arXiv subjects

Xiao-Ming Zhang

Publications and source records attributed to Xiao-Ming Zhang.

At least 19 recordsLinked to original sources

arXiv2026

From Bits to Qubits: The Theory and Practice of Quantum Data Encoding

Encoding classical data into quantum systems is a foundational step in the execution of nearly all quantum algorithms, and a critical bottleneck in realizing practical quantum advantage. This review provides a comprehensive account of the concepts, algorithms, and practical considerations associated with quantum data encoding. We trace the development from its early conceptual foundations to recent advances, considering commonly used access models, such as quantum state preparation, unitary synthesis, QRAM and block encoding. We survey the circuit size, depth, space-time tradeoffs, as well as non-Clifford resources required for fault-tolerant implementation. We also discuss the roles of different access models in quantum algorithms. Special attention is given to structured data, such as sparse data, Boolean functions and data represented by tensor networks. This review bridges theory and applications, serving both as a pedagogical guide for newcomers and as a reference for active researchers. We also highlight the pivotal role of quantum data encoding in quantum computing and provide insights into future directions that will enable quantum advantage.

quant-ph↗

arXiv2026

Scalable suppression of heating errors in large trapped-ion quantum processors

Trapped-ion processors are leading candidates for scalable quantum computation. However, motional heating remains a key obstacle to fault-tolerant operation, especially when system size increases. Heating error is particularly challenging to suppress due to is incoherence nature, and no general methods currently exist for mitigating their impact in large systems with multiple phonon modes. In this work, based on a careful analysis about the dependence of heating-induced infidelity on phase-space trajectories, we present a simple yet comprehensive framework for suppressing heating errors in large trapped-ion quantum processors. Our approach is flexible, allowing various control pulse bases, ion numbers, and noise levels. Our approach is also compatible with existing error-mitigation techniques, including those targeting laser phase and frequency noise. Crucially, it relies on an efficiently computable cost function that avoids the exponential overhead of full fidelity estimation. We perform numerical simulations for systems with up to 55 qubits, demonstrating up to a fivefold reduction in infidelities compared with the conventional method in typical regimes. We further show that our framework simultaneously reduces the sensitivity of the gate rotation angle to detuning errors, leading to an improvement in detuning-error tolerance. These results offer a practical route toward robust, large-scale quantum computation with trapped ions.

quant-ph↗

arXiv2026

Quantum-classical crossover in fault-tolerant quantum dynamics simulation

While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

quant-ph↗

arXiv2026

Reducing C-NOT Counts for State Preparation and Block Encoding via Diagonal Matrix Migration

Quantum state preparation and block encoding are versatile and practical input models for quantum algorithms in scientific computing. The circuit complexity of state preparation and block encoding frequently dominates the end-to-end gate complexity of quantum algorithms. We give algorithms with lower C-NOT counts for both the state preparation and block encoding. For a general $n$-qubit state, we improve the C-NOT count of the Plesch-Brukner algorithm (2011) from $(23/24)\times 2^n$ to $(11/12)\times2^n$. For block encoding, our single-ancilla protocol for $2^{n-1}\times 2^{n-1}$ matrices uses the spectral norm as subnormalization and achieves a C-NOT count leading term $(11/48)\times 4^n$. Further optimization is performed for low-rank matrices, which frequently arise in practical applications. Specifically, we achieve the C-NOT count leading term $(2^{\lceil\log_{2}K\rceil}+(11/12))\times 2^n$ for a rank-$K$ matrix. This is the first quantum algorithm that encodes matrices using the optimal normalization factor while also allowing the C-NOT count to be adjusted according to the matrix rank. Our approach builds upon the recursive Block-ZXZ decomposition from Krol et al. (2024) and introduces a diagonal matrix migration technique based on the commutativity of the diagonal matrix and the uniformly controlled rotation about the $z$-axis to minimize the use of C-NOT gates.

