arXiv subjects

Xingze Qiu

Publications and source records attributed to Xingze Qiu.

At least 19 recordsLinked to original sources

arXiv2026

Fisher-Orthogonal Memory in Quantum Reservoir Computing

Quantum reservoir computing processes temporal information through driven many-body dynamics, but its performance is ultimately limited by how accurately past inputs can be extracted from finite measurements. Here we formulate this limitation as a local multiparameter estimation problem and introduce a delay-space quantum Fisher information matrix to quantify the distinguishability of information stored at different delays. This perspective identifies Fisher-orthogonal memory as a measurement-efficient design principle: different delays should perturb the reservoir state along mutually Fisher-orthogonal directions. We first analyze the single-qubit limit using the Gill--Massar bound, revealing an optimal write-store-routing trade-off. Guided by this structure, we construct solvable multi-qubit reservoirs based on Clifford routing orbits and Singer-cycle Pauli algebra. The resulting dynamics yield diagonal delay-space QFIMs with analytically programmable fading profiles. Under finite-shot local Pauli readout, these reservoirs retain sharp memory windows that are absent in a validation-selected Ising baseline. Their product-task behavior is governed by second-order responses inherited from the same Pauli-routing algebra. Our results provide an analytically controlled route toward measurement-efficient quantum reservoir computing.

quant-ph↗

arXiv2026

Quantum magic and non-commutativity as computational resources in quantum reservoir computing

Quantum reservoir computing (QRC) provides a hardware-efficient paradigm for temporal information processing on near-term quantum devices. Despite rapid experimental progress, a rigorous understanding of the structural conditions required for its scalable quantum-enhanced performance remains lacking. Here, we develop a theoretical framework in Pauli-Liouville space that provides a unified analytical treatment of the echo state property (ESP), nonlinear expressive power, and quantum resources. We first analyze the widely used qubit-resetting scheme and establish that quantum magic generated by reservoir dynamics is a necessary condition for effective computation, a requirement more fundamental than ESP. However, we prove that this architecture faces inherent expressivity limitations: all nonlinear processing originates exclusively from the classical encoding map, imposing an unavoidable trade-off between nonlinearity and memory capacity. To circumvent this structural bottleneck, we rigorously analyze Hamiltonian encoding, in which temporal inputs are embedded directly into the continuous dynamics generator. We show that the ESP is natively guaranteed by the Liouvillian spectral gap, decoupling it from quantum magic. Crucially, for any non-trivial drive Hamiltonian, the discrete-time update map exhibits a transcendental, infinite-order nonlinear dependence on the instantaneous input. Moreover, the intrinsic non-commutativity of the open-system generators governs the temporal coupling of these nonlinearities, producing highly non-separable processing of the input history. Our results establish a rigorous theoretical hierarchy of QRC architectures and provide prescriptive design principles for experiments targeting genuine quantum advantages in temporal processing.

quant-ph↗

arXiv2026

Thermodynamics of Quantum Reservoir Computing

Quantum reservoir computing provides a framework for processing complex temporal data, yet its fundamental computational and energetic limits remain unresolved. Here, we establish a non-equilibrium thermodynamic framework that links the macroscopic predictive performance of driven open quantum systems to their microscopic energetic costs. By mapping Holevo capacities onto the Bogoliubov-Kubo-Mori geometric manifold, we analytically prove that the computational peak within the quantum critical region originates from a spectral resonance: the closing of the intrinsic energy gap forces the reservoir's internal transition frequencies to align with the chaotic drive. To evaluate the associated thermodynamic costs, we introduce quantum informational dissipation to quantify the non-predictive historical data retained by the reservoir. This allows us to derive a generalized Landauer bound for continuous temporal processing, which reveals a fundamental thermodynamic trade-off: the critical resonance that maximizes predictive capacity simultaneously maximizes informational dissipation and the irreversible work required for environmental erasure. Furthermore, coherence decomposition demonstrates that quantum coherences amplify predictive capacity without demanding additional mechanical work. These findings establish the fundamental energetic limits of quantum learning devices, providing theoretical principles for designing energy-efficient quantum neuromorphic hardware.

