arXiv subjects

Xiaoming Sun

Publications and source records attributed to Xiaoming Sun.

At least 37 records · Page 2Linked to original sources

arXiv2025

Practical Homodyne Shadow Estimation

Shadow estimation provides an efficient framework for estimating observable expectation values using randomized measurements. While originally developed for discrete-variable systems, its recent extensions to continuous-variable (CV) quantum systems face practical limitations due to idealized assumptions of continuous phase modulation and infinite measurement resolution. In this work, we develop a practical shadow estimation protocol for CV systems using discretized homodyne detection with a finite number of phase settings and quadrature bins. We construct an unbiased estimator for the quantum state and establish both sufficient conditions and necessary conditions for informational completeness within a truncated Fock space up to $n_{\mathrm{max}}$ photons. We further provide a comprehensive variance analysis, showing that the shadow norm scales as $\mathcal{O}(n_{\mathrm{max}}^4)$, improving upon previous $\mathcal{O}(n_{\mathrm{max}}^{13/3})$ bounds. Our work bridges the gap between theoretical shadow estimation and experimental implementations, enabling robust and scalable quantum state characterization in realistic CV systems.

quant-ph↗

arXiv2025

Almost Optimal Synthesis of Reversible Function in Qudit Model

Quantum oracles are widely adopted in problems, like query oracle in Grover's algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a given classical function, emerges as a fundamental component in the design and construction of quantum algorithms. Devising methods to optimally implement the bit-flip oracle essentially translates to the efficient synthesis of reversible functions. Prior research has primarily focused on the qubit model, leaving the higher dimensional systems, i.e. qudit model, largely unexplored. By allowing more than two computational bases, qudit model can fully utilize the multi-level nature of the underlying physical mechanism. We propose a method to synthesize even permutations in $A_{d^{n}}$ using $Θ(d)$ $(n - 1)$-qudit sub-circuits, which achieve asymptotic optimality in the count of sub-circuits. Moreover, we introduce a technique for synthesizing reversible functions employing $O\left( n d^{n} \right)$ gates and only a single ancilla. This is asymptotically tight in terms of $d$ and asymptotically almost tight in terms of $n$.

quant-ph↗

arXiv2025

A Unified Complexity-Algorithm Account of Constant-Round QAOA Expectation Computation

The Quantum Approximate Optimization Algorithm (QAOA) is widely studied for combinatorial optimization and has achieved significant advances both in theoretical guarantees and practical performance, yet for general combinatorial optimization problems the expected performance and classical simulability of fixed-round QAOA remain unclear. Focusing on Max-Cut, we first show that for general graphs and any fixed round $p\ge2$, exactly evaluating the expectation of fixed-round QAOA at prescribed angles is $\mathrm{NP}$-hard, and that approximating this expectation within additive error $2^{-O(n)}$ in the number $n$ of vertices is already $\mathrm{NP}$-hard. To evaluate the expected performance of QAOA, we propose a dynamic programming algorithm leveraging tree decomposition. As a byproduct, when the $p$-local treewidth grows at most logarithmically with the number of vertices, this yields a polynomial-time \emph{exact} evaluation algorithm in the graph size $n$. Beyond Max-Cut, we extend the framework to general Binary Unconstrained Combinatorial Optimization (BUCO). Finally, we provide reproducible evaluations for rounds up to $p=3$ on representative structured families, including the generalized Petersen graph $GP(15,2)$, double-layer triangular 2-lifts, and the truncated icosahedron graph $C_{60}$, and report cut ratios while benchmarking against locality-matched classical baselines.

quant-ph↗

arXiv2025

Logical operations with a dynamical qubit in Floquet-Bacon-Shor code

Quantum error correction (QEC) protects quantum systems against inevitable noises and control inaccuracies, providing a pathway towards fault-tolerant (FT) quantum computation. Stabilizer codes, including surface code and color code, have long been the focus of research and have seen significant experimental progress in recent years. Recently proposed time-dynamical QEC, including Floquet codes and generalized time-dynamical code implementations, opens up new opportunities for FT quantum computation. By employing a periodic schedule of low-weight parity checks, Floquet codes can generate additional dynamical logical qubits, offering enhanced error correction capabilities and potentially higher code performance. Here, we experimentally implement the Floquet-Bacon-Shor code on a superconducting quantum processor. We encode a dynamical logical qubit within a $3\times 3$ lattice of data qubits, alongside a conventional static logical qubit. We demonstrate FT encoding and measurement of the two-qubit logical states, and stabilize these states using repeated error detection. We showcase universal single-qubit logical gates on the dynamical qubit. Furthermore, by implementing a logical CNOT gate, we entangle the dynamical and static logical qubits, generating an error-detected logical Bell state with a fidelity of 75.9\%. Our results highlight the potential of Floquet codes for resource-efficient FT quantum computation.