quant-ph↗

arXiv2026

Geometric encoding of turbulence for end-to-end quantum simulation

Multiscale organization is a hallmark of fluid turbulence in aerospace, energy, and transport systems. While quantum computing promises exponential speedups for solving the evolution equations governing flow fields, this potential is fundamentally hindered by the quantum state preparation bottleneck, the prohibitive cost of loading classical complex data into quantum states. Here, we overcome this barrier by introducing a physics-informed, three-stage geometric encoding method "turbuloscope", which efficiently generates turbulent fields relevant to high-Reynolds-number engineering flows. Rather than brute-force data loading, our approach acts as a kaleidoscope, leveraging the multiscale structures of turbulence. We capture scale-invariant self-similarity via a hyperplane approximation in high-dimensional feature space, and utilize the Hopf fibration to map quantum observables directly onto vortex tubes, the fundamental building blocks of turbulence that control mixing, drag, and heat transfer in mechanical systems. Remarkably, the algorithm requires no ancillary qubits, utilizes a linear-depth quantum circuit, and scales logarithmically with the Reynolds number, an exponential speedup compared to classical methods. We demonstrate the power of this method by generating an instantaneous turbulent field at a high Reynolds number of 35,000 across over one billion grid points using only 30 qubits, reproducing Kolmogorov's 5/3 energy spectrum, tangled vortex structures, and strong intermittency. This asymptotically optimal approach not only signals a near-term pathway to practical quantum advantage in engineering simulation, but establishes a scalable foundation for the quantum simulation of broad multiscale systems.

quant-ph↗

arXiv2026

Efficient Preparation of Quantum States via Randomized Truncation

While the preparation of a general quantum state is challenging, realistic problem instances, such as those encountered in quantum chemistry and quantum machine learning-typically exhibit hierarchical amplitude structures, consisting of a small number of large components alongside a vast number of small but non-negligible ones. Standard approaches deterministically truncate the small amplitude would incur an approximation error that scales linearly with the discarded amplitude mass, enforcing a rigid trade-off between precision and circuit depth. Here, we circumvent the challenge by introducing a randomized state-preparation protocol with probabilistic amplification of small amplitudes using ensembles of low-complexity circuits. Analytically, we prove that this approach significantly reduces the number of encoded amplitudes, halving the requirement for exponentially decaying states and offering asymptotically larger gains for heavy-tailed power-law decays. Numerical simulations on LiH molecular wavefunctions and deep-learning-derived states demonstrate reductions of up to 99 percent in CNOT and T-gate counts compared with deterministic methods. These results establish a resource-efficient paradigm for initializing complex states, relaxing gate-synthesis precision requirements for both near-term and fault-tolerant hardware, and improving the end-to-end feasibility of quantum computing.

quant-ph↗

arXiv2025

Robust and optimal loading of general classical data into quantum computers

As standard data loading processes, quantum state preparation and block-encoding are critical and necessary processes for quantum computing applications, including quantum machine learning, Hamiltonian simulation, and many others. Yet, existing protocols suffer from poor robustness under device imperfection, thus limiting their practicality for real-world applications. Here, this limitation is overcome based on a fanin process designed in a tree-like bucket-brigade architecture. It suppresses the error propagation between different branches, thus exponentially improving the robustness compared to existing depth-optimal methods. Moreover, the approach here simultaneously achieves the state-of-the-art fault-tolerant circuit depth, gate count, and STA. As an example of application, we show that for quantum simulation of geometrically local Hamiltonian, the code distance of each logic qubit can potentially be reduced exponentially using our technique. We believe that our technique can significantly enhance the power of quantum computing in the near-term and fault-tolerant regimes.

quant-ph↗

arXiv2025

Exponential quantum advantages for practical non-Hermitian eigenproblems

Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or classically tractable systems. While quantum computing has shown strong performance in Hermitian eigenproblems, its extension to the non-Hermitian regime remains largely unexplored. Here, we develop a quantum algorithm to address general non-Hermitian eigenvalue problems, specifically targeting eigenvalues near a given line in the complex plane -- thereby generalizing previous results on ground state energy and spectral gap estimation for Hermitian matrices. Our method combines a fuzzy quantum eigenvalue detector with a divide-and-conquer strategy to efficiently isolate relevant eigenvalues. This yields a provable exponential quantum speedup for non-Hermitian eigenproblems. Furthermore, we discuss the broad applications in detecting spontaneous $PT$-symmetry breaking, estimating Liouvillian gaps, and analyzing classical Markov processes. These results highlight the potential of quantum algorithms in tackling challenging problems across quantum physics and beyond.

