Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

• URL: http://arxiv.org/abs/2110.12354v2
• Date: Fri, 29 Apr 2022 15:23:19 GMT
• Title: Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian
• Authors: Bin Yan and Nikolai A. Sinitsyn
• Abstract summary: 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.
• Score: 3.800391908440439
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, $H_I$. Here, we point to the existence of an analytical solution for such a problem for an arbitrary $H_I$ beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time $T$ of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of $H_I$, the solution also shows a considerable quantum speedup in computations.

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)
• 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)
• Quantum computational advantage with constant-temperature Gibbs sampling [1.1930434318557157]
  A quantum system coupled to a bath at some fixed, finite temperature converges to its Gibbs state. This thermalization process defines a natural, physically-motivated model of quantum computation. We consider sampling from the measurement outcome distribution of quantum Gibbs states at constant temperatures.
  arXiv  Detail & Related papers  (2024-04-23T00:29:21Z)
• Variational Coherent Quantum Annealing [0.0]
  We present a hybrid classical-quantum computing paradigm where the quantum part strictly runs within the coherence time of a quantum annealer. We introduce auxiliary Hamiltonians that vanish at the beginning and end of the evolution to increase the energy gap during the process. We achieve a substantial reduction in the ground-state error with just six variational parameters and a duration within the device coherence times.
  arXiv  Detail & Related papers  (2023-10-03T17:53:03Z)
• Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers [49.1574468325115]
  We introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.
  arXiv  Detail & Related papers  (2023-05-30T18:00:05Z)
• 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)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy [0.0]
  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.
  arXiv  Detail & Related papers  (2022-12-20T04:43:40Z)
• 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)
• Bridging the Gap Between the Transient and the Steady State of a Nonequilibrium Quantum System [58.720142291102135]
  Many-body quantum systems in nonequilibrium remain one of the frontiers of many-body physics. Recent work on strongly correlated electrons in DC electric fields illustrated that the system may evolve through successive quasi-thermal states. We demonstrate an extrapolation scheme that uses the short-time transient calculation to obtain the retarded quantities.
  arXiv  Detail & Related papers  (2021-01-04T06:23:01Z)
• Excited state search using quantum annealing [0.0]
  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.
  arXiv  Detail & Related papers  (2020-02-28T09:44:18Z)

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.