Sketching phase diagrams using low-depth variational quantum algorithms
arXiv:2301.09369 · doi:10.1088/2058-9565/ad4979
Abstract
Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the Variational Quantum Eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.
arXiv comment10 + 5 pages, 8 + 10 figures, added data link to v2
References in corpus (37)
- A variational eigenvalue solver on a quantum processor
- Barren plateaus in quantum neural network training landscapes
- The theory of variational hybrid quantum-classical algorithms
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Towards Practical Quantum Variational Algorithms
- Connecting ansatz expressibility to gradient magnitudes and barren plateaus
- Spectral Gap and Exponential Decay of Correlations
- Quantum Criticality
- Sequential generation of entangled multi-qubit states
- Classical simulation of noninteracting-fermion quantum circuits
- Fluctuations and correlations in high temperature QCD
- Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
- Higher order fluctuations and correlations of conserved charges from lattice QCD
- Strategies for solving the Fermi-Hubbard model on near-term quantum computers
- Spin nematic correlations in bilinear-biquadratic S=1 spin chains
- Spin nematics in the bilinear-biquadratic S=1 spin chain
- Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
- Quantum algorithms to simulate many-body physics of correlated fermions
- Triviality of Bloch and Bloch-Dirac bundles
- Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design
- A Compact Fermion to Qubit Mapping
- Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer
- Quantum Critical Points and the Sign Problem
- Probable absence of a quadrupolar spin-nematic phase in the bilinear-biquadratic spin-1 chain
- Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements
- Variational Quantum Eigensolver for Frustrated Quantum Systems
- Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
- The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
- A scaling hypothesis for matrix product states
- Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
- Disorder-assisted error correction in Majorana chains
- Simulating large-size quantum spin chains on cloud-based superconducting quantum computers
- Variational quantum algorithm with information sharing
- Quantum computing critical exponents
- Chiral magnetic properties of QCD phase-diagram
- Circuit Complexity through phase transitions: consequences in quantum state preparation
- Real space circuit complexity as a probe of phase diagrams