quant-ph↗

arXiv2025

Quantum-Trajectory-Inspired Lindbladian Simulation

Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. We introduce a new approximation channel for short-time evolution, inspired by the quantum trajectory method, which underpins the efficiency of our algorithms. The first algorithm achieves a gate complexity independent of the number of jump operators, $m$, marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time $t$ and precision $ε$ and introduces only an additional $\tilde{O}(m)$ factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an $\tilde O(m^2)$ factor. The improvement stems from the integration of the new approximation channel with a novel structured linear combination of unitaries method. In both our algorithms, the reduction of dependence on $m$ significantly enhances the efficiency of simulating practical dissipative processes characterized by a large number of jump operators.

quant-ph↗

arXiv2025

Quantum circuit synthesis with SQiSW

The primary objective of quantum circuit synthesis is to efficiently and accurately realize specific quantum algorithms or operations utilizing a predefined set of quantum gates, while also optimizing the circuit size. It holds a pivotal position in Noisy Intermediate-Scale Quantum (NISQ) computation. Historically, most synthesis efforts have predominantly utilized CNOT or CZ gates as the 2-qubit gates. However, the SQiSW gate, also known as the square root of iSWAP gate, has garnered considerable attention due to its outstanding experimental performance with low error rates and high efficiency in 2-qubit gate synthesis. In this paper, we investigate the potential of the SQiSW gate in various synthesis problems by utilizing only the SQiSW gate along with arbitrary single-qubit gates, while optimizing the overall circuit size. For exact synthesis, the upper bound of SQiSW gates to synthesize arbitrary 3-qubit and $n$-qubit gates are 24 and $\frac{139}{192}4^n(1+o(1))$ respectively, which relies on the properties of SQiSW gate in Lie theory and Quantum Shannon Decomposition. We also introduce an exact synthesis scheme for Toffoli gate using only 8 SQiSW gates, which is grounded in numerical observation. More generally, with respect to numerical approximations, we provide a theoretical analysis of a pruning algorithm to reduce the size of the searching space in numerical experiment to $\frac{1}{12}+o(1)$ of previous size, helping us reach the result that 11 SQiSW gates are enough in arbitrary 3-qubit gates synthesis up to an acceptable numerical error.

quant-ph↗

arXiv2025

Toward Minimum Graphic Parity Networks

Quantum circuits composed of CNOT and $R_z$ are fundamental building blocks of many quantum algorithms, so optimizing the synthesis of such quantum circuits is crucial. We address this problem from a theoretical perspective by studying the graphic parity network synthesis problem. A graphic parity network for a graph $G$ is a quantum circuit composed solely of CNOT gates where each edge of $G$ is represented in the circuit, and the final state of the wires matches the original input. We aim to synthesize graphic parity networks with the minimum number of gates, specifically for quantum algorithms addressing combinatorial optimization problems with Ising formulations. We demonstrate that a graphic parity network for a connected graph with $n$ vertices and $m$ edges requires at least $m+n-1$ gates. This lower bound can be improved to $m+Ω(m) = m+Ω(n^{1.5})$ when the shortest cycle in the graph has a length of at least five. We complement this result with a simple randomized algorithm that synthesizes a graphic parity network with expected $m + O(n^{1.5}\sqrt{\log n})$ gates. Additionally, we begin exploring connected graphs that allow for graphic parity networks with exactly $m+n-1$ gates. We conjecture that all such graphs belong to a newly defined graph class. Furthermore, we present a linear-time algorithm for synthesizing minimum graphic parity networks for graphs within this class. However, this graph class is not closed under taking induced subgraphs, and we show that recognizing it is $\textsf{NP}$-complete, which is complemented with a fixed-parameter tractable algorithm parameterized by the treewidth.

