Haoya Li
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Haoya Li has a total of 19 co-authors. Here are the top co-authors by number of shared publications:
- Lexing Ying
Department of Mathematics, Stanford University, Stanford, CA 94305 USA
16 shared publications - Hongkang Ni
Institute for Computational and Mathematical Engineering Stanford University 94305 Stanford CA
10 shared publications - Inderjit S. Dhillon
University of Texas at Austin
2 shared publications Lexing Ying
2 shared publicationsHongkang Ni
1 shared publicationHsiang-Fu Yu
Amazon Search, Palo Alto, CA 94301 USA
1 shared publication
Latest Publications
- 1 April 2025
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 103 (2) , 1-23
An Analysis of Offline Model-Based Learning with Action Noise
- 1 April 2025
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 103 (2) , 1-23
An Analysis of Offline Model-Based Learning with Action Noise
- Open Access
- 2 October 2024
- Published by Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften in Quantum
- Vol. 8, 1487
Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the Hadamard test circuit structure and only requires simple classical postprocessing. QMEGS is the first algorithm to simultaneously satisfy the following two properties: (1) It can achieve the Heisenberg-limited scaling without relying on any spectral gap assumption. (2) With a positive energy gap and additional assumptions on the initial state, QMEGS can estimate all dominant eigenvalues to accuracy utilizing a significantly reduced circuit depth compared to the standard quantum phase estimation algorithm. In the most favorable scenario, the maximal runtime can be reduced to as low as . This implies that QMEGS serves as an efficient and versatile approach, achieving the best-known results for both gapped and gapless systems. Numerical results validate the efficiency of our proposed algorithm in various regimes.- 2 October 2024
- Published by Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften in Quantum
- Vol. 8, 1487
Open AccessQuantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the Hadamard test circuit structure and only requires simple classical postprocessing. QMEGS is the first algorithm to simultaneously satisfy the following two properties: (1) It can achieve the Heisenberg-limited scaling without relying on any spectral gap assumption. (2) With a positive energy gap and additional assumptions on the initial state, QMEGS can estimate all dominant eigenvalues to accuracy utilizing a significantly reduced circuit depth compared to the standard quantum phase estimation algorithm. In the most favorable scenario, the maximal runtime can be reduced to as low as . This implies that QMEGS serves as an efficient and versatile approach, achieving the best-known results for both gapped and gapless systems. Numerical results validate the efficiency of our proposed algorithm in various regimes. - Open Access
Quantum Hamiltonian Learning for the Fermi-Hubbard Model
This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve $ε$-accurate estimation for all parameters, only $\tilde{\mathcal{O}}(ε^{-1})$ total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation.Open AccessQuantum Hamiltonian Learning for the Fermi-Hubbard Model
This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve $ε$-accurate estimation for all parameters, only $\tilde{\mathcal{O}}(ε^{-1})$ total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation. - 30 April 2024
- Published by Springer Nature in Acta Applicandae Mathematicae
- Vol. 191 (1) , 1-16
Quantum Hamiltonian Learning for the Fermi-Hubbard Model
- 30 April 2024
- Published by Springer Nature in Acta Applicandae Mathematicae
- Vol. 191 (1) , 1-16
Quantum Hamiltonian Learning for the Fermi-Hubbard Model
- 20 February 2024
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 34 (1) , 764-789
Accelerating Primal-Dual Methods for Regularized Markov Decision Processes
Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow convergence due to the lack of strict convexity and concavity. To address this issue, we first introduce a new quadratically convexified primal-dual formulation. The natural gradient ascent descent of the new formulation enjoys global convergence guarantee and exponential convergence rate. We also propose a new interpolating metric that further accelerates the convergence significantly. Numerical results are provided to demonstrate the performance of the proposed methods under multiple settings.
- 20 February 2024
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 34 (1) , 764-789
Accelerating Primal-Dual Methods for Regularized Markov Decision Processes
Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow convergence due to the lack of strict convexity and concavity. To address this issue, we first introduce a new quadratically convexified primal-dual formulation. The natural gradient ascent descent of the new formulation enjoys global convergence guarantee and exponential convergence rate. We also propose a new interpolating metric that further accelerates the convergence significantly. Numerical results are provided to demonstrate the performance of the proposed methods under multiple settings.
