arXiv subjects

Tongyang Li

Publications and source records attributed to Tongyang Li.

At least 37 records · Page 2Linked to original sources

arXiv2026

DC-MBQC: A Distributed Compilation Framework for Measurement-Based Quantum Computing

Distributed quantum computing (DQC) is a promising technique for scaling up quantum systems. While significant progress has been made in DQC for quantum circuit models, there exists much less research on DQC for measurement-based quantum computing (MBQC), which is a universal quantum computing model that is essentially different from the circuit model and particularly well-suited to photonic quantum platforms. In this paper, we propose DC-MBQC, the first distributed quantum compilation framework tailored for MBQC. We identify and address two key challenges in enabling DQC for MBQC. First, for task allocation among quantum processing units (QPUs), we develop an adaptive graph partitioning algorithm that preserves the structure of the graph state while balancing the workload across QPUs. Second, for inter-QPU communication, we introduce the layer scheduling problem and propose an algorithm to solve it. Regrading realistic hardware requirements, we optimize the execution time of running quantum programs and the corresponding required photon lifetime to avoid fatal failures caused by photon loss. Our experiments demonstrate a $7.46\times$ improvement on required photon lifetime and $6.82\times$ speedup with 8 fully-connected QPUs, which further confirm the advantage of distributed quantum computing in photonic systems. The source code is publicly available at https://github.com/qfcwj/DC-MBQC.

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arXiv2025

QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design

Quantum computing is an emerging field recognized for the significant speedup it offers over classical computing through quantum algorithms. However, designing and implementing quantum algorithms pose challenges due to the complex nature of quantum mechanics and the necessity for precise control over quantum states. Despite the significant advancements in AI, there has been a lack of datasets specifically tailored for this purpose. In this work, we introduce QCircuitBench, the first benchmark dataset designed to evaluate AI's capability in designing and implementing quantum algorithms using quantum programming languages. Unlike using AI for writing traditional codes, this task is fundamentally more complicated due to highly flexible design space. Our key contributions include: 1. A general framework which formulates the key features of quantum algorithm design for Large Language Models. 2. Implementations for quantum algorithms from basic primitives to advanced applications, spanning 3 task suites, 25 algorithms, and 120,290 data points. 3. Automatic validation and verification functions, allowing for iterative evaluation and interactive reasoning without human inspection. 4. Promising potential as a training dataset through preliminary fine-tuning results. We observed several interesting experimental phenomena: LLMs tend to exhibit consistent error patterns, and fine-tuning does not always outperform few-shot learning. In all, QCircuitBench is a comprehensive benchmark for LLM-driven quantum algorithm design, and it reveals limitations of LLMs in this domain.

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arXiv2025

Fast-forwardable Lindbladians imply quantum phase estimation

Quantum phase estimation (QPE) and Lindbladian dynamics are both foundational in quantum information science and central to quantum algorithm design. In this work, we bridge these two concepts: certain simple Lindbladian processes can be adapted to perform QPE-type tasks. However, unlike QPE, which achieves Heisenberg-limit scaling, these Lindbladian evolutions are restricted to standard quantum limit complexity. This indicates that, different from Hamiltonian dynamics, the natural dissipative evolution speed of such Lindbladians does not saturate the fundamental quantum limit, thereby suggesting the potential for quadratic fast-forwarding. We confirm this by presenting a quantum algorithm that simulates these Lindbladians for time $t$ within an error $\varepsilon$ using $\mathcal{O}\left(\sqrt{t\log(\varepsilon^{-1})}\right)$ cost, whose mechanism is fundamentally different from the fast-forwarding examples of Hamiltonian dynamics. As a bonus, this fast-forwarded simulation naturally serves as a new Heisenberg-limit QPE algorithm. Therefore, our work explicitly bridges the standard quantum limit-Heisenberg limit transition to the fast-forwarding of dissipative dynamics. We also adopt our fast-forwarding algorithm for efficient Gibbs state preparation and demonstrate the counter-intuitive implication: the allowance of a quadratically accelerated decoherence effect under arbitrary Pauli noise.

