Equivariant Variational Quantum Eigensolver to detect Phase Transitions through Energy Level Crossings

Abstract

Level spectroscopy stands as a powerful method for identifying the transition point that delineates distinct quantum phases. Since each quantum phase exhibits a characteristic sequence of excited states, the crossing of energy levels between low-lying excited states offers a reliable mean to estimate the phase transition point. While approaches like the Variational Quantum Eigensolver are useful for approximating ground states of interacting systems using quantum computing, capturing low-energy excitations remains challenging. In our study, we introduce an equivariant quantum circuit that preserves the total spin and the translational symmetry to accurately describe singlet and triplet excited states in the $J_1$-$J_2$ Heisenberg model on a chain, which are crucial for characterizing its transition point. Additionally, we assess the impact of noise on the variational state, showing that conventional mitigation techniques like Zero Noise Extrapolation reliably restore its physical properties.

14 pages (including Appendix), 7 figures

References in corpus (47)

• Quantum Computing in the NISQ era and beyond
• Variational Quantum Algorithms
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Quantum Engineer's Guide to Superconducting Qubits
• Error mitigation for short-depth quantum circuits
• Towards Practical Quantum Variational Algorithms
• Efficient variational quantum simulator incorporating active error minimisation
• A short introduction to the Lindblad Master Equation
• Computational Studies of Quantum Spin Systems
• Optimal Quantum Circuits for General Two-Qubit Gates
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Detecting crosstalk errors in quantum information processors
• Digital zero noise extrapolation for quantum error mitigation
• Exploiting symmetry in variational quantum machine learning
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Model-free readout-error mitigation for quantum expectation values
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits
• Efficient variational simulation of non-trivial quantum states
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Ground state phases of the Half-Filled One-Dimensional Extended Hubbard Model
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• Ground states of a frustrated quantum spin chain with long-range interactions
• Transformer variational wave functions for frustrated quantum spin systems
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Symmetry-adapted variational quantum eigensolver
• Quantum-number projection in the path-integral renormalization group method
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• The Adjoint Is All You Need: Characterizing Barren Plateaus in Quantum Ansätze
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Symmetry enhanced variational quantum spin eigensolver
• Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation
• A programming guide for tensor networks with global $SU(2)$ symmetry
• Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo
• A novel approach to noisy gates for simulating quantum computers
• Simulating strongly interacting Hubbard chains with the Variational Hamiltonian Ansatz on a quantum computer
• Symmetry breaking in geometric quantum machine learning in the presence of noise
• Quantum Optical Communication in the presence of strong attenuation noise
• Variational Quantum Eigensolver Ansatz for the $J_1$-$J_2$-model

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