Digital Quantum Simulation of Quantum Many-Body Systems

Citation

Sun, Shi-Ning (2024) Digital Quantum Simulation of Quantum Many-Body Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xm9j-9x23. https://resolver.caltech.edu/CaltechTHESIS:05292024-213136069

Abstract

Quantum computing has emerged as a promising technology, heralding a new era of computational capabilities, with the simulation of quantum many-body systems as one of its primary objectives. Although fault-tolerant quantum computers are still years away, noisy intermediate-scale quantum (NISQ) devices have been fabricated and leveraged to perform small-scale quantum simulations. In this thesis, we demonstrate simulations of quantum many-body systems on these near-term quantum computers. We specifically focus on physical quantities pertaining to the linear-response framework, which include two-point correlation functions and Green's functions, of small-scale spin and molecular models. Additionally, as quantum hardware increases in qubit count, simulation of these quantum algorithms on classical computers that closely resemble those planned for execution on quantum hardware becomes increasingly critical. The final part of this thesis examines such a simulation using tensor network algorithms on classical computers.

We first present the study of finite-temperature physics of spin models on quantum hardware. Employing the quantum imaginary time evolution (QITE) algorithm, we demonstrate the computation of diverse finite-temperature observables, including energy, static and dynamical correlation functions, and excitation spectra of the Heisenberg model and the transverse-field Ising model of up to four sites on five-qubit IBM Quantum devices. Accurate determination of these finite-temperature properties on quantum computers is made possible by several algorithmic improvements, including a method to exploit symmetries that reduces the quantum resources required by QITE, circuit optimization procedures to reduce circuit depth, and error-mitigation techniques to improve the quality of raw hardware data. This work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices.

The second work implements an algorithm for frequency-domain response properties of diatomic molecules using a novel high-fidelity three-qubit iToffoli gate. Although it is natural to compute response properties in the time domain due to the natural ability of quantum computers to apply unitary time evolutions, obtaining the frequency-domain properties from the time-domain properties typically requires a time duration that results in quantum circuits exceeding the circuit depth limitations of near-term quantum computers. In this work, we carry out computations of the response properties directly in the frequency domain using the linear combination of unitaries (LCU) algorithm. Execution of the LCU-based protocol on quantum hardware is enabled by the iToffoli gate, which enables a ~50\% reduction in circuit depth and ~40\% reduction in circuit execution time in the LCU circuits compared to the traditional gate set. We show that the molecular properties obtained with the iToffoli gate exhibit comparable or better agreement with analytical results than those obtained when CZ gates are the only multi-qubit gates. This work is among the first demonstrations of the practical usage of a native multi-qubit gate in quantum simulation, with diverse potential applications to near-term quantum computation.

Finally, this thesis conducts a tensor network simulation of measurement-induced state preparation on classical computers. Specifically, we simulate the phase transition in random-bond Ising models (RBIM) by performing measurements on the cluster states. The simulation is carried out on NVIDIA H100 graphical processing units (GPUs) using the cuQuantum library. We present simulation of correlation functions in one dimension (1D) and ferromagnetic susceptibilities in two dimensions (2D), observing a phase transition from the ferromagnetic phase to spin-glass phase in the 2D model. The tensor network simulation incorporates up to 176 qubits on the 2D lattice. This work paves the way for future explorations of tensor network simulations of measurement-induced quantum computation protocols with GPU-accelerated tensor network libraries.

Thesis Files