Jinzhao Sun

Abstract:

The efficient probing of spectral features is important for characterising and understanding the structure and dynamics of quantum materials. In this work, we establish a framework for probing the excitation spectrum of quantum many-body systems with quantum simulators. Our approach effectively realises a spectral detector by processing the dynamics of observables with time intervals drawn from a defined probability distribution, which only requires native time evolution governed by the Hamiltonian without ancilla. The critical element of our method is the engineered emergence of frequency resonance such that the excitation spectrum can be probed. We show that the time complexity for transition energy estimation has a logarithmic dependence on simulation accuracy and how such observation can be guaranteed in certain many-body systems. We discuss the noise robustness of our spectroscopic method and show that the total running time maintains polynomial dependence on accuracy in the presence of device noise. We further numerically test the error dependence and the scalability of our method for lattice models. We present simulation results for the spectral features of typical quantum systems, either gapped or gapless, including quantum spins, fermions and bosons. We demonstrate how excitation spectra of spin-lattice models can be probed experimentally with IBM quantum devices.

Abstract:

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to 48 qubits only using an 8+1 qubit quantum hardware. We demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.

Abstract:

Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g., time evolution operator or block encoding of the Hamiltonian), which, however, become suboptimal for actual implementation at the quantum circuit level. Here, we present a full-stack design of quantum algorithms for estimating the eigenenergy and eigenstate properties, which can achieve high precision and good scaling with system size. The gate complexity per circuit for estimating generic Hamiltonians' eigenstate properties is [Formula: see text], which has a logarithmic dependence on the inverse precision ε. For lattice Hamiltonians, the circuit depth of our design achieves near-optimal system-size scaling, even with local qubit connectivity. Our full-stack algorithm has low overhead in circuit compilation, which thus results in a small actual gate count (cnot and non-Clifford gates) for lattice and molecular problems compared to advanced eigenstate algorithms. The algorithm is implemented on IBM quantum devices using up to 2000 two-qubit gates and 20,000 single-qubit gates and achieves high-precision eigenenergy estimation for Heisenberg-type Hamiltonians, demonstrating its noise robustness.

Abstract:

Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate dependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we show it can be effectively suppressed by a stochastic QEM method. Since our method assumes only accurate single qubit controls, it is applicable to all digital quantum computers and various analog simulators. Meanwhile, errors in the mitigation procedure can be suppressed by leveraging the Richardson extrapolation method. As we numerically test our method with various Hamiltonians under energy relaxation and dephasing noise and digital quantum circuits with additional two-qubit crosstalk, we show an improvement of simulation accuracy by 2 orders. We assess the resource cost of our scheme and conclude the feasibility of accurate quantum computing with NISQ devices.

Abstract:

Quantum computing (QC) and quantum Monte Carlo (QMC) represent state-of-the-art quantum and classical computing methods, respectively, for understanding many-body quantum systems. However, straightforward integration of the two methods may encounter significant challenges, such as exponential sampling cost and inefficient walker propagation. Here, we propose an efficient hybrid quantum-classical algorithm that integrates the two methods, overcoming these limitations while leveraging their strengths in representing and manipulating quantum states. To measure the effectiveness of the hybrid approach, we first introduce nonstoquasticity indicators (NSIs) and their theoretical upper bounds, which quantify the severity of the sign problem, a major limitation of QMC. Next, we present a hybrid QC-QMC method where the walkers are represented by quantum states prepared by a shallow quantum circuit. Although the Hamiltonian in the quantum state walker basis is not sparse, we offer an efficient and scalable approach to implement walker propagation using a quantum computer. From the QMC perspective, our algorithm significantly mitigates the sign problem in the quantum state walker basis. From the QC perspective, integrating QMC increases the expressivity of shallow quantum circuits, enabling more accurate computations that are traditionally achievable only with much deeper quantum circuits. Our method has immediate applications in tackling complex quantum many-body problems. We numerically test and verify it for the N2 molecule (12 qubits) and the Hubbard model (16 qubits), observing a significant suppression of the sign problem (which exponentially decreases with circuit depth) and a notable improvement in calculation accuracy (which is about two to three orders compared to variational quantum algorithms). Our work paves the way to solving practical problems with intermediate-scale and early fault-tolerant quantum computers, with broad applications in chemistry, condensed matter physics, and materials.