quant-ph↗

arXiv2026

Topological Sensing in the Dynamics of Quantum Walks with Defects

Topological quantum sensing leverages unique topological features to suppress noise and improve the precision of parameter estimation, emerging as a promising tool in both fundamental research and practical application. In this Letter, we propose a sensing protocol that exploits the dynamics of topological quantum walks incorporating localized defects. Unlike conventional schemes that rely on topological protection to suppress disorder and defects, our protocol harnesses the evolution time as a resource to enable precise estimation of the defect parameter. By utilizing topologically nontrivial properties of the quantum walks, the sensing precision can approach the Heisenberg limit. We further demonstrate the performance and robustness of the protocol through Bayesian estimation. Our results show that this approach maintains high precision over a broad range of parameters and exhibits strong robustness against disorder, offering a practical pathway for topologically enhanced quantum metrology.

quant-ph↗

arXiv2025

Uncertainty Principle from Operator Asymmetry

The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an observable's intrinsic, state-independent capacity to break the symmetry associated with another. This ``operator asymmetry,'' formalized as the incompatibility norm, leads to a variance-based uncertainty relation for pure states that can be tighter than the standard Robertson bound. Most significantly, this framework resolves a long-standing open problem in quantum information theory: the formulation of a universally valid, product-form uncertainty relation for the Wigner-Yanase skew information. We demonstrate the practical power of our framework by deriving tighter quantum speed limits for the dynamics of nearly conserved quantities, which are crucial for understanding non-equilibrium phenomena such as prethermalization and many-body localization. This work provides both a new conceptual lens for understanding quantum uncertainty and a powerful, versatile toolkit for its application.

quant-ph↗

arXiv2025

Universally Robust Control of Open Quantum Systems

Mitigating noise-induced decoherence is the central challenge in controlling open quantum systems. While existing robust protocols often require precise noise models, we introduce a universal framework for noise-agnostic quantum control that achieves high-fidelity operations without prior environmental noise characterization. This framework capitalizes on the dynamical modification of the system-environment coupling through control drives, an effect rigorously encoded in the dynamical equation. Since the derived noise sensitivity metric remains independent of the coupling details between the system and the environment, our protocol demonstrates provable robustness against arbitrary Markovian noises. Numerical validation through quantum state transfer and gate operations reveals near-unity fidelity ($>\!99\%$) across diverse noise regimes, achieving orders-of-magnitude error suppression compared to target-only approaches. This framework bridges critical gaps between theoretical control design and experimental constraints, establishing a hardware-agnostic pathway toward fault-tolerant quantum technologies across platforms such as superconducting circuits, trapped ions, and solid-state qubits.

quant-ph↗

arXiv2025

Quantum Sensing with Topological-Paired Bound States

We present an efficient and robust protocol for quantum-enhanced sensing using a single qubit in the topological waveguide system. Our method relies on the topological-paired bound states, which are localized near the qubit and can be effectively regarded as a two-level system. Through the lens of Bayesian inference theory, we show that the sensitivity can reach the Heisenberg limit across a large field range. Inheriting from the topological robustness of the waveguide, our sensing protocol is robust against local perturbations. Besides, our sensing protocol utilizes a product state as the initial state, which can be easily prepared in experiments. We expect this approach would pave the way toward robust topological quantum sensors based on near-term quantum platforms such as superconducting qubits and Rydberg arrays.

quant-ph↗

arXiv2025

Quantum complexity phase transition in fermionic quantum circuits

Understanding the complexity of quantum many-body systems has been attracting much attention recently for its fundamental importance in characterizing complex quantum phases beyond the scope of quantum entanglement. Here, we investigate Krylov complexity in quantum percolation models (QPM) and establish unconventional phase transitions emergent from the interplay of exponential scaling of the Krylov complexity and the number of spanning clusters in QPM. We develop a general scaling theory for Krylov complexity phase transitions (KCPT) on QPM, and obtain exact results for the critical probabilities and exponents. For non-interacting systems across diverse lattices (1D/2D/3D regular, Bethe, and quasicrystals), our scaling theory reveals that the KCPT coincides with the classical percolation transition. In contrast, for interacting systems, we find the KCPT develops a generic separation from the percolation transition due to the highly complex quantum many-body effects, which is analogous to the Griffiths effect in the critical disorder phase transition. To test our theoretical predictions, we provide a concrete protocol for measuring the Krylov complexity, which is accessible to present experiments.

