Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model

• URL: http://arxiv.org/abs/2209.01737v2
• Date: Mon, 8 May 2023 01:39:46 GMT
• Title: Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Authors: Yuki Susa, Takashi Imoto, Yuichiro Matsuzaki
• Abstract summary: We propose a nonstoquastic catalyst to improve the efficiency of a ground-state search. A semiclassical analysis shows that the problematic first-order phase transition can be eliminated. We find that while the energy gap decreases with increasing system size for the original Hamiltonian, it decreases exponentially against the system size for the Hamiltonian with the nonstoquastic catalyst.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Introducing a nonstoquastic catalyst is a promising avenue to improve quantum annealing with the transverse field. In the present paper, we propose a nonstoquastic catalyst for bifurcation-based quantum annealing described by the spin-1 operators to improve the efficiency of a ground-state search. To investigate the effect of the nonstoquastic catalyst, we study the ferromagnetic $p$-spin model, which has difficulty with finding the ground state due to the first-order phase transition for quantum annealing. A semiclassical analysis shows that the problematic first-order phase transition can be eliminated by introducing the proposed nonstoquastic catalyst with the appropriate amplitude. We also numerically calculate the minimum energy gap for a finite-size system by diagonalizing the Hamiltonian. We find that while the energy gap decreases exponentially with increasing system size for the original Hamiltonian, it decreases polynomially against the system size for the Hamiltonian with the nonstoquastic catalyst. This result implies that the proposed nonstoquastic catalyst has the potential to improve the performance of bifurcation-based quantum annealing.

Related papers

• Enhancing the Energy Gap of Random Graph Problems via XX-catalysts in Quantum Annealing [0.0]
  We show that employing multiple XX-catalysts on the edges of a graph significantly enhances the minimum energy gap. Remarkably, our analysis shows that the more severe the first-order phase transition, the more effective the catalyst is in opening the gap.
  arXiv  Detail & Related papers  (2024-09-24T18:00:01Z)
• Exponential speed-up of quantum annealing via n-local catalysts [0.0]
  We show that $n-$local catalysts can re-open the gap or prevent it from closing during the anneal process. Our analysis suggests that non-local quantum fluctuations entangling multiple qubits are key to achieving the desired quantum advantage.
  arXiv  Detail & Related papers  (2024-09-19T18:01:53Z)
• Quantum metrology enhanced by the $XY$ spin interaction in a generalized Tavis-Cummings model [0.0]
  We explore the impact of the many-body effect on estimation precision, quantified by the quantum Fisher information (QFI) We emphasize the indispensable role of the spin anisotropy in achieving the Heisenberg-scaling precision.
  arXiv  Detail & Related papers  (2023-07-30T08:20:26Z)
• Qubit dephasing by spectrally diffusing quantum two-level systems [44.99833362998488]
  We investigate the pure dephasing of a Josephson qubit due to the spectral diffusion of two-level systems that are close to resonance with the qubit. We show that this pure dephasing mechanism can be mitigated, allowing enhancement of superconducting qubits coherence time.
  arXiv  Detail & Related papers  (2023-06-27T07:48:42Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• 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)
• Enhanced nonlinear quantum metrology with weakly coupled solitons and particle losses [58.720142291102135]
  We offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg scaling levels. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe. We illustrate that such states are close to the optimal ones even with moderate losses.
  arXiv  Detail & Related papers  (2021-08-07T09:29:23Z)
• Detectable Signature of Quantum Friction on a Sliding Particle in Vacuum [58.720142291102135]
  We show traces of quantum friction in the degradation of the quantum coherence of a particle. We propose to use the accumulated geometric phase acquired by a particle as a quantum friction sensor. The experimentally viable scheme presented can spark renewed optimism for the detection of non-contact friction.
  arXiv  Detail & Related papers  (2021-03-22T16:25:27Z)
• Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts [0.0]
  We study how a first-order phase transition with a topological origin is affected by interactions of the $pm XX$-type. This is the first study of the effects of nonstoquasticity on a first-order phase transition between topologically distinct phases.
  arXiv  Detail & Related papers  (2020-12-13T20:36:34Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Reduction of the energy-gap scaling by coherent catalysis in models of quantum annealing [0.0]
  We show that some Hamiltonians still exhibit unavoidable first-order transitions even with non-stoquastic drivers. This opens up the possibility of using coherent to search for exponential speedups in systems previously thought to be exponentially slow.
  arXiv  Detail & Related papers  (2019-12-27T00:34:09Z)

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.