Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy

• URL: http://arxiv.org/abs/2212.09995v2
• Date: Tue, 27 Aug 2024 04:28:21 GMT
• Title: Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy
• Authors: Hiroshi Hayasaka, Takashi Imoto, Yuichiro Matsuzaki, Shiro Kawabata,
• Abstract summary: Adiabatic condition consists of two parts: an energy gap and a transition matrix. The success probability of QA is considered to decrease exponentially owing to the exponentially decreasing energy gap. We numerically show the scaling of the computational cost is quadratically improved compared to the conventional QA.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition matrix. Most past studies have focused on the relationship between the energy gap and computational time. The success probability of QA is considered to decrease exponentially owing to the exponentially decreasing energy gap at the first-order phase-transition point. In this study, through a detailed analysis of the relationship between the energy gap, transition matrix, and computational cost during QA, we propose a general method for constructing counterintuitive models wherein QA with a constant annealing time fails despite a constant energy gap, based on polynomial energy. We assume that the energy of the total Hamiltonian is at most $\Theta(L)$, where $L$ is the number of qubits. In our formalism, we choose a known model that exhibits an exponentially small energy gap during QA, and modify the model by adding a specific penalty term to the Hamiltonian. In the modified model, the transition matrix in the adiabatic condition becomes exponentially large as the number of qubits increases, while the energy gap remains constant. Moreover, we achieve a quadratic speedup, for which the upper bound for improvement in the adiabatic condition is determined by the polynomial energy. As examples, we consider the adiabatic Grover search and the $p$-spin model. In these cases, with the addition of the penalty term, although the success probability of QA on the modified models becomes exponentially small despite a constant energy gap; we can achieve a success probability considerably higher than that of conventional QA. Moreover, we numerically show the scaling of the computational cost is quadratically improved compared to the conventional QA.

Related papers

• Quantum battery supercharging via counter-diabatic dynamics [0.0]
  We introduce a counter-diabatic approach for deriving Hamiltonians for superchargable quantum batteries. We show that QB supercharging can be achieved by $O(n)$ terms of multipartite connections.
  arXiv  Detail & Related papers  (2024-06-21T16:09:26Z)
• Benchmarking a heuristic Floquet adiabatic algorithm for the Max-Cut problem [0.0]
  We show that adiabatic evolution can be performed with a fixed, finite Trotter step. We give numerical evidence using matrix-product-state simulations that it can optimally solve the Max-Cut problem. Extrapolating our numerical results, we estimate the resources needed for a quantum computer to compete with classical exact or approximate solvers.
  arXiv  Detail & Related papers  (2024-04-24T17:29:03Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Simulating scalar field theories on quantum computers with limited resources [62.997667081978825]
  We present a quantum algorithm for implementing $phi4$ lattice scalar field theory on qubit computers. The algorithm allows efficient $phi4$ state preparation for a large range of input parameters in both the normal and broken symmetry phases.
  arXiv  Detail & Related papers  (2022-10-14T17:28:15Z)
• Power of Sine Hamiltonian Operator for Estimating the Eigenstate Energies on Quantum Computers [4.814804579035369]
  We propose a new classical quantum hybrid method, named as power of sine Hamiltonian operator (PSHO) In PSHO, for any reference state, the normalized energy of the sine Hamiltonian power state can be determined. The performance of the PSHO method is demonstrated by numerical calculations of the H4 and LiH molecules.
  arXiv  Detail & Related papers  (2022-09-29T14:07:12Z)
• Quantum annealing with symmetric subspaces [0.0]
  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.
  arXiv  Detail & Related papers  (2022-09-20T09:44:23Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• 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)
• 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.