Quantum Electronic Circuits for Multicritical Ising Models
- URL: http://arxiv.org/abs/2306.04346v1
- Date: Wed, 7 Jun 2023 11:24:43 GMT
- Title: Quantum Electronic Circuits for Multicritical Ising Models
- Authors: Ananda Roy
- Abstract summary: Multicritical Ising models and their perturbations are paradigmatic models of statistical mechanics.
Quantum circuits are constructed with Josephson junctions with $cos(nphi + delta_n)$ potential with $1leq nleq p$ and $delta_nin[-pi,pi]$.
The lattice models for the Ising and tricritical Ising models are analyzed numerically using the density matrix renormalization group technique.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Multicritical Ising models and their perturbations are paradigmatic models of
statistical mechanics. In two space-time dimensions, these models provide a
fertile testbed for investigation of numerous non-perturbative problems in
strongly-interacting quantum field theories. In this work, analog
superconducting quantum electronic circuit simulators are described for the
realization of these multicritical Ising models. The latter arise as
perturbations of the quantum sine-Gordon model with $p$-fold degenerate minima,
$p =2, 3,4,\ldots$. The corresponding quantum circuits are constructed with
Josephson junctions with $\cos(n\phi + \delta_n)$ potential with $1\leq n\leq
p$ and $\delta_n\in[-\pi,\pi]$. The simplest case, $p = 2$, corresponds to the
quantum Ising model and can be realized using conventional Josephson junctions
and the so-called $0-\pi$ qubits. The lattice models for the Ising and
tricritical Ising models are analyzed numerically using the density matrix
renormalization group technique. Evidence for the multicritical phenomena are
obtained from computation of entanglement entropy of a subsystem and
correlation functions of relevant lattice operators. The proposed quantum
circuits provide a systematic approach for controlled numerical and
experimental investigation of a wide-range of non-perturbative phenomena
occurring in low-dimensional quantum field theories.
Related papers
- Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon [34.80375275076655]
Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions.
We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon.
arXiv Detail & Related papers (2024-07-03T18:00:52Z) - Utilizing Quantum Processor for the Analysis of Strongly Correlated Materials [34.63047229430798]
This study introduces a systematic approach for analyzing strongly correlated systems by adapting the conventional quantum cluster method to a quantum circuit model.
We have developed a more concise formula for calculating the cluster's Green's function, requiring only real-number computations on the quantum circuit instead of complex ones.
arXiv Detail & Related papers (2024-04-03T06:53:48Z) - Probing Confinement Through Dynamical Quantum Phase Transitions: From
Quantum Spin Models to Lattice Gauge Theories [0.0]
We show that a change in the type of dynamical quantum phase transitions accompanies the confinement-deconfinement transition.
Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.
arXiv Detail & Related papers (2023-10-18T18:00:04Z) - Towards a Quantum Simulation of Nonlinear Sigma Models with a
Topological Term [0.0]
We show that the quantum theory is massless in the strong-coupling regime.
We also highlight the limitations of current quantum algorithms, designed for noisy intermediate-scale quantum devices.
arXiv Detail & Related papers (2022-10-07T16:35:03Z) - Tuning the Topological $\theta$-Angle in Cold-Atom Quantum Simulators of
Gauge Theories [3.4075669047370125]
We show how a tunable topological $theta$-term can be added to a prototype theory with gauge symmetry.
The model can be realized experimentally in a single-species Bose--Hubbard model in an optical superlattice with three different spatial periods.
This work opens the door towards studying the rich physics of topological gauge-theory terms in large-scale cold-atom quantum simulators.
arXiv Detail & Related papers (2022-04-13T18:00:01Z) - Variational Adiabatic Gauge Transformation on real quantum hardware for
effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
We introduce the Variational Adiabatic Gauge Transformation (VAGT)
VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit.
The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
arXiv Detail & Related papers (2021-11-16T20:50:08Z) - Simulating Quantum Mechanics with a $\theta$-term and an 't Hooft
Anomaly on a Synthetic Dimension [2.710787786741731]
A topological $theta$-term in gauge theories, including quantum chromodynamics in 3+1 dimensions, gives rise to a sign problem that makes classical Monte Carlo simulations impractical.
Quantum simulations are not subject to such sign problems and are a promising approach to studying these theories in the future.
We propose an experimental scheme for the real-time simulation of a particle on a circle with a $theta$-term and a $mathbbZ_n$ potential using a synthetic dimension encoded in a Rydberg atom.
arXiv Detail & Related papers (2021-07-16T18:34:46Z) - Engineering analog quantum chemistry Hamiltonians using cold atoms in
optical lattices [69.50862982117127]
We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups.
We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
arXiv Detail & Related papers (2020-11-28T11:23:06Z) - The quantum sine-Gordon model with quantum circuits [0.0]
We numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator built out of Josephson junctions.
We provide numerical evidence that the parameters required to realize the quantum sine-Gordon model are accessible with modern-day superconducting circuit technology.
arXiv Detail & Related papers (2020-07-14T07:39:31Z) - Hartree-Fock on a superconducting qubit quantum computer [30.152226344347064]
Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates.
We model the binding energy of $rm H_6$, $rm H_8$, $rm H_10$ and $rm H_12$ chains as well as the isomerization of diazene.
We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments.
arXiv Detail & Related papers (2020-04-08T18:00:06Z) - Quantum Statistical Complexity Measure as a Signalling of Correlation
Transitions [55.41644538483948]
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions.
We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain.
We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
arXiv Detail & Related papers (2020-02-05T00:45:21Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.