Quantum simulation of operator spreading in the chaotic Ising model.

@article{Geller2022QuantumSO,
  title={Quantum simulation of operator spreading in the chaotic Ising model.},
  author={Michael R. Geller and Andrew Arrasmith and Zoe Holmes and Bin Yan and Patrick J. Coles and Andrew T. Sornborger},
  journal={Physical review. E},
  year={2022},
  volume={105 3-2},
  pages={
          035302
        }
}
There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a four-spin Ising model as a function of space, time, and integrability. Reaching four spins while retaining high circuit… 

Figures and Tables from this paper

Benchmarking Information Scrambling
TLDR
This work provides a simple and robust approach to single out the degree of genuine scrambling from the noisy backgrounds of information scrambling, and demonstrates the protocol with simulations on IBM cloud-based quantum computers.
Quantum Algorithms for Testing Hamiltonian Symmetry
TLDR
This paper proposes quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group and demonstrates that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance probabilities of these algorithms.

References

SHOWING 1-10 OF 75 REFERENCES
Information scrambling in quantum circuits
TLDR
It is shown that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate.
Signatures of quantum chaos transition in short spin chains
The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space. Among different indicators signaling
Verified quantum information scrambling
TLDR
A quantum circuit in an ion-trap quantum computer provides a positive test for the scrambling features of a given unitary process, and is implemented as part of a seven-qubit circuit on an ion trap quantum computer to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.
Detecting the out-of-time-order correlations of dynamical quantum phase transitions in a solid-state quantum simulator
Quantum many-body systems in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, there still exist a lot of questions regarding how to
Variational fast forwarding for quantum simulation beyond the coherence time
Trotterization-based, iterative approaches to quantum simulation (QS) are restricted to simulation times less than the coherence time of the quantum computer (QC), which limits their utility in the
Unfolding quantum computer readout noise
In the current era of noisy intermediate-scale quantum computers, noisy qubits can result in biased results for early quantum algorithm applications. This is a significant challenge for interpreting
Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
TLDR
A simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes, which relies on performing classical post-processing which is preceded by Quantum Detector Tomography, and results showing improvement for the implementation of certain probability distributions in the case of five qubits are presented.
An efficient quantum algorithm for the time evolution of parameterized circuits
TLDR
A novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits realizes an iterative, global projection of the exact time evolution onto the parameterized manifold, equivalent to the McLachlan's variational principle.
Many-Body Localization and Thermalization in Quantum Statistical Mechanics
We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate
Quantum chaos: an introduction via chains of interacting spins-1/2
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ
...
...