quant-ph↗

arXiv2025

Binary Tree Block Encoding of Classical Matrix

Block-encoding is a critical subroutine in quantum computing, enabling the transformation of classical data into a matrix representation within a quantum circuit. The resource trade-offs in simulating a block-encoding can be quantified by the circuit size, the normalization factor, and the time and space complexity of parameter computation. Previous studies have primarily focused either on the time and memory complexity of computing the parameters, or on the circuit size and normalization factor in isolation, often neglecting the balance between these trade-offs. In early fault-tolerant quantum computers, the number of qubits is limited. For a classical matrix of size $2^{n}\times 2^{n}$, our approach not only improves the time of decoupling unitary for block-encoding with time complexity $\mathcal{O}(n2^{2n})$ and memory complexity $Θ(2^{2n})$ using only a few ancilla qubits, but also demonstrates superior resource trade-offs. Our proposed block-encoding protocol is named Binary Tree Block-encoding (\texttt{BITBLE}). Under the benchmark, \textit{size metric}, defined by the product of the number of gates and the normalization factor, numerical experiments demonstrate the improvement of both resource trade-off and classical computing time efficiency of the \texttt{BITBLE} protocol. The algorithms are all open-source.

quant-ph↗

arXiv2025

Robust Mølmer-Sørensen Gate Against Symmetric and Asymmetric Errors

To achieve the entangling gate fidelity above the quantum error correction threshold, it is critical to suppress errors due to experimental imperfection. We consider the Mølmer-Sørensen gates in trapped-ion systems, and develop a general approach to suppress a family of noise sources that appeared as either symmetric or asymmetric errors. Using the time-average displacement minimization technique, both symmetric error and displacement-dependent part of the asymmetric errors are eliminated. Then, by analyzing the tangent space of displacement-independent errors, we obtain the analytic form of the generators of the correction operator to the remaining error terms. We then develop a compensation pulse to fully suppress the remaining displacement-independent errors. The effectiveness of our scheme is further verified by numerical analysis, through which we observe a significant reduction of entangling gate infidelity. Our findings enhance gate fidelity and robustness to noise for ion trap quantum computing.

quant-ph↗

arXiv2024

Properties of the QCD Matter: A Review of Selected Results from the ALICE Experiment

The Large Hadron Collider (LHC), the world's largest and most powerful particle accelerator, has been a pivotal tool in advancing our understanding of fundamental physics. By colliding heavy ions (such as lead ions), the LHC recreates conditions similar to those just after the Big Bang. This allows scientists to study the Quark-Gluon Plasma (QGP), a state of matter where quarks and gluons are not confined within protons and neutrons. These studies provide insights into the strong force and the early universe's behavior. In this paper, we provide a comprehensive overview of recent significant findings from A Large Ion Collider Experiment (ALICE) at LHC. The topics encompass measurements regarding to properties of the QGP, particle production, flow and correlations, dileptons, quarkonia and electromagnetic probes, heavy flavor, and jets. Additionally, we introduce future plans for detector upgrades of the ALICE experiment.

nucl-ex↗

arXiv2024

Graph Neural Networks on Quantum Computers

Graph Neural Networks (GNNs) are powerful machine learning models that excel at analyzing structured data represented as graphs, demonstrating remarkable performance in applications like social network analysis and recommendation systems. However, classical GNNs face scalability challenges when dealing with large-scale graphs. This paper proposes frameworks for implementing GNNs on quantum computers to potentially address the challenges. We devise quantum algorithms corresponding to the three fundamental types of classical GNNs: Graph Convolutional Networks, Graph Attention Networks, and Message-Passing GNNs. A complexity analysis of our quantum implementation of the Simplified Graph Convolutional (SGC) Network shows potential quantum advantages over its classical counterpart, with significant improvements in time and space complexities. Our complexities can have trade-offs between the two: when optimizing for minimal circuit depth, our quantum SGC achieves logarithmic time complexity in the input sizes (albeit at the cost of linear space complexity). When optimizing for minimal qubit usage, the quantum SGC exhibits space complexity logarithmic in the input sizes, offering an exponential reduction compared to classical SGCs, while still maintaining better time complexity. These results suggest our Quantum GNN frameworks could efficiently process large-scale graphs. This work paves the way for implementing more advanced Graph Neural Network models on quantum computers, opening new possibilities in quantum machine learning for analyzing graph-structured data.