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arXiv2025

Near-Optimal Quantum Algorithms for Computing (Coarse) Correlated Equilibria of General-Sum Games

Computing Nash equilibria of zero-sum games in classical and quantum settings is extensively studied. For general-sum games, computing Nash equilibria is PPAD-hard and the computing of a more general concept called correlated equilibria has been widely explored in game theory. In this paper, we initiate the study of quantum algorithms for computing $\varepsilon$-approximate correlated equilibria (CE) and coarse correlated equilibria (CCE) in multi-player normal-form games. Our approach utilizes quantum improvements to the multi-scale Multiplicative Weight Update (MWU) method for CE calculations, achieving a query complexity of $\tilde{O}(m\sqrt{n})$ for fixed $\varepsilon$. For CCE, we extend techniques from quantum algorithms for zero-sum games to multi-player settings, achieving query complexity $\tilde{O}(m\sqrt{n}/\varepsilon^{2.5})$. Both algorithms demonstrate a near-optimal scaling in the number of players $m$ and actions $n$, as confirmed by our quantum query lower bounds.

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arXiv2025

Randomized Quantum Singular Value Transformation

We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework for many quantum algorithms. Standard implementations of QSVT rely on block encodings of the Hamiltonian, which are costly to construct, requiring a logarithmic number of ancilla qubits, intricate multi-qubit control, and circuit depth scaling linearly with the number of Hamiltonian terms. In contrast, our algorithms use only a single ancilla qubit and entirely avoid block encodings. We develop two methods: (i) a direct randomization of QSVT, where block encodings are replaced by importance sampling, and (ii) an approach that integrates qDRIFT into the generalized quantum signal processing framework, with the dependence on precision exponentially improved through classical extrapolation. Both algorithms achieve gate complexity independent of the number of Hamiltonian terms, a hallmark of randomized methods, while incurring only quadratic dependence on the degree of the target polynomial. We identify natural parameter regimes where our methods outperform even standard QSVT, making them promising for early fault-tolerant quantum devices. We also establish a fundamental lower bound showing that the quadratic dependence on the polynomial degree is optimal within this framework. We apply our framework to two fundamental tasks: solving quantum linear systems and estimating ground-state properties of Hamiltonians, obtaining polynomial advantages over prior randomized algorithms. Finally, we benchmark our ground-state property estimation algorithm on electronic structure Hamiltonians and the transverse-field Ising model with long-range interactions. In both cases, our approach outperforms prior work by several orders of magnitude in circuit depth, establishing randomized QSVT as a practical and resource-efficient alternative for early fault-tolerant quantum devices.

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arXiv2025

Efficient Classical Sampling from Gaussian Boson Sampling Distributions on Unweighted Graphs

Gaussian Boson Sampling (GBS) is a promising candidate for demonstrating quantum computational advantage and can be applied to solving graph-related problems. In this work, we propose Markov chain Monte Carlo-based algorithms to sample from GBS distributions on undirected, unweighted graphs. Our main contribution is a double-loop variant of Glauber dynamics, whose stationary distribution matches the GBS distribution. We further prove that it mixes in polynomial time for dense graphs using a refined canonical path argument. Numerically, we conduct experiments on unweighted graphs with 256 vertices, larger than the scales in former GBS experiments as well as classical simulations. In particular, we show that both the single-loop and double-loop Glauber dynamics improve the performance of original random search and simulated annealing algorithms for the max-Hafnian and densest $k$-subgraph problems up to 10$\times$. Overall, our approach offers both theoretical guarantees and practical advantages for efficient classical sampling from GBS distributions on unweighted graphs.