- 11 December 2023
- Published by American Physical Society (APS) in Physical Review A
- Vol. 108 (6) , 062408
Adaptive low-depth quantum algorithms for robust multiple-phase estimation
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the idea of single-phase estimation methods by combining carefully designed signal processing routines and an adaptive determination of runtime amplifying factors. They address both the integer-power model, where the unitary is given as a black box with only integer runtime accessible, and the real-power model, where is defined through a Hamiltonian by with any real runtime allowed. These algorithms are particularly suitable for early fault-tolerant quantum computers in the following senses: (1) a minimal number of ancilla qubits are used, (2) an imperfect initial state with a significant residual is allowed, (3) the prefactor in the maximum runtime can be arbitrarily small given that the residual is sufficiently small and a gap among the dominant eigenvalues is known in advance. Even if the eigenvalue gap does not exist, the proposed RMPE algorithms can achieve the Heisenberg limit while maintaining (1) and (2).- 11 December 2023
- Published by American Physical Society (APS) in Physical Review A
- Vol. 108 (6) , 062408
Adaptive low-depth quantum algorithms for robust multiple-phase estimation
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the idea of single-phase estimation methods by combining carefully designed signal processing routines and an adaptive determination of runtime amplifying factors. They address both the integer-power model, where the unitary is given as a black box with only integer runtime accessible, and the real-power model, where is defined through a Hamiltonian by with any real runtime allowed. These algorithms are particularly suitable for early fault-tolerant quantum computers in the following senses: (1) a minimal number of ancilla qubits are used, (2) an imperfect initial state with a significant residual is allowed, (3) the prefactor in the maximum runtime can be arbitrarily small given that the residual is sufficiently small and a gap among the dominant eigenvalues is known in advance. Even if the eigenvalue gap does not exist, the proposed RMPE algorithms can achieve the Heisenberg limit while maintaining (1) and (2).- Open Access
- 6 November 2023
- Published by Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften in Quantum
- Vol. 7, 1165
On low-depth algorithms for quantum phase estimation
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.
- 6 November 2023
- Published by Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften in Quantum
- Vol. 7, 1165
Open AccessOn low-depth algorithms for quantum phase estimation
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.
- Open Access
On low-depth algorithms for quantum phase estimation
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.
Open AccessOn low-depth algorithms for quantum phase estimation
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.
- Open Access
On adaptive low-depth quantum algorithms for robust multiple-phase estimation
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the idea of single-phase estimation methods by combining carefully designed signal processing routines and an adaptive determination of runtime amplifying factors. They address both the {\em integer-power} model, where the unitary $U$ is given as a black box with only integer runtime accessible, and the {\em real-power} model, where $U$ is defined through a Hamiltonian $H$ by $U = \exp(-2π\mathrm{i} H)$ with any real runtime allowed. These algorithms are particularly suitable for early fault-tolerant quantum computers in the following senses: (1) a minimal number of ancilla qubits are used, (2) an imperfect initial state with a significant residual is allowed, (3) the prefactor in the maximum runtime can be arbitrarily small given that the residual is sufficiently small and a gap among the dominant eigenvalues is known in advance. Even if the eigenvalue gap does not exist, the proposed RMPE algorithms can achieve the Heisenberg limit while maintaining (1) and (2).Open AccessOn adaptive low-depth quantum algorithms for robust multiple-phase estimation
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the idea of single-phase estimation methods by combining carefully designed signal processing routines and an adaptive determination of runtime amplifying factors. They address both the {\em integer-power} model, where the unitary $U$ is given as a black box with only integer runtime accessible, and the {\em real-power} model, where $U$ is defined through a Hamiltonian $H$ by $U = \exp(-2π\mathrm{i} H)$ with any real runtime allowed. These algorithms are particularly suitable for early fault-tolerant quantum computers in the following senses: (1) a minimal number of ancilla qubits are used, (2) an imperfect initial state with a significant residual is allowed, (3) the prefactor in the maximum runtime can be arbitrarily small given that the residual is sufficiently small and a gap among the dominant eigenvalues is known in advance. Even if the eigenvalue gap does not exist, the proposed RMPE algorithms can achieve the Heisenberg limit while maintaining (1) and (2). - 26 September 2023
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 45 (5) , A2585-A2609
Approximate Newton Policy Gradient Algorithms
Policy gradient algorithms have been widely applied to Markov decision processes and reinforcement learning problems in recent years. Regularization with various entropy functions is often used to encourage exploration and improve stability. This paper proposes an approximate Newton method for the policy gradient algorithm with entropy regularization. In the case of Shannon entropy, the resulting algorithm reproduces the natural policy gradient algorithm. For other entropy functions, this method results in brand-new policy gradient algorithms. We prove that all these algorithms enjoy Newton-type quadratic convergence and that the corresponding gradient flow converges globally to the optimal solution. We use synthetic and industrial-scale examples to demonstrate that the proposed approximate Newton method typically converges in single-digit iterations, often orders of magnitude faster than other state-of-the-art algorithms.
- 26 September 2023
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 45 (5) , A2585-A2609
Approximate Newton Policy Gradient Algorithms
Policy gradient algorithms have been widely applied to Markov decision processes and reinforcement learning problems in recent years. Regularization with various entropy functions is often used to encourage exploration and improve stability. This paper proposes an approximate Newton method for the policy gradient algorithm with entropy regularization. In the case of Shannon entropy, the resulting algorithm reproduces the natural policy gradient algorithm. For other entropy functions, this method results in brand-new policy gradient algorithms. We prove that all these algorithms enjoy Newton-type quadratic convergence and that the corresponding gradient flow converges globally to the optimal solution. We use synthetic and industrial-scale examples to demonstrate that the proposed approximate Newton method typically converges in single-digit iterations, often orders of magnitude faster than other state-of-the-art algorithms.