quant-ph↗

arXiv2025

Quantum Annealing Algorithms for Estimating Ising Partition Functions

Estimating partition functions of Ising spin glasses is a cornerstone of statistical physics and computational science, yet it remains classically challenging due to its $\#$P-hard complexity. While Jarzynski's equality offers a theoretical pathway, its practical application is crippled at low temperatures by rare, divergent statistical fluctuations. Here, we introduce a quantum protocol that overcomes this fundamental limitation by synergizing reverse quantum annealing with optimized nonequilibrium initial distributions. Our method dramatically suppresses the estimator variance, achieving saturation in the low-temperature regime where existing methods fail. Numerical benchmarks on the Sherrington-Kirkpatrick spin glass and the 3-SAT problem demonstrate that our protocol reduces computational scaling exponents by over an order of magnitude (e.g., from $\sim 8.5$ to $\sim 0.5$), despite retaining exponential system-size dependence. Crucially, our protocol circumvents stringent adiabatic constraints, making it feasible for near-term quantum devices like superconducting qubits, trapped ions, and Rydberg atom arrays. This work provides a methodological framework for quantum-enhanced estimation in spin glass thermodynamics and beyond by harnessing non-adiabatic quantum dynamics to address a classically difficult problem.

quant-ph↗

arXiv2024

Coherent Quantum Speed Limits

We establish a comprehensive theoretical framework for coherent quantum speed limits (QSLs), deriving fundamental bounds on the rate of quantum evolution that explicitly isolate the contribution of quantum coherence. By applying H\"older's inequality for matrix norms to the Liouville-von Neumann equation, we construct two infinite families of QSLs for general unitary dynamics. These bounds are characterized by coherence measures based on Schatten $p$-norms and Hellinger distance, respectively, defined with respect to the instantaneous energy eigenbasis. Unlike traditional Mandelstam-Tamm bounds, our approach disentangles the quantum state's coherence structure from the Hamiltonian's energy scale. Using the Landau-Zener model accelerated by shortcuts to adiabaticity, we demonstrate that coherence functions as a critical kinematic resource: achieving faster evolution entails maintaining a state with high coherence relative to the instantaneous basis. Our results provide a resource-theoretic perspective on time-energy uncertainty, offering insights into the fundamental limits of quantum control and information processing.

quant-ph↗

arXiv2023

Adiabatically compressing chiral p-wave Bose-Einstein condensates into the lowest landau level

There has been much recent progress in controlling $p$-orbital degrees of freedom in optical lattices, for example with lattice shaking, sublattice swapping, and lattice potential programming. Here, we present a protocol of preparing lowest Landau level (LLL) states of cold atoms by adiabatically compressing $p$-orbital Bose-Einstein condensates confined in two-dimensional optical lattices. The system starts from a chiral $p+ip$ Bose-Einstein condensate (BEC) state, which acquires finite angular momentum by spontaneous symmetry breaking. Such chiral BEC states have been achieved in recent optical lattice experiments for cold atoms loaded in the $p$-bands. Through an adiabatic adjustment of the lattice potential, we compress the three-dimensional BEC into a two-dimensional system, in which the orbital degrees of freedom continuously morph into LLL states. This process is enforced by the discrete rotation symmetry of the lattice potential. The final quantum state inherits large angular momentum from the original chiral $p+ip$ state, with one quantized unit per particle. We investigate the quantum many-body ground state of interacting bosons in the LLL considering contact repulsion. This leads to an exotic gapped BEC state. Our theory can be readily tested in experiments for the required techniques are all accessible to the current optical lattice experiments.