quant-ph↗

arXiv2025

Sampling permutations satisfying constraints within the lopsided local lemma regime

Sampling a random permutation with restricted positions, or equivalently approximating the permanent of a 0-1 matrix, is a fundamental problem in computer science, with several notable results achieved over the years. However, existing algorithms typically exhibit high computational complexity. Achieving the optimal running time remains elusive, even for nontrivial subsets of the problem. Furthermore, existing algorithms primarily focus on a single permutation, leaving many combinatorial problems involving multiple constrained permutations unaddressed. For a single permutation, we achieve the optimal running time $O(n^2)$ for approximating the permanent of a very dense $n \times n$ 0-1 matrix, where each row and column contains at most $\sqrt{(n-2)/20}$ zeros. This result serves as a fundamental building block in our sampling algorithm for multiple permutations. We further introduce a general model called permutations with disjunctive constraints (PDC) for handling multiple constrained permutations. We propose a novel Markov chain-based algorithm for sampling nearly uniform solutions of PDC within a lopsided Lovász Local Lemma (LLL) regime. For uniform PDC formulas, where all constraints are of the same width and all permutations are of the same size, our algorithm runs in nearly linear time with respect to the number of variables. Previous approaches for sampling LLL relied on the variable model. In contrast, the sampling problem of PDC encounters a fundamental challenge: the random variables within each permutation in the joint probability space are not mutually independent, leading to long-range correlations. To tackle this challenge, we introduce a novel sampling framework called correlated factorization and a new concept in the path coupling analysis, termed the inactive vertex.

cs.DS↗

arXiv2025

Stochastic Quantum Hamiltonian Descent

Stochastic Gradient Descent (SGD) and its variants underpin modern machine learning by enabling efficient optimization of large-scale models. However, their local search nature limits exploration in complex landscapes. In this paper, we introduce Stochastic Quantum Hamiltonian Descent (SQHD), a quantum optimization algorithm that integrates the computational efficiency of stochastic gradient methods with the global exploration power of quantum dynamics. We propose a Lindbladian dynamics as the quantum analogue of continuous-time SGD. We further propose a discrete-time gate-based algorithm that approximates these dynamics while avoiding direct Lindbladian simulation, enabling practical implementation on near-term quantum devices. We rigorously prove the convergence of SQHD for convex and smooth objectives. Numerical experiments demonstrate that SQHD also exhibits advantages in non-convex optimization. All these results highlight its potential for quantum-enhanced machine learning.

quant-ph↗

arXiv2025

Quantum circuit synthesis with qudit phase gadget method

Current quantum devices have unutilized high-level quantum resources. More and more attention has been paid to the qudit quantum systems with larger than two dimensions to maximize the potential computing power of quantum computation. Then, a natural problem arises: How do we implement quantum algorithms on qudit quantum systems? In this work, we propose a novel qudit phase gadget method for synthesizing the qudit diagonal unitary matrices. This method is suitable for the Noisy Intermediate-Scale Quantum (NISQ) and fault-tolerant eras due to its versatility in different connectivity architectures and the optimality of its resource consumption. The method can work on any connectivity architecture with asymptotic optimal circuit depth and size. For a 10-qutrit diagonal unitary, our algorithm reduces the circuit depth form about 100000 to 500 with 300 ancillary qutrits. Further, this method can be promoted to different quantum circuit synthesis problems, such as quantum state preparation problems, general unitary synthesis problems, etc.

quant-ph↗

arXiv2025

Constant-Depth Quantum Circuits for Arbitrary Quantum State Preparation via Measurement and Feedback

The optimization of quantum circuit depth is crucial for practical quantum computing, as limited coherence times and error-prone operations constrain executable algorithms. Measurement and feedback operations are fundamental in quantum computing (e.g., quantum error correction); we develop a framework using them to achieve constant-depth implementations of essential quantum tasks. This includes preparing arbitrary quantum states with constant-depth circuits through measurement and feedback, breaking the linear-depth lower bound that is required without these operations. Our result paves the way for general quantum circuit compression using measurement and feedback.

