Simulating large-size quantum spin chains on cloud-based superconducting quantum computers (2207.09994v2)

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.

• The paper presents a variational quantum algorithm simulating up to 102-qubit spin chains with an innovative error mitigation strategy.
• Hybrid cloud experiments with IBM's superconducting quantum computers achieved ground-state energies within a few percent of theoretical predictions.
• Robust measurement techniques and zero-noise extrapolation demonstrate practical quantum simulations on NISQ devices.

Simulating Large-Size Quantum Spin Chains on Cloud-Based Superconducting Quantum Computers

The paper by Hongye Yu, Yusheng Zhao, and Tzu-Chieh Wei explores the feasibility of simulating large quantum spin systems using cloud-based superconducting quantum computers. The authors focus on the quantum variational approach to simulate ground states of spin chains, specifically up to 102 qubits, across different system sizes and quantum devices provided by IBM's cloud quantum computing platform.

The motivation for this research lies in the burgeoning capabilities and ongoing challenges of Noisy Intermediate-Scale Quantum (NISQ) devices. Despite unprecedented advancements, these devices still suffer from noise and errors that compromise their ability to simulate quantum systems accurately. The authors address these limitations by implementing a comprehensive error mitigation strategy that combines variational Ansatzes, energy measurement protocols, and zero-noise extrapolation techniques.

Methodology

The authors employ a physics-motivated variational Ansatz designed using the adiabatic evolution of the system. This Ansatz is tested for accuracy by comparing its energy estimates with those derived from MPS methods and exact diagonalization for small systems. The insights from these comparisons guide the organization of cloud-based experiments.

Three measurement techniques are articulated:

1. State Information Measurement with Tomography: This approach obtains the reduced density matrix for pairs of qubits.
2. Measurement in Distinct Bases: This involves measuring all qubits in varied bases, obtaining classical expectations for product observables.
3. Bell-State Measurement: Exploiting the eigenstates of XXZ interaction, the energy contributions of Bell states are measured, which is effective given the device constraints.

Error mitigation is crucial, with the authors employing both readout error mitigation and gate error mitigation through zero-noise extrapolation. The reference Bell state introduces an innovative aspect in error estimation, particularly for larger circuit depths that come with size scaling in simulations.

Results and Insights

The experiments demonstrate successful state preparation and energy measurement for various spin chain sizes, up to 102 qubits, with mitigated errors within a few percent. The ground-state energy extracted from the experiments closely aligns with theoretical predictions. For example, their estimation of the ground-state energy per site in the thermodynamic limit is consistent with the Bethe Ansatz solutions.

Implications and Future Directions

These findings imply substantial progress toward practical quantum simulations on NISQ devices. The work lays groundwork for further exploration into large-scale quantum simulations and variational quantum algorithms (VQAs). The paper also suggests potential for wider application, such as optimization problems, by demonstrating the effective hybrid use of quantum and classical resources.

Future research directions could explore the application of these methodologies to two-dimensional quantum models, where classical computational techniques struggle due to extensive entanglement. While the immediate results pertain primarily to quantum spin chains, the overarching methods and insights are broadly applicable and stand to inform developments not just in quantum simulations but also in general quantum computation paradigms.

In conclusion, this research underscores the promise of harnessing cloud-based superconducting quantum platforms to explore and solve large quantum many-body systems challenges, contributing to the evolution of quantum technology as it advances towards practical, scalable implementations.