cond-mat.quant-gas↗

arXiv2023

Quantum optimization within lattice gauge theory model on a quantum simulator

Simulating lattice gauge theory (LGT) Hamiltonian and its nontrivial states by programmable quantum devices has attracted numerous attention in recent years. Rydberg atom arrays constitute one of the most rapidly developing arenas for quantum simulation and quantum computing. The $\mathbb{Z}_2$ LGT and topological order has been realized in experiments while the $U(1)$ LGT is being worked hard on the way. States of LGT have local constraint and are fragmented into several winding sectors with topological protection. It is therefore difficult to reach the ground state in target sector for experiments, and it is also an important task for quantum topological memory. Here, we propose a protocol of sweeping quantum annealing (SQA) for searching the ground state among topological sectors. With the quantum Monte Carlo method, we show that this SQA has linear time complexity of size with applications to the antiferromagnetic transverse field Ising model, which has emergent $U(1)$ gauge fields. This SQA protocol can be realized easily on quantum simulation platforms such as Rydberg array and D-wave annealer. We expect this approach would provide an efficient recipe for resolving the topological hindrances in quantum optimization and the preparation of quantum topological state.

quant-ph↗

arXiv2023

Configured Quantum Reservoir Computing for Multi-Task Machine Learning

Amidst the rapid advancements in experimental technology, noise-intermediate-scale quantum (NISQ) devices have become increasingly programmable, offering versatile opportunities to leverage quantum computational advantage. Here we explore the intricate dynamics of programmable NISQ devices for quantum reservoir computing. Using a genetic algorithm to configure the quantum reservoir dynamics, we systematically enhance the learning performance. Remarkably, a single configured quantum reservoir can simultaneously learn multiple tasks, including a synthetic oscillatory network of transcriptional regulators, chaotic motifs in gene regulatory networks, and the fractional-order Chua's circuit. Our configured quantum reservoir computing yields highly precise predictions for these learning tasks, outperforming classical reservoir computing. We also test the configured quantum reservoir computing in foreign exchange (FX) market applications and demonstrate its capability to capture the stochastic evolution of the exchange rates with significantly greater accuracy than classical reservoir computing approaches. Through comparison with classical reservoir computing, we highlight the unique role of quantum coherence in the quantum reservoir, which underpins its exceptional learning performance. Our findings suggest the exciting potential of configured quantum reservoir computing for exploiting the quantum computation power of NISQ devices in developing artificial general intelligence.

quant-ph↗

arXiv2023

The Sub-Exponential Critical Slowing Down at Floquet Time Crystal Phase Transition

Critical slowing down (CSD) has been a trademark of critical dynamics for equilibrium phase transitions of a many-body system, where the relaxation time for the system to reach thermal equilibrium or quantum ground state diverges with system size. The time crystal phase transition has attracted much attention in recent years for it provides a scenario of phase transition of quantum dynamics, unlike conventional equilibrium phase transitions. Here, we study critical dynamics near the Floquet time crystal phase transition. Its critical behavior is described by introducing a space-time coarse grained correlation function, whose relaxation time diverges at the critical point revealing the CSD. This is demonstrated by investigating the Floquet dynamics of one-dimensional disordered spin chain. Through finite-size scaling analysis, we show the relaxation time has a universal sub-exponential scaling near the critical point, in sharp contrast to the standard power-law behavior for CSD in equilibrium phase transitions. This prediction can be readily tested in present quantum simulation experiments.

quant-ph↗

arXiv2022

Programmable Hamiltonian engineering with quadratic quantum Fourier transform

Quantum Fourier transform (QFT) is a widely used building block for quantum algorithms, whose scalable implementation is challenging in experiments. Here, we propose a protocol of quadratic quantum Fourier transform (QQFT), considering cold atoms confined in an optical lattice. This QQFT is equivalent to QFT in the single-particle subspace, and produces a different unitary operation in the entire Hilbert space. We show this QQFT protocol can be implemented using programmable laser potential with the digital-micromirror-device techniques recently developed in the experiments. The QQFT protocol enables programmable Hamiltonian engineering, and allows quantum simulations of Hamiltonian models, which are difficult to realize with conventional approaches. The flexibility of our approach is demonstrated by performing quantum simulations of one-dimensional Poincaré crystal physics and two-dimensional topological flat bands, where the QQFT protocol effectively generates the required long-range tunnelings despite the locality of the cold atom system. We find the discrete Poincaré symmetry and topological properties in the two examples respectively have robustness against a certain degree of noise that is potentially existent in the experimental realization. We expect this approach would open up wide opportunities for optical lattice based programmable quantum simulations.

