Simulating large-size quantum spin chains on cloud-based superconducting quantum computers

Abstract

Quantum computers have the potential to efficiently simulate large-scale quantum systems for which classical approaches are bound to fail. Even though several existing quantum devices now feature total qubit numbers of more than one hundred, their applicability remains plagued by the presence of noise and errors. Thus, the degree to which large quantum systems can successfully be simulated on these devices remains unclear. Here, we report on cloud simulations performed on several of IBM's superconducting quantum computers to simulate ground states of spin chains having a wide range of system sizes up to one hundred and two qubits. We find that the ground-state energies extracted from realizations across different quantum computers and system sizes reach the expected values to within errors that are small (i.e. on the percent level), including the inference of the energy density in the thermodynamic limit from these values. We achieve this accuracy through a combination of physics-motivated variational Ansatzes, and efficient, scalable energy-measurement and error-mitigation protocols, including the use of a reference state in the zero-noise extrapolation. By using a 102-qubit system, we have been able to successfully apply up to 3186 CNOT gates in a single circuit when performing gate-error mitigation. Our accurate, error-mitigated results for random parameters in the Ansatz states suggest that a standalone hybrid quantum-classical variational approach for large-scale XXZ models is feasible.

21 pages, 12 figures, 4 tables; title change; substantial revision

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• Optimal realization of Yang-Baxter gate on quantum computers
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• Sketching phase diagrams using low-depth variational quantum algorithms
• Efficient Frequency Allocation for Superconducting Quantum Processors Using Improved Optimization Techniques
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
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• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Capturing the Page Curve and Entanglement Dynamics of Black Holes in Quantum Computers
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Sampling (noisy) quantum circuits through randomized rounding
• Nontrivial multi-product commutation relation toward reducing T-count in sequential Pauli-based computation
• Evaluating Sample-Based Krylov Quantum Diagonalization for Heisenberg Models with Applications to Materials Science