Measuring complex-partition-function zeros of Ising models in quantum simulators

@article{Krishnan2019MeasuringCZ,
  title={Measuring complex-partition-function zeros of Ising models in quantum simulators},
  author={Abijith Krishnan and Markus Schmitt and Roderich Moessner and Markus Heyl},
  journal={Physical Review A},
  year={2019}
}
Studying the zeros of partition functions in the space of complex control parameters allows one to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit despite various no-go theorems for finite systems. In this work we propose protocols that can be realized in quantum simulators to measure the location of complex-partition-function zeros of classical Ising models. The protocols are solely based on the implementation of simple two-qubit gates… 

Figures from this paper

Many-body thermodynamics on quantum computers via partition function zeros

TLDR
This work shows how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observes their transition from XY-like behavior to Ising-likebehavior as a function of the anisotropy.

Lee-Yang theory of the two-dimensional quantum Ising model

Determining the phase diagram of interacting quantum many-body systems is an important task for a wide range of problems such as the understanding and design of quantum materials. For classical

Measuring entanglement of a rank-2 mixed state prepared on a quantum computer

We study the entanglement between a certain qubit and the remaining system in rank- 2 mixed states prepared on the quantum computer. The protocol, which we propose for this purpose, is based on the

Lee-Yang theory of the Curie-Weiss model and its rare fluctuations

Phase transitions are typically accompanied by non-analytic behaviors of the free energy, which can be explained by considering the zeros of the partition function in the complex plane of the control

Determination of universal critical exponents using Lee-Yang theory

Lee-Yang zeros are complex values of an external control parameter at which the partition function vanishes for a many-body system of finite size. In the thermodynamic limit, the Lee-Yang zeros

Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states

TLDR
A new PITE approach that uses only one ancillary qubit is proposed that constructs the circuit from forward and backward real-time evolution (RTE) gates as black boxes for the original Hamiltonian and can be used to obtain the Gibbs state at a temperature and partition function.

Dynamical Quantum Phase Transitions in the 1D Nonintegrable Spin‐1/2 Transverse Field XZZ Model

Using the Jordan–Wigner mean‐field (JW‐MF) approach, the dynamical quantum phase transition (DQPT) in the 1D spin‐1/2 XZZ model is studied, where the presence of the transverse magnetic field breaks

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

The authors determine the Lee-Yang zeros of an Ising spin lattice in one, two, and three dimensions from the thermodynamic fluctuations that are inherent to critical regions. They can thereby predict

Path optimization for U(1) gauge theory with complexified parameters

In this article, we apply the path optimization method to handle the complexified parameters in the $1+1$ dimensional pure $U(1)$ gauge theory on the lattice. Complexified parameters make it possible

Designing Quantum Algorithms for State Preparation and Thermal Field Theory

a Computational Science Initiative, Brookhaven National Laboratory, Upton, New York, 11973 b Universität Regensburg, Fakultät für Physik, 93040 Regensburg, Germany c Yukawa Institute for Theoretical

References

SHOWING 1-10 OF 61 REFERENCES

Quantum algorithms for spin models and simulable gate sets for quantum computation

TLDR
It is shown that classically simulating these (complex-parameter) spin models is as hard as simulating universal quantum computation, i.e., BQP complete (BQP denotes bounded-error quantum polynomial time).

Classical spin models and the quantum-stabilizer formalism.

We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we

Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator

TLDR
Here, a quantum simulator composed of up to 53 qubits is used to study non-equilibrium dynamics in the transverse-field Ising model with long-range interactions, enabling the dynamical phase transition to be probed directly and revealing computationally intractable features that rely on the long- range interactions and high connectivity between qubits.

Self-verifying variational quantum simulation of lattice models

TLDR
Experiments are presented that demonstrate self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics, enabling the study of a wide variety of previously intractable target models.

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

TLDR
This work reports the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer and explores the Schwinger mechanism of particle–antiparticle generation by monitoring the mass production and the vacuum persistence amplitude.

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

TLDR
A Rydberg atom quantum simulator with programmable interactions is used to experimentally verify the quantum Kibble–Zurek mechanism through the growth of spatial correlations during quantum phase transitions, and is subsequently used to measure the critical exponents associated with chiral clock models.

Probing many-body dynamics on a 51-atom quantum simulator

TLDR
This work demonstrates a method for creating controlled many-body quantum matter that combines deterministically prepared, reconfigurable arrays of individually trapped cold atoms with strong, coherent interactions enabled by excitation to Rydberg states, and realizes a programmable Ising-type quantum spin model with tunable interactions and system sizes of up to 51 qubits.

Experimental observation of Lee-Yang zeros.

TLDR
The first observation of Lee-Yang zeros is reported, by measuring quantum coherence of a probe spin coupled to an Ising-type spin bath, and the quantum evolution of the probe spin introduces a complex phase factor and therefore effectively realizes an imaginary magnetic field.

On the quantum computational complexity of the Ising spin glass partition function and of knot invariants

It is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of ±J Ising spin glasses a particular instance of certain

Quantum Simulation of Gauge Theories and Inflation 1 . Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model

We have entered a new era of rapidly growing ability to precisely control and measure the complex states of quantum systems with ever larger Hilbert space dimensions. These capabilities are giving us
...