Quantum information science has emerged as one of the most promising fields in contemporary research, relying on both software and hardware innovations. This thesis looks for both algorithms with quantum features that provide advantages over classical algorithms, and better hardware platforms for experiments and quantum computing. The work spans theoretical studies in both algorithm and hardware design, including hybrid quantum-classical algorithms and the development of quantum information processing platforms. The algorithmic part has focused on the performance of a hybrid quantum algorithm - the Grover Quantum Approximate Optimization Algorithm (Grover QAOA) - designed for problems with multiple solutions. In practice, we find its potential for speedup in solution search and its ability to find all solutions. Furthermore, we propose a simplified protocol that reduces the classical complexity of optimizing the algorithm’s parameters, enhancing its practicality for future applications. Our implementation of Grover QAOA for multiple combinatorial optimization problems on trapped-ion quantum computers demonstrates that the algorithm can fulfill its fair-sampling advantage even on noisy devices. In the hardware part, we mainly explore how the motion of cold atoms can either be used to engineer interactions or lead to previously overlooked decoherence. The first hardware platform we discuss is trapped ions, where we focus on implementing individual addressing to natively simulate new types of many-body systems. Our proposal leverages the exceptional controllability of trapped ions to explore dynamical models such as topological pumping. The second hardware platform we study is Rydberg atom lattices, where we investigate the decoherence processes introduced by atomic motion during dynamics. Using the numerical tool of discrete truncated Wigner approximation, we simulate the coupled dynamics of electronic and motional degrees of freedom, demonstrating that atom motion induced by strong van der Waals interactions in Rydberg atoms can lead to significant decoherence in analog simulation experiments. We have also explored specialized topics involving other quantum hardware platforms. One area of study is the reduction of frequency crowding in superconducting circuit quantum chips. By properly designing the frequencies for each transmon qubit, we can improve the manufacturing yield of collision-free processors. Another area focuses on the SU(N) Fermi-Hubbard models on alkaline-earth-metal optical lattice platforms. We have obtained the phase diagram of unit-filling models with imbalanced spin flavors. This work aids future experiments in searching for potential ground states of the unit-filling SU(N) model.
The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling MAX
k-SAT problems, specifically for
k=3and
k=4. The novel 4-SAT QAOA circuit construction we present uses measurement based uncomputation, followed by classical feed forward conditional operations. The QAOA circuit parameters for 3-SAT are optimized via exact classical (noise-free) simulation, using HPC resources to simulate up to 20 rounds on 10 qubits. In order to explore the limits of current NISQ devices we execute these optimized QAOA circuits for random 3-SAT test instances with clause-to-variable ratio 4 on four trapped ion quantum computers: Quantinuum H1-1 (20 qubits), IonQ Harmony (11 qubits), IonQ Aria 1 (25 qubits), and IonQ Forte (30 qubits). The QAOA circuits that are executed include
n=10up to
p=20, and
n=22for
p=1and
p=2. The high round circuits use upwards of 9,000 individual gate instructions, making these some of the largest QAOA circuits executed on NISQ devices. Our main finding is that current NISQ devices perform best at low round counts (i.e.,
p=1,…,5) and then – as expected due to noise – gradually start returning satisfiability truth assignments that are no better than randomly picked solutions as the number of QAOA rounds are further increased.
Quantum computers and simulators may offer significant advantages over their
classical counterparts, providing insights into quantum many-body systems and
possibly solving exponentially hard problems, such as optimization and
satisfiability. Here we report the first implementation of a shallow-depth
Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum
simulator to estimate the ground state energy of the transverse field Ising
model with tunable long-range interactions. First, we exhaustively search the
variational control parameters to approximate the ground state energy with up
to 40 trapped-ion qubits. We then interface the quantum simulator with a
classical algorithm to more efficiently find the optimal set of parameters that
minimizes the resulting energy of the system. We finally sample from the full
probability distribution of the QAOA output with single-shot and efficient
measurements of every qubit.