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arXiv2025

Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications

The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well known that MMWU achieves the minimax-optimal regret bound of $O(\sqrt{T\log d})$, where $T$ is the time horizon. In this paper, we present an improved algorithm achieving the instance-optimal regret bound of $O(\sqrt{T\cdot S(X||d^{-1}I_d)})$, where $X$ is the comparator in the regret, $I_d$ is the identity matrix, and $S(\cdot||\cdot)$ denotes the quantum relative entropy. Furthermore, our algorithm has the same computational complexity as MMWU, indicating that the improvement in the regret bound is ``free''. Technically, we first develop a general potential-based framework for matrix LEA, with MMWU being its special case induced by the standard exponential potential. Then, the crux of our analysis is a new ``one-sided'' Jensen's trace inequality built on a Laplace transform technique, which allows the application of general potential functions beyond exponential to matrix LEA. Our algorithm is finally induced by an optimal potential function from the vector LEA problem, based on the imaginary error function. Complementing the above, we provide a memory lower bound for matrix LEA, and explore the applications of our algorithm in quantum learning theory. We show that it outperforms the state of the art for learning quantum states corrupted by depolarization noise, random quantum states, and Gibbs states. In addition, applying our algorithm to linearized convex losses enables predicting nonlinear quantum properties, such as purity, quantum virtual cooling, and Rényi-$2$ correlation.

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arXiv2025

Quantum singular value transformation without block encodings: Near-optimal complexity with minimal ancilla

We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block encoding, incurring an intrinsic $O(\log L)$ ancilla overhead and circuit depth $\widetilde{O}(L dλ)$ for polynomial transformations of a Hamiltonian $H=\sum_{k=1}^L H_k$, where $d$ is the polynomial degree and $λ=\sum_{k}\|H_k\|$. We introduce a simple yet powerful approach that utilizes only basic Hamiltonian simulation techniques, namely, Trotter methods, to: (i) eliminate the need for block encoding, (ii) reduce the ancilla overhead to only a single qubit, and (iii) still maintain near-optimal complexity. Our method achieves a circuit depth of $\widetilde{O}(L(dλ_{\mathrm{comm}})^{1+o(1)})$, without requiring any complicated multi-qubit controlled gates. Moreover, $λ_{\mathrm{comm}}$ depends on the nested commutators of the terms of $H$ and can be substantially smaller than $λ$ for many physically relevant Hamiltonians, a feature absent in standard QSVT. To achieve these results, we make use of Richardson extrapolation in a novel way, systematically eliminating errors in any interleaved sequence of arbitrary unitaries and Hamiltonian evolution operators, thereby establishing a general framework that encompasses QSVT but is more broadly applicable. As applications, we develop end-to-end quantum algorithms for solving linear systems and estimating ground state properties of Hamiltonians, both achieving near-optimal complexity without relying on oracular access. Overall, our results establish a new framework for quantum algorithms, significantly reducing hardware overhead while maintaining near-optimal performance, with implications for both near-term and fault-tolerant quantum computing.

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arXiv2025

Quantum Algorithms for Bandits with Knapsacks with Improved Regret and Time Complexities

Bandits with knapsacks (BwK) constitute a fundamental model that combines aspects of stochastic integer programming with online learning. Classical algorithms for BwK with a time horizon $T$ achieve a problem-independent regret bound of ${O}(\sqrt{T})$ and a problem-dependent bound of ${O}(\log T)$. In this paper, we initiate the study of the BwK model in the setting of quantum computing, where both reward and resource consumption can be accessed via quantum oracles. We establish both problem-independent and problem-dependent regret bounds for quantum BwK algorithms. For the problem-independent case, we demonstrate that a quantum approach can improve the classical regret bound by a factor of $(1+\sqrt{B/\mathrm{OPT}_\mathrm{LP}})$, where $B$ is budget constraint in BwK and $\mathrm{OPT}_{\mathrm{LP}}$ denotes the optimal value of a linear programming relaxation of the BwK problem. For the problem-dependent setting, we develop a quantum algorithm using an inexact quantum linear programming solver. This algorithm achieves a quadratic improvement in terms of the problem-dependent parameters, as well as a polynomial speedup of time complexity on problem's dimensions compared to classical counterparts. Compared to previous works on quantum algorithms for multi-armed bandits, our study is the first to consider bandit models with resource constraints and hence shed light on operations research.

