Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Abstract

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

arXiv comment17 pages and 11 figures final version

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• Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
• Fermionic approach to variational quantum simulation of Kitaev spin models
• Robust measurement of wave function topology on NISQ quantum computers
• Pattern-dependent proximity effect and Majorana edge mode in one-dimensional quasicrystals
• Simulating a ring-like Hubbard system with a quantum computer
• Simulating spectroscopy experiments with a superconducting quantum computer
• Noise-Robust Detection of Quantum Phase Transitions
• Quantum computing topological invariants of two-dimensional quantum matter
• Error estimation in current noisy quantum computers
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Engineering the Kitaev spin liquid in a quantum dot system
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• A Useful Metric for the NISQ Era: Qubit Error Probability and Its Role in Zero Noise Extrapolation
• Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation