Excited state search using quantum annealing

• URL: http://arxiv.org/abs/2002.12621v2
• Date: Mon, 30 Mar 2020 10:03:27 GMT
• Title: Excited state search using quantum annealing
• Authors: Yuya Seki, Yuichiro Matsuzaki, Shiro Kawabata
• Abstract summary: We propose the QA scheme to search arbitrary excited states of the problem Hamiltonian. In our scheme, an $n$-th excited state of the trivial Hamiltonian is initially prepared and is adiabatically changed into an $n$-th excited state of the target Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum annealing (QA) is one of the ways to search the ground state of the problem Hamiltonian. Here, we propose the QA scheme to search arbitrary excited states of the problem Hamiltonian. In our scheme, an $n$-th excited state of the trivial Hamiltonian is initially prepared and is adiabatically changed into an $n$-th excited state of the target Hamiltonian. Although our scheme is general such that we can search any excited states, we especially discuss the first excited state search in this paper. As a comparison, we consider a non-adiabatic scheme to find the first excited state with non-adiabatic transitions from the ground state. By solving the Lindblad master equation, we evaluate the performance of each scheme under the influence of decoherence. Our conclusion is that the adiabatic scheme show better performance than the non-adiabatic scheme as long as the coherence time of qubits is sufficiently long. These results are important for applications in the area of quantum chemistry, quantum simulation, and post-quantum cryptography.

Related papers

• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• 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)
• An efficient and exact noncommutative quantum Gibbs sampler [0.0]
  We construct the first efficiently implementable and exactly detailed-balanced Lindbladian for Gibbs states of arbitrary noncommutative Hamiltonians. Our construction can also be regarded as a continuous-time quantum analog of the Metropolis-Hastings algorithm.
  arXiv  Detail & Related papers  (2023-11-15T18:51:24Z)
• Local Hamiltonian Problem with succinct ground state is MA-Complete [0.788657961743755]
  Finding the ground energy of a quantum system is a fundamental problem in condensed matter physics and quantum chemistry. Existing classical algorithms for tackling this problem often assume that the ground state has a succinct classical description. We study the complexity of the local Hamiltonian problem with succinct ground state and prove it is MA-Complete.
  arXiv  Detail & Related papers  (2023-09-18T21:08:51Z)
• Demonstration of the excited-state search on the D-wave quantum annealer [0.0]
  We demonstrate the excited-state search by using the D-wave processor. We adopt a two-qubit Ising model as the problem Hamiltonian and succeed to prepare the excited state. Our results pave the way for new applications of quantum annealers to use the excited states.
  arXiv  Detail & Related papers  (2023-05-25T12:12:11Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• 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)
• Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian [3.800391908440439]
  We show an analytical solution for a problem for an arbitrary $H_I$ beyond the adiabatic limit for Quantum Annealing (QA) computing. This solution provides insights into the accuracy of nonadiabatic computations.
  arXiv  Detail & Related papers  (2021-10-24T05:36:27Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• 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)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.