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arXiv2025

Quantum Langevin Dynamics for Optimization

We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms. Specifically, we examine the dynamics of a system coupled with an infinite heat bath. This interaction induces both random quantum noise and a deterministic damping effect to the system, which nudge the system towards a steady state that hovers near the global minimum of objective functions. We theoretically prove the convergence of QLD in convex landscapes, demonstrating that the average energy of the system can approach zero in the low temperature limit with an exponential decay rate correlated with the evolution time. Numerically, we first show the energy dissipation capability of QLD by retracing its origins to spontaneous emission. Furthermore, we conduct detailed discussion of the impact of each parameter. Finally, based on the observations when comparing QLD with classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by making temperature and $\hbar$ time-dependent parameters, which can be theoretically proven to converge better than the time-independent case and also outperforms a series of state-of-the-art quantum and classical optimization algorithms in many non-convex landscapes.

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arXiv2025

Quantum Approximate Optimization Algorithms for Maximum Cut on Low-Girth Graphs

Maximum cut (MaxCut) on graphs is a classic NP-hard problem. In quantum computing, Farhi, Gutmann, and Goldstone proposed the Quantum Approximate Optimization Algorithm (QAOA) for solving the MaxCut problem. Its guarantee on cut fraction (the fraction of edges in the output cut over all edges) was mainly studied for high-girth graphs, i.e., graphs with only long cycles. On the other hand, low-girth graphs are ubiquitous in theoretical computer science, including expander graphs being outstanding examples with wide applications in theory and beyond. In this paper, we apply QAOA to MaxCut on a set of expander graphs proposed by Mohanty and O'Donnell known as additive product graphs. Additionally, we apply multi-angle QAOA (ma-QAOA) to better utilize the graph structure of additive product graphs in ansatz design. In theory, we derive an iterative formula to calculate the expected cut fraction of such graphs. This formula also extends to the quantum MaxCut problem. On the other hand, we conduct numerical experiments to compare between best-known classical local algorithms and QAOA with constant depth. Our results demonstrate that QAOA outperforms the best-known classical algorithms by 0.3% to 5.2% on several additive product graphs, while ma-QAOA further enhances this advantage by an additional 0.6% to 2.5%. In particular, we observe cases that ma-QAOA exhibits superiority over best-known classical algorithms but QAOA does not. Furthermore, we extend our experiments to planar graphs such as tiling grid graphs, where QAOA also demonstrates an advantage.

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arXiv2024

Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games

We propose the first online quantum algorithm for solving zero-sum games with $\widetilde O(1)$ regret under the game setting. Moreover, our quantum algorithm computes an $\varepsilon$-approximate Nash equilibrium of an $m \times n$ matrix zero-sum game in quantum time $\widetilde O(\sqrt{m+n}/\varepsilon^{2.5})$. Our algorithm uses standard quantum inputs and generates classical outputs with succinct descriptions, facilitating end-to-end applications. Technically, our online quantum algorithm "quantizes" classical algorithms based on the optimistic multiplicative weight update method. At the heart of our algorithm is a fast quantum multi-sampling procedure for the Gibbs sampling problem, which may be of independent interest.

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arXiv2024

Adaptive Online Learning of Quantum States

The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements, environmental noise, or inherent Hamiltonian state transitions. This paper leverages techniques from adaptive online learning to keep pace with such state changes. The key metrics considered for learning in these mutable environments are enhanced notions of regret, specifically adaptive and dynamic regret. We present adaptive and dynamic regret bounds for online shadow tomography, which are polynomial in the number of qubits and sublinear in the number of measurements. To support our theoretical findings, we include numerical experiments that validate our proposed models.

