scholarly journals Testing a Quantum Annealer as a Quantum Thermal Sampler

2021 ◽  
Vol 2 (2) ◽  
pp. 1-20
Author(s):  
Zoe Gonzalez Izquierdo ◽  
Itay Hen ◽  
Tameem Albash
Keyword(s):  
Thermal Properties ◽  
Quantum Monte Carlo ◽  
Thermal State ◽  
Transverse Field ◽  
Quantum Annealing ◽  
Many Body ◽  
Expectation Values ◽  
Many Body Systems ◽  
Transverse Field Ising Model ◽  
Open Question

Motivated by recent experiments in which specific thermal properties of complex many-body systems were successfully reproduced on a commercially available quantum annealer, we examine the extent to which quantum annealing hardware can reliably sample from the thermal state in a specific basis associated with a target quantum Hamiltonian. We address this question by studying the diagonal thermal properties of the canonical one-dimensional transverse-field Ising model on a D-Wave 2000Q quantum annealing processor. We find that the quantum processor fails to produce the correct expectation values predicted by Quantum Monte Carlo. Comparing to master equation simulations, we find that this discrepancy is best explained by how the measurements at finite transverse fields are enacted on the device. Specifically, measurements at finite transverse field require the system to be quenched from the target Hamiltonian to a Hamiltonian with negligible transverse field, and this quench is too slow. The limitations imposed by such hardware make it an unlikely candidate for thermal sampling, and it remains an open question what thermal expectation values can be robustly estimated in general for arbitrary quantum many-body systems.

scholarly journals FIDELITY APPROACH TO QUANTUM PHASE TRANSITIONS

2010 ◽  
Vol 24 (23) ◽  
pp. 4371-4458 ◽  
Author(s):  
SHI-JIAN GU
Keyword(s):  
Phase Transitions ◽  
Thermal State ◽  
Quantum Phase Transitions ◽  
Transverse Field ◽  
Quantum Phase ◽  
Leading Term ◽  
Many Body Systems ◽  
The One ◽  
Definition Of ◽  
Transverse Field Ising Model

We review the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin–Meshkov–Glick model, are introduced at the graduate-student level. Besides, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.

scholarly journals Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

2019 ◽  
Vol 10 (1) ◽  
pp. 337-356 ◽  
Author(s):  
Zi-Xiang Li ◽  
Hong Yao
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Hot Spot ◽  
High Temperature Superconductors ◽  
System Size ◽  
Many Body ◽  
Broken Symmetries ◽  
Sign Problem ◽  
Universal Quantum ◽  
Many Body Systems

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

scholarly journals Quantum echo dynamics in the Sherrington-Kirkpatrick model

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Silvia Pappalardi ◽  
Anatoli Polkovnikov ◽  
Alessandro Silva
Keyword(s):  
Quantum Physics ◽  
Transverse Field ◽  
Many Body ◽  
Initial State ◽  
Large N ◽  
Semiclassical Dynamics ◽  
Long Time ◽  
Kirkpatrick Model ◽  
Ehrenfest Time ◽  
Many Body Systems

Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-N) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins N. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on N and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.

scholarly journals Particle entanglement in continuum many-body systems via quantum Monte Carlo

2014 ◽  
Vol 89 (14) ◽  
Author(s):  
C. M. Herdman ◽  
P.-N. Roy ◽  
R. G. Melko ◽  
A. Del Maestro
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Many Body ◽  
Many Body Systems

scholarly journals Obstructions to classically simulating the quantum adiabatic algorithm

2013 ◽  
Vol 13 (11&12) ◽  
pp. 1038-1076
Author(s):  
Matthew B. Hastings
Keyword(s):  
Ising Model ◽  
Fundamental Group ◽  
Quantum Monte Carlo ◽  
Spectral Gap ◽  
Initial Conditions ◽  
Quantum Algorithm ◽  
Transverse Field ◽  
Equilibration Time ◽  
Negligible Probability ◽  
Transverse Field Ising Model

We consider the adiabatic quantum algorithm for systems with ``no sign problem", such as the transverse field Ising model, and analyze the equilibration time for quantum Monte Carlo (QMC) on these systems. We ask: if the spectral gap is only inverse polynomially small, will equilibration methods based on slowly changing the Hamiltonian parameters in the QMC simulation succeed in a polynomial time? We show that this is {\it not} true, by constructing counter-examples. In some examples, the space of configurations where the wavefunction has non-negligible amplitude has a nontrivial fundamental group, causing the space of trajectories in imaginary time to break into disconnected components with only negligible probability outside these components. For the simplest example we give with an abelian fundamental group, QMC does not equilibrate but still solves the optimization problem. More severe effects leading to failure to solve the optimization can occur when the fundamental group is a free group on two generators. Other examples where QMC fails have a {\it trivial} fundamental group, but still use ideas from topology relating group presentations to simplicial complexes. We define gadgets to realize these Hamiltonians as the effective low-energy dynamics of a transverse field Ising model. We present some analytic results on equilibration times which may be of some independent interest in the theory of equilibration of Markov chains. Conversely, we show that a small spectral gap implies slow equilibration at low temperature for some initial conditions and for a natural choice of local QMC updates.

scholarly journals Manipulating Quantum Many-Body Systems in the Presence of Controllable Dissipation

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 8
Author(s):  
Davide Rossini
Keyword(s):  
Gauge Field ◽  
Annealing Time ◽  
Quantum Simulation ◽  
Quantum Annealing ◽  
Many Body ◽  
Persistent Currents ◽  
Dissipative Processes ◽  
Nonadiabatic Effects ◽  
Many Body Systems ◽  
Many Body Physics

We discuss two quantum simulation schemes in which the coupling to an external bath may give rise to novel and interesting many-body physics. Namely, we first address the effect of local Markovian baths on the quantum annealing dynamics of an Ising-like chain: deviations from adiabaticity may display a nonmonotonic trend as a function of the annealing time, as a result of the competition between nonadiabatic effects and dissipative processes. Secondly, we provide a framework to induce persistent currents through the coupling with a structured reservoir which generates nonreciprocity, without the need of any applied gauge field.

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