Towards the real-time evolution of gauge-invariant ${\mathbb{Z}}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation

Abstract

Practical quantum computing holds clear promise in addressing problems not generally tractable with classical simulation techniques, and some key physically interesting applications are those of real-time dynamics in strongly coupled lattice gauge theories. In this article, we benchmark the real-time dynamics of ${\mathbb{Z}}_2$ and $U(1)$ gauge invariant plaquette models using noisy intermediate scale quantum (NISQ) hardware, specifically the superconducting-qubit-based quantum IBM Q computers. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges. NISQ hardware suffers from significant decoherence and corresponding difficulty to interpret the results. We demonstrate the use of hardware-agnostic error mitigation techniques, such as circuit folding methods implemented via the Mitiq package, and show what they can achieve within the quantum volume restrictions for the hardware. Our study provides insight into the choice of Hamiltonians, construction of circuits, and the utility of error mitigation methods to devise large-scale quantum computation strategies for lattice gauge theories.

20 pages, 15 figures

References in corpus (16)

• Probing many-body dynamics on a 51-atom quantum simulator
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Experimental Comparison of Two Quantum Computing Architectures
• Exponential suppression of bit or phase flip errors with repetitive error correction
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• SU(2) hadrons on a quantum computer
• Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice
• Quantum simulation of scattering in the quantum Ising model
• Improved Hamiltonians for Quantum Simulations
• Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED
• Simulating quench dynamics on a digital quantum computer with data-driven error mitigation
• Hierarchical Qubit Maps and Hierarchical Quantum Error Correction
• General error mitigation for quantum circuits

Cited by in corpus (9)

• Quench dynamics of the Schwinger model via variational quantum algorithms
• Dynamical quantum phase transitions of the Schwinger model: real-time dynamics on IBM Quantum
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Topological Defects in Floquet Circuits
• Zero noise extrapolation on logical qubits by scaling the error correction code distance
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms
• Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model
• Shearing approach to gauge-invariant Trotterization