detail & Related papers  (2021-06-04T14:25:48Z)
• Stoquasticity in circuit QED [78.980148137396]
  We show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. We corroborate the recent finding that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits.
  arXiv  Detail & Related papers  (2020-11-02T16:41:28Z)
• 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.