arXiv subjects

Sanjiang Li

Publications and source records attributed to Sanjiang Li.

At least 19 recordsLinked to original sources

arXiv2026

dSABRE: A SABRE-Style Router for Multi-Core Distributed Quantum Computers

Minimising EPR consumption is the dominant objective when routing a quantum circuit on a distributed quantum computer (DQC). We present dSABRE, a SABRE-style router for multi-core processors that, on each iteration of a lookahead-driven loop, first resolves any intra-core front-layer gates by SWAP scoring and only falls back to scoring inter-core teleportation candidates when the intra-core front is empty. Three mechanisms drive the improvement over the state of the art: a five-term gate-centric teleportation score that generalises the local SWAP heuristic to the inter-core setting, whose explicit capacity-penalty term keeps the scorer from teleporting into saturated cores; a proactive congestion-relief pass that redistributes idle qubits out of high-demand cores before deadlock; and a BFS-layer construction of the inter-core extended set that respects DAG dependencies layer by layer rather than mixing wires in topological order. Across 18 MQT-Bench circuits at 25, 36, and 64 logical qubits, dSABRE reduces geometric-mean EPR consumption by 41-44% over TeleSABRE and by 16-68% over the gate-teleportation-based pytket-dqc, using standard Qiskit SabreLayout for the initial layout. A large-circuit QFT sweep at 100-360 qubits confirms scalability. Code and online appendices are available at https://github.com/ebony72/dsabre.

quant-ph↗

arXiv2025

Advancing Quantum State Preparation Using Decision Diagram with Local Invertible Maps

Quantum state preparation (QSP) is a fundamental task in quantum computing and quantum information processing. It is critical to the execution of many quantum algorithms, including those in quantum machine learning. In this paper, we propose a family of efficient QSP algorithms tailored to different numbers of available ancilla qubits - ranging from no ancilla qubits, to a single ancilla qubit, to a sufficiently large number of ancilla qubits. Our approach exploits the power of Local Invertible Map Tensor Decision Diagrams (LimTDDs) - a highly compact representation of quantum states that combines tensor networks and decision diagrams to reduce quantum circuit complexity. Extensive experiments demonstrate that our methods significantly outperform existing approaches and exhibit better scalability for large-scale quantum states, both in terms of runtime and gate complexity. Furthermore, our method shows exponential improvement in best-case scenarios.

cs.DS↗

arXiv2025

Quantum State Preparation Based on LimTDD

Quantum state preparation is a fundamental task in quantum computing and quantum information processing. With the rapid advancement of quantum technologies, efficient quantum state preparation has become increasingly important. This paper proposes a novel approach for quantum state preparation based on the Local Invertible Map Tensor Decision Diagram (LimTDD). LimTDD combines the advantages of tensor networks and decision diagrams, enabling efficient representation and manipulation of quantum states. Compared with the state-of-the-art quantum state preparation method, LimTDD demonstrates substantial improvements in efficiency when dealing with complex quantum states, while also reducing the complexity of quantum circuits. Examples indicate that, in the best-case scenario, our method can achieve exponential efficiency gains over existing methods. This study not only highlights the potential of LimTDD in quantum state preparation but also provides a robust theoretical and practical foundation for the future development of quantum computing technologies.

quant-ph↗

arXiv2025

Optimal Compilation Strategies for QFT Circuits in Neutral-Atom Quantum Computing

Neutral-atom quantum computing (NAQC) offers distinct advantages such as dynamic qubit reconfigurability, long coherence times, and high gate fidelities, making it a promising platform for scalable quantum computing. Despite these strengths, efficiently implementing quantum circuits like the Quantum Fourier Transform (QFT) remains a significant challenge due to atom movement overheads and connectivity constraints. This paper introduces optimal compilation strategies tailored to QFT circuits and NAQC systems, addressing these challenges for both linear and grid-like architectures. By minimizing atom movements, the proposed methods achieve theoretical lower bounds in atom movements while preserving high circuit fidelity. Comparative evaluations against state-of-the-art compilers demonstrate the superior performance of the proposed methods. These methods could serve as benchmarks for evaluating the performance of NAQC compilers.

quant-ph↗

arXiv2025

LimTDD: A Compact Decision Diagram Integrating Tensor and Local Invertible Map Representations