quant-ph↗

arXiv2022

Peratic Phase Transition by Bulk-to-Surface Response

The study of dynamical phase transitions has been attracting considerable research efforts in the last decade. One theme of present interest is to search for exotic scenarios beyond the framework of equilibrium phase transitions. Here, we establish a duality between many-body dynamics and static Hamiltonian ground states for both classical and quantum systems. We construct frustration free Hamiltonians whose ground state phase transitions have rigorous duality to chaotic transitions in dynamical systems. By this duality, we show the corresponding ground state phase transitions are characterized by bulk-to-surface response, which are then dubbed "peratic" meaning defined by response to the boundary. For the classical system, we show how the time-like dimension emerges in the static ground states. For the quantum system, the ground state is a superposition of geometrical lines on a two dimensional array, which encode the dynamical Floquet evolution history of one dimensional disordered spin chains. Our prediction of peratic phase transition has direct consequences in quantum simulation platforms such as Rydberg atoms and superconducting qubits, as well as anisotropic spin glass materials. The discovery would shed light on the unification of dynamical phase transitions with equilibrium systems.

cond-mat.stat-mech↗

arXiv2022

Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation

Computing finite temperature properties of a quantum many-body system is key to describing a broad range of correlated quantum many-body physics from quantum chemistry and condensed matter to thermal quantum field theories. Quantum computing with rapid developments in recent years has a huge potential to impact the computation of quantum thermodynamics. To fulfill the potential impacts, it is crucial to design quantum algorithms that utilize the computation power of the quantum computing devices. Here we present a quantum kernel function expansion (QKFE) algorithm for solving thermodynamic properties of quantum many-body systems. In this quantum algorithm, the many-body density of states is approximated by a kernel-Fourier expansion, whose expansion moments are obtained by random state sampling and quantum interferometric measurements. As compared to its classical counterpart, namely the kernel polynomial method (KPM), QKFE has an exponential advantage in the cost of both time and memory. In computing low temperature properties, QKFE becomes inefficient, as similar to classical KPM. To resolve this difficulty, we further construct a thermal ensemble and approaches the low temperature regime step-by-step. For quantum Hamiltonians, whose ground states are preparable with polynomial quantum circuits, THEI has an overall polynomial complexity. We demonstrate its efficiency with applications to one and two-dimensional quantum spin models, and a fermionic lattice. With our analysis on the realization with digital and analogue quantum devices, we expect the quantum algorithm is accessible to current quantum technology.

quant-ph↗

arXiv2021

The Reservoir Learning Power across Quantum Many-Boby Localization Transition

Harnessing the quantum computation power of the present noisy-intermediate-size-quantum devices has received tremendous interest in the last few years. Here we study the learning power of a one-dimensional long-range randomly-coupled quantum spin chain, within the framework of reservoir computing. In time sequence learning tasks, we find the system in the quantum many-body localized (MBL) phase holds long-term memory, which can be attributed to the emergent local integrals of motion. On the other hand, MBL phase does not provide sufficient nonlinearity in learning highly-nonlinear time sequences, which we show in a parity check task. This is reversed in the quantum ergodic phase, which provides sufficient nonlinearity but compromises memory capacity. In a complex learning task of Mackey-Glass prediction that requires both sufficient memory capacity and nonlinearity, we find optimal learning performance near the MBL-to-ergodic transition. This leads to a guiding principle of quantum reservoir engineering at the edge of quantum ergodicity reaching optimal learning power for generic complex reservoir learning tasks. Our theoretical finding can be readily tested with present experiments.

quant-ph↗