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arXiv2024

Exponential speedups for quantum walks in random hierarchical graphs

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into "supervertices" which are arranged according to a $d$-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification.

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arXiv2024

Complexity of Digital Quantum Simulation in the Low-Energy Subspace: Applications and a Lower Bound

Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert space. In this paper, we systematically investigate the complexity of digital quantum simulation based on product formulas in the low-energy subspace. We show that the simulation error depends on the effective low-energy norm of the Hamiltonian for a variety of digital quantum simulation algorithms and quantum systems, allowing improvements over the previous complexities for full unitary simulations even for imperfect state preparations due to thermalization. In particular, for simulating spin models in the low-energy subspace, we prove that randomized product formulas such as qDRIFT and random permutation require smaller Trotter numbers. Such improvement also persists in symmetry-protected digital quantum simulations. We prove a similar improvement in simulating the dynamics of power-law quantum interactions. We also provide a query lower bound for general digital quantum simulations in the low-energy subspace.

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arXiv2024

Provably Efficient Exploration in Quantum Reinforcement Learning with Logarithmic Worst-Case Regret

While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited. In particular, it remains elusive how to design provably efficient quantum RL algorithms that can address the exploration-exploitation trade-off. To this end, we propose a novel UCRL-style algorithm that takes advantage of quantum computing for tabular Markov decision processes (MDPs) with $S$ states, $A$ actions, and horizon $H$, and establish an $\mathcal{O}(\mathrm{poly}(S, A, H, \log T))$ worst-case regret for it, where $T$ is the number of episodes. Furthermore, we extend our results to quantum RL with linear function approximation, which is capable of handling problems with large state spaces. Specifically, we develop a quantum algorithm based on value target regression (VTR) for linear mixture MDPs with $d$-dimensional linear representation and prove that it enjoys $\mathcal{O}(\mathrm{poly}(d, H, \log T))$ regret. Our algorithms are variants of UCRL/UCRL-VTR algorithms in classical RL, which also leverage a novel combination of lazy updating mechanisms and quantum estimation subroutines. This is the key to breaking the $Ω(\sqrt{T})$-regret barrier in classical RL. To the best of our knowledge, this is the first work studying the online exploration in quantum RL with provable logarithmic worst-case regret.

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arXiv2024

Quantum Algorithms and Lower Bounds for Finite-Sum Optimization

Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum computing. Specifically, let $f_1,\ldots,f_n\colon\mathbb{R}^d\to\mathbb{R}$ be $\ell$-smooth convex functions and $ψ\colon\mathbb{R}^d\to\mathbb{R}$ be a $μ$-strongly convex proximal function. The goal is to find an $ε$-optimal point for $F(\mathbf{x})=\frac{1}{n}\sum_{i=1}^n f_i(\mathbf{x})+ψ(\mathbf{x})$. We give a quantum algorithm with complexity $\tilde{O}\big(n+\sqrt{d}+\sqrt{\ell/μ}\big(n^{1/3}d^{1/3}+n^{-2/3}d^{5/6}\big)\big)$, improving the classical tight bound $\tildeΘ\big(n+\sqrt{n\ell/μ}\big)$. We also prove a quantum lower bound $\tildeΩ(n+n^{3/4}(\ell/μ)^{1/4})$ when $d$ is large enough. Both our quantum upper and lower bounds can extend to the cases where $ψ$ is not necessarily strongly convex, or each $f_i$ is Lipschitz but not necessarily smooth. In addition, when $F$ is nonconvex, our quantum algorithm can find an $ε$-critial point using $\tilde{O}(n+\ell(d^{1/3}n^{1/3}+\sqrt{d})/ε^2)$ queries.

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arXiv2024

Efficient Optimal Control of Open Quantum Systems

The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables. At the technical level, we provide the first (to the best of our knowledge) simulation algorithm for time-dependent Lindbladians with an $\ell_1$-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest.

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