UC Berkeley

In recent years, the realms of deep learning and variational quantum algorithms have undergone significant advancements. These innovative algorithms have proven to be exceptionally efficient and robust in addressing complex problems within quantum chemistry, condensed matter physics, and quantum field theory simulations, surpassing the capabilities of traditional classical algorithms. A key factor driving this progress is the development of hybrid quantum algorithms, which blend quantum and classical computational techniques.

Prominent examples of these hybrid algorithms include the Quantum Approximate Optimization Algorithm (QAOA), the Variational Quantum Eigensolver (VQE), and various Variational Quantum Algorithms (VQAs). These methods enable the construction of parameterized quantum circuits (PQCs), which are central to the operation of these algorithms. By employing PQCs, these algorithms leverage the unique properties of quantum computing, such as superposition and entanglement, to explore solution spaces more comprehensively than classical methods.

Furthermore, the optimization process in these hybrid algorithms involves a sophisticated interplay between quantum and classical computing resources. The quantum computer is used to evaluate the performance of the quantum circuit for given parameters, and classical optimization techniques are then applied to refine these parameters iteratively. This synergistic approach enhances the efficiency and effectiveness of the optimization process, making it particularly suitable for problems that are intractable for classical computers alone.

We primarily concentrate on a specific issue: the preparation of ground states. A notable challenge in this process is the noise originating from measurements or the device itself. It's crucial to consider this noise when preparing ground states. To address this, we need to develop algorithms that are robust to noise. Our approach involves the development of variational quantum algorithms, which allow for parameter updates during iterative processes. Effectively preparing the ground state is vital, as it has significant applications in subsequent downstream tasks.

In addressing the ground state preparation challenge, our objective is to generate the ground state, defined as the lowest eigenstate of the Hamiltonian H. Our exploration is two-pronged: firstly, we investigate various parametrization methods for the variational circuits, aiming to enhance the flexibility and efficiency of the quantum circuits. Secondly, we scrutinize different optimization strategies. This includes examining policy gradients and incorporating optimization challenges within the framework of reinforcement learning, thereby expanding the scope and capability of our optimization methodologies.

In evaluating the optimization process, we utilize two critical metrics: fidelity and ground state energy. Fidelity measures the overlap between the target quantum states and the evolved quantum states from the quantum circuit, serving as an indicator of the precision in achieving the desired quantum state. Ground state energy, conversely, relates to observables that can be measured in experimental settings, offering valuable insights into the physical characteristics of the quantum system under investigation.

The algorithms we discuss are specifically engineered to operate effectively in environments where quantum computer measurements are subject to noise. Demonstrating robustness against such measurement noise, these optimization algorithms efficiently identify optimal parameters for the variational quantum circuits. This efficiency and resilience are pivotal in advancing the field of quantum computing, particularly in the context of practical, noisy quantum systems.

Chapter 1 introduces the background knowledge and overview of deep learning techniques and optimization algorithms, quantum circuits, and variational quantum algorithms the basic problem setup and provides an overview of the results in this paper.

Chapter 2 introduces a policy gradient approach to the Quantum Approximate Optimization Algorithm (QAOA) using methods. Chapter 3 presents reinforcement learning techniques for the preparation of many-body ground states in quantum systems. It specifically leverages counter-diabatic driving, a method that guides the system adiabatically to avoid non-equilibrium excitations, thus ensuring more reliable ground state preparation. Chapter 4 presents a noise-robust, deep autoregressive policy networks based end-to-end quantum control framework as to the challenge of noise in quantum systems. Chapter 5 presents another approach which integrates MCTS with quantum circuit optimization, aiming to enhance the efficiency and effectiveness of the circuit design and operation. Chapter 6 presents a random coordinate descent method as a straightforward yet effective technique for optimizing parameterized quantum circuits.

Please note that Part 2 is based on [Yao, J., Bukov, M., & Lin, L. Mathematical and Scientific Machine Learning (pp. 605-634). PMLR.] (joint work with Marin Bukov, Lin Lin), Part 3 is based on [Yao, J., Lin, L., & Bukov, M. (2021). Physical Review X, 11(3), 031070.] (joint work with Marin Bukov, Lin Lin), Part 3 is based on [Yao, J., Kottering, P., Gundlach, H., Lin, L., & Bukov, M. Mathematical and Scientific Machine Learning (pp. 1044-1081). PMLR.] (joint work with Paul Kottering, Hans Gundlach, Lin Lin, Marin Bukov), and Part 5 is based on [Yao, J., Li, H., Bukov, M., Lin, L., & Ying, L. Mathematical and Scientific Machine Learning (pp. 49-64). PMLR.] (joint work with Haoya Li, Marin Bukov, Lin Lin, Lexing Ying). Finally, Part 6 is based on a joint work in preparation with Zhiyan Ding, Taehee Ko, Lin Lin, Xiantao Li).