Tensor networks serve as a powerful tool for efficiently representing and manipulating high-dimensional data in applications such as quantum physics, machine learning, and data compression. Tensor Decision Diagrams (TDDs) offer an efficient framework for tensor representation by leveraging decision diagram techniques. However, the current implementation of TDDs and other decision diagrams fail to exploit tensor isomorphisms, limiting their compression potential. This paper introduces Local Invertible Map Tensor Decision Diagrams (LimTDDs), an extension of TDDs that incorporates local invertible maps (LIMs) to achieve more compact representations. Unlike LIMDD, which uses Pauli operators for quantum states, LimTDD employs the $XP$-stabilizer group, enabling broader applicability across tensor-based tasks. We present efficient algorithms for normalization, slicing, addition, and contraction, critical for tensor network applications. Theoretical analysis demonstrates that LimTDDs achieve greater compactness than TDDs and, in best-case scenarios and for quantum state representations, offer exponential compression advantages over both TDDs and LIMDDs. Experimental results in quantum circuit tensor computation and simulation confirm LimTDD's superior efficiency. Open-source code is available at https://github.com/Veriqc/LimTDD.

cs.DS↗

arXiv2025

Image Computation for Quantum Transition Systems

With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its application to quantum systems is still an underdeveloped research area. This paper advances the development of model checking quantum systems by providing efficient image computation algorithms for quantum transition systems, which play a fundamental role in model checking. In our approach, we represent quantum circuits as tensor networks and design algorithms by leveraging the properties of tensor networks and tensor decision diagrams. Our experiments demonstrate that our contraction partition-based algorithm can greatly improve the efficiency of image computation for quantum transition systems.

cs.DS↗

arXiv2024

On the Trainability and Classical Simulability of Learning Matrix Product States Variationally

We prove that using global observables to train the matrix product state ansatz results in the vanishing of all partial derivatives, also known as barren plateaus, while using local observables avoids this. This ansatz is widely used in quantum machine learning for learning weakly entangled state approximations. Additionally, we empirically demonstrate that in many cases, the objective function is an inner product of almost sparse operators, highlighting the potential for classically simulating such a learning problem with few quantum resources. All our results are experimentally validated across various scenarios.

quant-ph↗

arXiv2024

Qubit Mapping: The Adaptive Divide-and-Conquer Approach

The qubit mapping problem (QMP) focuses on the mapping and routing of qubits in quantum circuits so that the strict connectivity constraints imposed by near-term quantum hardware are satisfied. QMP is a pivotal task for quantum circuit compilation and its decision version is NP-complete. In this study, we present an effective approach called Adaptive Divided-And-Conqure (ADAC) to solve QMP. Our ADAC algorithm adaptively partitions circuits by leveraging subgraph isomorphism and ensuring coherence among subcircuits. Additionally, we employ a heuristic approach to optimise the routing algorithm during circuit partitioning. Through extensive experiments across various NISQ devices and circuit benchmarks, we demonstrate that the proposed ADAC algorithm outperforms the state-of-the-art method. Specifically, ADAC shows an improvement of nearly 50\% on the IBM Tokyo architecture. Furthermore, ADAC exhibits an improvement of around 18\% on pseudo-realistic circuits implemented on grid-like architectures with larger qubit numbers, where the pseudo-realistic circuits are constructed based on the characteristics of widely existing realistic circuits, aiming to investigate the applicability of ADAC. Our findings highlight the potential of ADAC in quantum circuit compilation and the deployment of practical applications on near-term quantum hardware platforms.

quant-ph↗

arXiv2024

DasAtom: A Divide-and-Shuttle Atom Approach to Quantum Circuit Transformation

Neutral atom (NA) quantum systems are emerging as a leading platform for quantum computation, offering superior or competitive qubit count and gate fidelity compared to superconducting circuits and ion traps. However, the unique features of NA devices, such as long-range interactions, long qubit coherence time, and the ability to physically move qubits, present distinct challenges for quantum circuit compilation. In this paper, we introduce DasAtom, a novel divide-and-shuttle atom approach designed to optimise quantum circuit transformation for NA devices by leveraging these capabilities. DasAtom partitions circuits into subcircuits, each associated with a qubit mapping that allows all gates within the subcircuit to be directly executed. The algorithm then shuttles atoms to transition seamlessly from one mapping to the next, enhancing both execution efficiency and overall fidelity. For a 30-qubit Quantum Fourier Transform (QFT), DasAtom achieves a 414x improvement in fidelity over the move-based algorithm Enola and a 10.6x improvement over the SWAP-based algorithm Tetris. Notably, this improvement is expected to increase exponentially with the number of qubits, positioning DasAtom as a highly promising solution for scaling quantum computation on NA platforms.

