Non-Hermitian quantum annealing in the ferromagnetic Ising model

Nesterov, Alexander I.; Zepeda, Juan Carlos Beas; Berman, Gennady P.

doi:10.1103/PhysRevA.87.042332

Title: Non-Hermitian quantum annealing in the ferromagnetic Ising model

Full Record
Other Related Research

Authors:: Nesterov, Alexander I.; Zepeda, Juan Carlos Beas; Berman, Gennady P.

Publication Date:: Thu Apr 25 00:00:00 EDT 2013

Sponsoring Org.:: USDOE

OSTI Identifier:: 1102149

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Physical Review A

Additional Journal Information:: Journal Volume: 87; Journal Issue: 4; Journal ID: ISSN 1050-2947

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Citation Formats


                    Nesterov, Alexander I., Zepeda, Juan Carlos Beas, and Berman, Gennady P. Non-Hermitian quantum annealing in the ferromagnetic Ising model.  United States: N. p., 2013. 
Web.  doi:10.1103/PhysRevA.87.042332.

Copy to clipboard


                    Nesterov, Alexander I., Zepeda, Juan Carlos Beas, & Berman, Gennady P. Non-Hermitian quantum annealing in the ferromagnetic Ising model.  United States.  https://doi.org/10.1103/PhysRevA.87.042332

Copy to clipboard


                    Nesterov, Alexander I., Zepeda, Juan Carlos Beas, and Berman, Gennady P. Thu .  
"Non-Hermitian quantum annealing in the ferromagnetic Ising model".  United States.  https://doi.org/10.1103/PhysRevA.87.042332.

Copy to clipboard


                    
@article{osti_1102149,

  title        = {Non-Hermitian quantum annealing in the ferromagnetic Ising model},

  author       = {Nesterov, Alexander I. and Zepeda, Juan Carlos Beas and Berman, Gennady P.},

  abstractNote = {},

  doi          = {10.1103/PhysRevA.87.042332},

  journal      = {Physical Review A},

  number       = 4,

  volume       = 87,

  place        = {United States},

  year         = {Thu Apr 25 00:00:00 EDT 2013},

  month        = {Thu Apr 25 00:00:00 EDT 2013}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Publisher's Version of Record
https://doi.org/10.1103/PhysRevA.87.042332

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 9 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

Simulating the Shastry-Sutherland Ising Model Using Quantum Annealing

Journal Article Kairys, Paul ; King, Andrew D. ; Ozfidan, Isil ; ... - PRX Quantum

A core concept in condensed matter physics is geometric frustration that leads to emergent spin phases in magnetic materials. These distinct phases, which depart from the conventional ferromagnet or the antiferromagnet, require unique computational techniques to decipher. In this study, we use the canonical Ising Shastry-Sutherland lattice to demonstrate new techniques for solving frustrated Hamiltonians using a quantum annealer of programmable superconducting qubits. This Hamiltonian can be tuned to produce a variety of intriguing ground states ranging from short- and long-range orders and fractional order parameters. We show that a large-scale finite-field quantum annealing experiment is possible on 468 logicalmore »« less
https://doi.org/10.1103/prxquantum.1.020320
Short-Depth QAOA circuits and Quantum Annealing on Higher-Order Ising Models (Rev.2)

Technical Report Pelofske, Elijah ; Baertschi, Andreas ; Eidenbenz, Stephan

The Quantum Alternating Operator Ansatz (QAOA) and Quantum Annealing (QA) are quantum algorithms that are both based on the adiabatic theorem and both have the goal of sampling the optimal solution(s) of combinatorial optimization problems. Quantum annealing has been physically instantiated on D-Wave devices using superconducting flux qubits, and QAOA can be programmed on digital gate-model quantum computers such as the programmable superconducting transmon qubits devices of the IBMQ series, for instance ibm washington. QAOA and QA address the same types of problems, but it is unclear how they will scale to large problem sizes and to larger and higher-fidelitymore »« less
https://doi.org/10.2172/1985256

Full Text Available
Short-depth QAOA circuits and quantum annealing on higher-order ising models

Journal Article Pelofske, Elijah ; Bärtschi, Andreas ; Eidenbenz, Stephan - npj Quantum Information

Abstract We present a direct comparison between QAOA (Quantum Alternating Operator Ansatz), and QA (Quantum Annealing) on 127 qubit problem instances. QAOA with p = 1, 2 rounds is executed on the 127 qubit heavy-hex graph gate-model quantum computer ibm_washington, using on-device grid-searches for angle finding, and QA is executed on two Pegasus-chip D-Wave quantum annealers. The problems are random Ising models whose connectivity matches heavy-hex graphs and the Pegasus graph connectivity, and optionally include hardware-compatible cubic terms ( Z Z Z terms). The QAOA circuits are heavily optimized and of extremely short depth, with a CNOT depth of 6 per round,more »« less
https://doi.org/10.1038/s41534-024-00825-w
Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

Journal Article García-García, Antonio M. ; Sá, Lucas ; Verbaarschot, Jacobus J. M. - Physical Review. X

Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. Based on recent progress in the application of spectral analysis to non-Hermitian quantum systems, we show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitian q -body Sachdev-Ye-Kitev (nHSYK) model with N Majorana fermions, and its chiral and complex-fermion extensions, are also well described by random matrix theory for q > 2, while for q = 2, they are given by the equivalent of Poisson statistics.more »« less
https://doi.org/10.1103/PhysRevX.12.021040
Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model

Journal Article García-García, Antonio M. ; Sá, Lucas ; Verbaarschot, Jacobus J. M. - Physical Review. D.

Spectral rigidity in Hermitian quantum chaotic systems signals the presence of dynamical universal features at timescales that can be much shorter than the Heisenberg time. We study the analog of this timescale in many-body non-Hermitian quantum chaos by a detailed analysis of long-range spectral correlators. For that purpose, we investigate the number variance and the spectral form factor of a non-Hermitian q-body Sachdev-Ye-Kitaev (nHSYK) model, which describes N fermions in zero spatial dimensions. After an analytical and numerical analysis of these spectral observables for non-Hermitian random matrices, and a careful unfolding, we find good agreement with the nHSYK model for q > 2 starting at a timescale that decreases sharply with q. The source of deviation from universality, identified analytically, is ensemble fluctuations not related to the quantum dynamics. For fixed q and large enough N, these fluctuations become dominant up until after the Heisenberg time, so that the spectral form factor is no longer useful for the study of quantum chaos. In all cases, our results point to a weakened or vanishing spectral rigidity that effectively delays the observation of full quantum ergodicity. We also show that the number variance displays nonstationary spectral correlations for both the nHSYK model and random matrices. This nonstationarity, also not related to the quantum dynamics, points to intrinsic limitations of these observables to describe the quantum chaotic motion. On the other hand, we introduce the local spectral form factor, which is shown to be stationary and not affected by collective fluctuations, and propose it as an effective diagnostic of non-Hermitian quantum chaos. For q = 2, we find saturation to Poisson statistics at a timescale of log D, compared to a scale ofmore »« less
https://doi.org/10.1103/PhysRevD.107.066007

Similar Records