quant-ph↗

arXiv2024

Circuit complexity of quantum access models for encoding classical data

Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and study the Clifford$+T$ complexity of constructing some typical quantum access models. For general matrices, we show that both sparse-access input models and block-encoding require nearly linear circuit complexities relative to the matrix dimension, even if matrices are sparse. We also gives construction protocols achieving near-optimal gate complexities. On the other hand, the construction becomes efficient with respect to the data qubit when the matrix is the linear combination polynomial terms of efficient unitaries. As a typical example, we propose improved block encoding when these unitaries are Pauli strings. Our protocols are built upon improved quantum state preparation and a selective oracle for Pauli strings, which hold independent value. Our access model constructions offer considerable flexibility, allowing for tunable ancillary qubit number and offers corresponding space-time trade-offs.

quant-ph↗

arXiv2023

Scaling of entangling-gate errors in large ion crystals

Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for few ions, how to maintain the high fidelity for large scale trapped-ions still remains an open problem.Here, we present an analysis on arbitrary scale ion chain and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases of the Hilbert space dimension. For the motional heating error, We derive a much tighter bound of gate infidelity than previously estimated $O(NΓτ)$, and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals.

quant-ph↗

arXiv2023

Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $Θ(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with $d\geqslant2$ non-zero entries, we can reduce the circuit depth to $Θ(\log(nd))$ with $O(nd\log d)$ ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.

quant-ph↗

arXiv2022

Unbiased random circuit compiler for time-dependent Hamiltonian simulation

Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$ for product formula-based methods and could be improved to be polylogarithmic with complicated circuit constructions. Here, we develop an unbiased random compiler for TDHS by combining Dyson expansion, an unbiased continuous sampling method for quantum evolution, and leading order rotations, and it is free from algorithmic errors. Our method has the single- and two-qubit gate complexity $O(Λ^2)$ with a constant sampling overhead, where $Λ$ is the time integration of the Hamiltonian strength. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems. In both examples, we observe notable improvements of our method over existing ones. Our work paves the way to efficient realizations of TDHS.

quant-ph↗

arXiv2022

Revisiting the centrality definition and observable centrality dependence of relativistic heavy-ion collisions in PACIAE model

We improve the centrality definition in impact parameter in PACIAE model responding the fact reported by the ALICE, ATLAS, and CMS collaborations that the maximum impact parameter in heavy ion collisions should be extended to 20 $fm$. Meanwhile the PACIAE program is updated to a new version of PACIAE 2.2.2 with convenience of studying the elementary nuclear collisions, proton-nucleus collisions, and the nucleus-nucleus collisions in one unified program version. The new impact parameter definition together with the optical Glauber model calculated impact parameter bin, $N_{part}$, and $N_{coll}$ in proton-nucleus and nucleus-nucleus collisions at relativistic energies are consistent with the improved MC-Glauber model ones within the error bar. The charged-particle pseudorapidity and the transverse momentum distributions in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV simulated by PACIAE 2.2.2 well reproduce the ALICE experimental data.

nucl-th↗

arXiv2022

Linear scaling of lepton charge asymmetry in $W^\pm$ production in ultra-relativistic nuclear collisions

The lepton charge asymmetry in $W^\pm$ production in the nuclear collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV is investigated with a parton and hadron cascade model PACIAE. Recently published ALICE and the ATLAS data of lepton charge asymmetry are well reproduced. An interesting linear scaling behavior is observed in the lepton charge asymmetry as a function of the collision system valence quark number asymmetry among the different size of nuclear collision systems at $\sqrt{s_{\rm NN}}=5.02$ TeV. This linear scaling behavior may serve as an additional constraint on the PDF (nPDF) extractions.

hep-ph↗