scholarly journals Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Oleg Lychkovskiy
Keyword(s):  
Transverse Field ◽  
Integrable Models ◽  
Small Subset ◽  
Many Body ◽  
Analytical Treatment ◽  
System A ◽  
Onsager Algebra ◽  
Heisenberg Equations ◽  
Transverse Field Ising Model ◽  
Large Hierarchy

Dynamics of a quantum system can be described by coupled Heisenberg equations. In a generic many-body system these equations form an exponentially large hierarchy that is intractable without approximations. In contrast, in an integrable system a small subset of operators can be closed with respect to commutation with the Hamiltonian. As a result, the Heisenberg equations for these operators can form a smaller closed system amenable to an analytical treatment. We demonstrate that this indeed happens in a class of integrable models where the Hamiltonian is an element of the Onsager algebra. We explicitly solve the system of Heisenberg equations for operators from this algebra. Two specific models are considered as examples: the transverse field Ising model and the superintegrable chiral 3-state Potts model.

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 Generation of thermofield double states and critical ground states with a quantum computer

2020 ◽  
Vol 117 (41) ◽  
pp. 25402-25406
Author(s):  
D. Zhu ◽  
S. Johri ◽  
N. M. Linke ◽  
K. A. Landsman ◽  
C. Huerta Alderete ◽  
...  
Keyword(s):  
Ion Trap ◽  
Quantum Computer ◽  
Condensed Matter ◽  
Transverse Field ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Zero Temperature ◽  
Many Body ◽  
Transverse Field Ising Model ◽  
Entanglement Structure

Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum approximate optimization algorithm (QAOA), we generate nontrivial thermal quantum states of the transverse-field Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum–classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest-depth QAOA circuits provide the best results.

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 Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 780
Author(s):  
Liang-Jun Zhai ◽  
Guang-Yao Huang ◽  
Huai-Yu Wang
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Critical Behavior ◽  
Critical Region ◽  
Numerical Study ◽  
Transverse Field ◽  
Scaling Theory ◽  
New Order ◽  
Edge Singularity ◽  
Transverse Field Ising Model

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

scholarly journals Optimizing a quantum reservoir computer for time series prediction

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Aki Kutvonen ◽  
Keisuke Fujii ◽  
Takahiro Sagawa
Keyword(s):  
Time Series ◽  
Language Processing ◽  
Quantum Dynamics ◽  
Time Series Prediction ◽  
Transverse Field ◽  
Memory Capacity ◽  
Great Promise ◽  
Real World Data ◽  
Spin Interactions ◽  
Transverse Field Ising Model

Abstract Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient solving of temporal machine learning tasks such as speech recognition, time series prediction and natural language processing. Specifically, we study memory capacity and accuracy of a quantum reservoir computer based on the fully connected transverse field Ising model by investigating different forms of inter-spin interactions and computing timescales. We show that variation in inter-spin interactions leads to a better memory capacity in general, by engineering the type of interactions the capacity can be greatly enhanced and there exists an optimal timescale at which the capacity is maximized. To connect computational capabilities to physical properties of the underlaying system, we also study the out-of-time-ordered correlator and find that its faster decay implies a more accurate memory. Furthermore, as an example application on real world data, we use QRC to predict stock values.

scholarly journals Worm-algorithm-type simulation of the quantum transverse-field Ising model

2020 ◽  
Vol 102 (9) ◽  
Author(s):  
Chun-Jiong Huang ◽  
Longxiang Liu ◽  
Yi Jiang ◽  
Youjin Deng
Keyword(s):  
Ising Model ◽  
Transverse Field ◽  
Transverse Field Ising Model
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