quant-ph↗

arXiv2024

Quantum Walk Search on Complete Multipartite Graph with Multiple Marked Vertices

Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases of complete multipartite graphs are probed in this paper, and in both cases, each set consists of an equal number of vertices. We employ the coined quantum walk model and achieve quadratic speedup with a constant probability of finding a marked vertex. Furthermore, we investigate the robust quantum walk of two cases and demonstrate that even with an unknown number of marked vertices, it is still possible to achieve a quadratic speedup compared to classical algorithms and the success probability oscillates within a small range close to 1. This work addresses the overcooking problem in quantum walk search algorithms on some complete multipartite graphs. We also provide the numerical simulation and circuit implementation of our quantum algorithm.

quant-ph↗

arXiv2024

Quantum Lovász Local Lemma: Shearer's Bound is Tight

The Lovász Local Lemma (LLL) is a very powerful tool in combinatorics and probability theory to show the possibility of avoiding all bad events under some weakly dependent conditions. In a seminal paper, Ambainis, Kempe, and Sattath (JACM 2012) introduced a quantum version LLL (QLLL) which shows the possibility of avoiding all ``bad" Hamiltonians under some weakly dependent condition, and applied QLLL to the random k-QSAT problem. Sattath, Morampudi, Laumann, and Moessner (PNAS 2015) extended Ambainis, Kempe, and Sattath's result and showed that Shearer's bound is a sufficient condition for QLLL, and conjectured that Shearer's bound is indeed the tight condition for QLLL. In this paper, we affirm this conjecture. Precisely, we prove that Shearer's bound is tight for QLLL, i.e., the relative dimension of the smallest satisfying subspace is completely characterized by the independent set polynomial. Our result implies the tightness of Gilyén and Sattath's algorithm (FOCS 2017), and also implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits (Sattath, Morampudi, Laumann and Moessner, PNAS 2015). The commuting LLL (CLLL), which focuses on commuting local Hamiltonians, is also investigated here. We prove that the tight regions of CLLL and QLLL are different in general. This result indicates that it is possible to design an algorithm for CLLL which is still efficient beyond Shearer's bound.

cs.CC↗

arXiv2024

Towards determining the presence of barren plateaus in some chemically inspired variational quantum algorithms

In quantum chemistry, the variational quantum eigensolver (VQE) is a promising algorithm for molecular simulations on near-term quantum computers. However, VQEs using hardware-efficient circuits face scaling challenges due to the barren plateau problem. This raises the question of whether chemically inspired circuits from unitary coupled cluster (UCC) methods can avoid this issue. Here we provide theoretical evidence indicating they may not. By examining alternated dUCC ansätze and relaxed Trotterized UCC ansätze, we find that in the infinite depth limit, a separation occurs between particle-hole one- and two-body unitary operators. While one-body terms yield a polynomially concentrated energy landscape, adding two-body terms leads to exponential concentration. Numerical simulations support these findings, suggesting that popular 1-step Trotterized unitary coupled-cluster with singles and doubles (UCCSD) ansätze may not scale. Our results emphasize the link between trainability and circuit expressiveness, raising doubts about VQEs' ability to surpass classical methods.

quant-ph↗

arXiv2024

Quantum multi-row iteration algorithm for linear systems with non-square coefficient matrices

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms addressing non-square matrices. Towards this kind of problems defined by $ Ax = b $ where $ A $$ \in\mathbb{R}^{m \times n} $, we propose a quantum algorithm inspired by the classical multi-row iteration method and provide an explicit quantum circuit based on the quantum comparator and Quantum Random Access Memory (QRAM). The time complexity of our quantum multi-row iteration algorithm is $ O(K \log m) $, with $ K $ representing the number of iteration steps, which demonstrates an exponential speedup compared to the classical version. Based on the convergence of the classical multi-row iteration algorithm, we prove that our quantum algorithm converges faster than the quantum one-row iteration algorithm presented in [Phys. Rev. A, 101, 022322 (2020)]. Moreover, our algorithm places less demand on the coefficient matrix, making it suitable for solving inconsistent systems and quadratic optimization problems.