quant-ph↗

arXiv2024

Equivalence Checking of Parameterised Quantum Circuits

Parameterised quantum circuits (PQCs) hold great promise for demonstrating quantum advantages in practical applications of quantum computation. Examples of successful applications include the variational quantum eigensolver, the quantum approximate optimisation algorithm, and quantum machine learning. However, before executing PQCs on real quantum devices, they undergo compilation and optimisation procedures. Given the inherent error-proneness of these processes, it becomes crucial to verify the equivalence between the original PQC and its compiled or optimised version. Unfortunately, most existing quantum circuit verifiers cannot directly handle parameterised quantum circuits; instead, they require parameter substitution to perform verification. In this paper, we address the critical challenge of equivalence checking for PQCs. We propose a novel compact representation for PQCs based on tensor decision diagrams. Leveraging this representation, we present an algorithm for verifying PQC equivalence without the need for instantiation. Our approach ensures both effectiveness and efficiency, as confirmed by experimental evaluations. The decision-diagram representations offer a powerful tool for analysing and verifying parameterised quantum circuits, bridging the gap between theoretical models and practical implementations.

quant-ph↗

arXiv2023

Ansatz-Agnostic Exponential Resource Saving in Variational Quantum Algorithms Using Shallow Shadows

Variational Quantum Algorithms (VQA) have been identified as a promising candidate for the demonstration of near-term quantum advantage in solving optimization tasks in chemical simulation, quantum information, and machine learning. The standard model of training requires a significant amount of quantum resources, which led us to use classical shadows to devise an alternative that consumes exponentially fewer quantum resources. However, the approach only works when the observables are local and the ansatz is the shallow Alternating Layered Ansatz (ALA), thus severely limiting its potential in solving problems such as quantum state preparation, where the ideal state might not be approximable with an ALA. In this work, we present a protocol based on shallow shadows that achieves similar levels of savings for almost any shallow ansatz studied in the literature, when combined with observables of low Frobenius norm. We show that two important applications in quantum information for which VQAs can be a powerful option, namely variational quantum state preparation and variational quantum circuit synthesis, are compatible with our protocol. We also experimentally demonstrate orders of magnitude improvement in comparison to the standard VQA model.

quant-ph↗

arXiv2023

Decision Diagrams for Symbolic Verification of Quantum Circuits

With the rapid development of quantum computing, automatic verification of quantum circuits becomes more and more important. While several decision diagrams (DDs) have been introduced in quantum circuit simulation and verification, none of them supports symbolic computation. Algorithmic manipulations of symbolic objects, however, have been identified as crucial, if not indispensable, for several verification tasks. This paper proposes the first decision-diagram approach for operating symbolic objects and verifying quantum circuits with symbolic terms. As a notable example, our symbolic tensor decision diagrams (symbolic TDD) could verify the functionality of the 160-qubit quantum Fourier transform circuit within three minutes. Moreover, as demonstrated on Bernstein-Vazirani algorithm, Grover's algorithm, and the bit-flip error correction code, the symbolic TDD enables efficient verification of quantum circuits with user-supplied oracles and/or classical controls.

quant-ph↗

arXiv2023

Single-Qubit Gates Matter for Optimising Quantum Circuit Depth in Qubit Mapping

Quantum circuit transformation (QCT, a.k.a. qubit mapping) is a critical step in quantum circuit compilation. Typically, QCT is achieved by finding an appropriate initial mapping and using SWAP gates to route the qubits such that all connectivity constraints are satisfied. The objective of QCT can be to minimise circuit size or depth. Most existing QCT algorithms prioritise minimising circuit size, potentially overlooking the impact of single-qubit gates on circuit depth. In this paper, we first point out that a single SWAP gate insertion can double the circuit depth, and then propose a simple and effective method that takes into account the impact of single-qubit gates on circuit depth. Our method can be combined with many existing QCT algorithms to optimise circuit depth. The Qiskit SABRE algorithm has been widely accepted as the state-of-the-art algorithm for optimising both circuit size and depth. We demonstrate the effectiveness of our method by embedding it in SABRE, showing that it can reduce circuit depth by up to 50% and 27% on average on, for instance, Google Sycamore and 117 real quantum circuits from MQTBench.

