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

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Cited by in corpus (5)

• Unveiling quantum phase transitions from traps in variational quantum algorithms
• Entanglement-informed Construction of Variational Quantum Circuits
• Estimates of loss function concentration in noisy parametrized quantum circuits
• Learning Variational Quantum Circuit Parameters with Classical Artificial Intelligence for Quantum Phase Transition Detection
• Double-bracket quantum algorithms for high-fidelity ground state preparation