quant-ph↗

arXiv2024

Quantum Byzantine Agreement Against Full-information Adversary

We exhibit that, when given a classical Byzantine agreement protocol designed in the private-channel model, it is feasible to construct a quantum agreement protocol that can effectively handle a full-information adversary. Notably, both protocols have equivalent levels of resilience, round complexity, and communication complexity. In the classical private-channel scenario, participating players are limited to exchanging classical bits, with the adversary lacking knowledge of the exchanged messages. In contrast, in the quantum full-information setting, participating players can exchange qubits, while the adversary possesses comprehensive and accurate visibility into the system's state and messages. By showcasing the reduction from quantum to classical frameworks, this paper demonstrates the strength and flexibility of quantum protocols in addressing security challenges posed by adversaries with increased visibility. It underscores the potential of leveraging quantum principles to improve security measures without compromising on efficiency or resilience. By applying our reduction, we demonstrate quantum advantages in the round complexity of asynchronous Byzantine agreement protocols in the full-information model. It is well known that in the full-information model, any classical protocol requires $Ω(n)$ rounds to solve Byzantine agreement with probability one even against Fail-stop adversary when resilience $t=Θ(n)$. We show that quantum protocols can achieve $O(1)$ rounds (i) with resilience $t 0$, therefore surpassing the classical lower bound.

quant-ph↗

arXiv2024

Boosting Gradient Ascent for Continuous DR-submodular Maximization

Projected Gradient Ascent (PGA) is the most commonly used optimization scheme in machine learning and operations research areas. Nevertheless, numerous studies and examples have shown that the PGA methods may fail to achieve the tight approximation ratio for continuous DR-submodular maximization problems. To address this challenge, we present a boosting technique in this paper, which can efficiently improve the approximation guarantee of the standard PGA to \emph{optimal} with only small modifications on the objective function. The fundamental idea of our boosting technique is to exploit non-oblivious search to derive a novel auxiliary function $F$, whose stationary points are excellent approximations to the global maximum of the original DR-submodular objective $f$. Specifically, when $f$ is monotone and $γ$-weakly DR-submodular, we propose an auxiliary function $F$ whose stationary points can provide a better $(1-e^{-γ})$-approximation than the $(γ^2/(1+γ^2))$-approximation guaranteed by the stationary points of $f$ itself. Similarly, for the non-monotone case, we devise another auxiliary function $F$ whose stationary points can achieve an optimal $\frac{1-\min_{\boldsymbol{x}\in\mathcal{C}}\|\boldsymbol{x}\|_{\infty}}{4}$-approximation guarantee where $\mathcal{C}$ is a convex constraint set. In contrast, the stationary points of the original non-monotone DR-submodular function can be arbitrarily bad~\citep{chen2023continuous}. Furthermore, we demonstrate the scalability of our boosting technique on four problems. In all of these four problems, our resulting variants of boosting PGA algorithm beat the previous standard PGA in several aspects such as approximation ratio and efficiency. Finally, we corroborate our theoretical findings with numerical experiments, which demonstrate the effectiveness of our boosting PGA methods.

cs.LG↗

arXiv2024

Efficient Deterministic Algorithms for Maximizing Symmetric Submodular Functions

Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio of $0.432$. The algorithm applies the canonical continuous greedy technique that involves a sampling process. It, therefore, suffers from high query complexity and is inherently randomized. In this paper, we present several efficient deterministic algorithms for maximizing a symmetric submodular function under various constraints. Specifically, for the cardinality constraint, we design a deterministic algorithm that attains a $0.432$ ratio and uses $O(kn)$ queries. Previously, the best deterministic algorithm attains a $0.385-ε$ ratio and uses $O\left(kn (\frac{10}{9ε})^{\frac{20}{9ε}-1}\right)$ queries. For the matroid constraint, we design a deterministic algorithm that attains a $1/3-ε$ ratio and uses $O(kn\log ε^{-1})$ queries. Previously, the best deterministic algorithm can also attain $1/3-ε$ ratio but it uses much larger $O(ε^{-1}n^4)$ queries. For the packing constraints with a large width, we design a deterministic algorithm that attains a $0.432-ε$ ratio and uses $O(n^2)$ queries. To the best of our knowledge, there is no deterministic algorithm for the constraint previously. The last algorithm can be adapted to attain a $0.432$ ratio for single knapsack constraint using $O(n^4)$ queries. Previously, the best deterministic algorithm attains a $0.316-ε$ ratio and uses $\widetilde{O}(n^3)$ queries.

cs.DS↗