quant-ph↗

arXiv2023

Benchmarking Quantum Circuit Transformation with QKNOB Circuits

Current superconducting quantum devices impose strict connectivity constraints on quantum circuit execution, necessitating circuit transformation before executing quantum circuits on physical hardware. Numerous quantum circuit transformation (QCT) algorithms have been proposed. To enable faithful evaluation of state-of-the-art QCT algorithms, this paper introduces QKNOB (Qubit mapping Benchmark with Known Near-Optimality), a novel benchmark construction method for QCT. QKNOB circuits have built-in transformations with near-optimal (close to the theoretical optimum) SWAP count and depth overhead. QKNOB provides general and unbiased evaluation of QCT algorithms. Using QKNOB, we demonstrate that SABRE, the default Qiskit compiler, consistently achieves the best performance on the 53-qubit IBM Q Rochester and Google Sycamore devices for both SWAP count and depth objectives. Our results also reveal significant performance gaps relative to the near-optimal transformation costs of QKNOB. Our construction algorithm and benchmarks are open-source.

quant-ph↗

arXiv2022

Alternating Layered Variational Quantum Circuits Can Be Classically Optimized Efficiently Using Classical Shadows

Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2--3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.

quant-ph↗

arXiv2022

Abstract interpretation, Hoare logic, and incorrectness logic for quantum programs

Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in parallel. In this paper, we examine the relationship between these techniques in the context of verifying quantum while-programs, where the abstract domain and the set of assertions for quantum states are well-structured. In particular, we show that any complete quantum abstract interpretation induces a quantum Hoare logic and a quantum incorrectness logic, both of which are sound and relatively complete. Unlike the logics proposed in the literature, the induced logic systems are in a forward manner, making them more useful in certain applications. Conversely, any sound and relatively complete quantum Hoare logic or quantum incorrectness logic induces a complete quantum abstract interpretation. As an application, we are able to show the non-existence of any sound and relatively complete quantum Hoare logic or incorrectness logic if tuples of local subspaces are taken as assertions.

cs.LO↗

arXiv2022

Supervised Learning Enhanced Quantum Circuit Transformation

A quantum circuit transformation (QCT) is required when executing a quantum program in a real quantum processing unit (QPU). Through inserting auxiliary SWAP gates, a QCT algorithm transforms a quantum circuit to one that satisfies the connectivity constraint imposed by the QPU. Due to the non-negligible gate error and the limited qubit coherence time of the QPU, QCT algorithms which minimize gate number or circuit depth or maximize the fidelity of output circuits are in urgent need. Unfortunately, finding optimized transformations often involves exhaustive searches, which are extremely time-consuming and not practical for most circuits. In this paper, we propose a framework that uses a policy artificial neural network (ANN) trained by supervised learning on shallow circuits to help existing QCT algorithms select the most promising SWAP gate. ANNs can be trained off-line in a distributed way. The trained ANN can be easily incorporated into QCT algorithms without bringing too much overhead in time complexity. Exemplary embeddings of the trained ANNs into target QCT algorithms demonstrate that the transformation performance can be consistently improved on QPUs with various connectivity structures and random or realistic quantum circuits.

quant-ph↗

arXiv2022

Quantum Circuit Transformation: A Monte Carlo Tree Search Framework

In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation process is necessary to transform it, with overhead cost the smaller the better, into a functionally equivalent one so that the connectivity constraints imposed by the QPU are satisfied. While several algorithms have been proposed for this goal, the overhead costs are often very high, which degenerates the fidelity of the obtained circuits sharply. One major reason for this lies in that, due to the high branching factor and vast search space, almost all these algorithms only search very shallowly and thus, very often, only (at most) locally optimal solutions can be reached. In this paper, we propose a Monte Carlo Tree Search (MCTS) framework to tackle the circuit transformation problem, which enables the search process to go much deeper. The general framework supports implementations aiming to reduce either the size or depth of the output circuit through introducing SWAP or remote CNOT gates. The algorithms, called MCTS-Size and MCTS-Depth, are polynomial in all relevant parameters. Empirical results on extensive realistic circuits and IBM Q Tokyo show that the MCTS-based algorithms can reduce the size (depth, resp.) overhead by, on average, 66% (84%, resp.) when compared with tket, an industrial level compiler.

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