arXiv subjects

Dan-Bo Zhang

Publications and source records attributed to Dan-Bo Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Physics-informed quantum algorithms for glueball-like excitations in a $\mathbb{Z}_2$ lattice gauge theory

Glueball spectroscopy and real-time production with quantum computing require three distinct ingredients: a correlated gauge vacuum, a controlled construction of pure-gauge excitations, and a dynamical detector. We develop a physics-informed quantum-algorithm toolbox for these tasks in a $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory. We use the term \emph{glueball-like} for localized closed-flux excitations on the confining side of this Abelian model, without identifying them with the non-Abelian glueballs of QCD. A loop-gas circuit and Hamiltonian variational ansatz prepare the gauge vacuum, Wilson-loop quantum subspace expansion constructs and characterizes low-lying excitations, and eigenvector continuation imports parameter-dependent dressing without a rapidly enlarged explicit loop basis. A Bethe--Salpeter-type transition amplitude quantifies the spatial broadening of the lightest state. For dynamics, a vacuum-dressed contractible-loop counter measures excess production of localized glueball-like structures. Although demonstrated in an Abelian model, the toolbox separates preparation, construction, compression, characterization, and dynamical detection in a form that is naturally extensible to non-Abelian lattice gauge theories.

hep-lat↗

arXiv2026

Interference Engineering for Quantum Imaginary-Time Evolution through Multiple Energy Shifts

Energy shifting is usually trivial in imaginary-time evolution because it changes only the normalization of the evolved state. On a quantum computer, however, imaginary-time evolution can be implemented as a coherent or sampled superposition of real-time evolutions, in which energy shifts generate relative phases that can interfere. Here we introduce multi-shift quantum imaginary-time evolution (MS-QITE), which uses a distribution of energy shifts to engineer this interference and optimize different implementations. In a Monte Carlo realization, multi-shift reshapes the normalized sampling distribution and concentrates it within a shorter real-time window, thereby reducing the typical Hamiltonian-evolution time and improving the stability of ground-state-energy estimation. In a continuous-variable-assisted realization, it enables projection onto a state supported over a finite quadrature interval, substantially reducing the required squeezing over an intermediate temperature range while retaining accurate thermal-state preparation. Numerical results for transverse-field Ising models demonstrate that energy shifts provide an interference-based degree of freedom for optimizing quantum imaginary-time evolution.

quant-ph↗

arXiv2026

Unifying Charge-Learnability Transitions in U(1)-Symmetric Quantum Circuits through Informational Power of Local Measurement

Charge-learnability transitions in monitored symmetric quantum circuits reveal how local measurement records acquire sufficient information to infer a conserved charge. Here we extend charge learnability to probabilistic weak measurements, for which the measurement probability and measurement strength are independently tunable. We find that the learnability phase boundary is organized by the informational power of local measurement. We further introduce cross entropy as a label-sensitive diagnostic that distinguishes unbiased, biased, and antibiased decoder variants. Finally, the exact record--label mutual information provides a decoder-independent benchmark for the information fundamentally available for charge inference. Our results establish informational power of local measurement as a unifying principle for charge learnability under general monitoring protocols.

quant-ph↗

arXiv2026

Interlocked Time Crystal in Coupled Spin-1/2 Ensembles under Local Dissipation

Multilevel dissipative systems can exploit multiple local transitions and coherence channels to generate nonstationary time-crystalline dynamics. Here we show that an analogous mechanism can be synthesized without enlarging the local Hilbert space by coupling two locally pumped and decaying spin-1/2 ensembles into a composite dissipative unit.Neither ensemble supports an autonomous oscillatory phase; instead, opposite pump-decay imbalances and inter-ensemble exchange coupling can lead to a single interlocked time crystal with a fixed internal phase relation and no single-ensemble counterpart. The time-crystalline character is consistently established through the mean-field analysis, exact calulation of Liouvillian spectra at finite size, and temporal correlations with cumulant expansion. Our work establishes a route to dissipative time-crystalline order in which coupling between simple two-level subsystems generates the effective internal structure otherwise provided by multilevel constituents.

quant-ph↗

arXiv2026

Probing Quantum Information Scrambling via Local Randomized Measurements

In quantum many-body dynamics, locally encoded information typically scrambles across the entire system, becoming inaccessible to local probes. The upper bound of accessible information of local probes can be characterized by the Holevo information via optimal measurement. In this work, we investigate the information dynamics of quantum scrambling utilizing local randomized probes, quantified by the averaged accessible information (AAI). We derive an analytical expression for the AAI under Haar-random measurements and demonstrate that it is a function of purity of local reduced density matrix. Operationally, we employ the classical shadow protocol, using only single-qubit randomized Pauli measurements, to efficiently extract the AAI across extended subsystems. Through numerical simulations across diverse many-body paradigms, we show that the AAI can reveal distinct scrambling behaviors, resolving phenomena that range from dynamical confinement and ballistic transport to persistent scar revivals and many-body localization. This work highlights a pragmatic paradigm shift, from relying on optimal measurements to utilizing randomized local probes, for the characterization of complex quantum information dynamics.

quant-ph↗

arXiv2025

Spontaneous Macroscopic Quantum Synchronization in an Ensemble of Two-level Systems

Spontaneous macroscopic quantum synchronization is an emergent phenomenon where an ensemble of quantum oscillators achieves global phase coherence through the interplay of interaction and dissipation. To illuminate this phenomenon, we study an ensemble of two-level systems (TLS) and establish its associated nonlinear quantum master equation, for which self-consistent analytical solutions of quantum synchronization can be obtained. The trajectories on the Bloch sphere vividly illustrate how dissipation and interaction drive the system toward a synchronized state. We present a phase diagram for macroscopic synchronization as a function of interaction strength and the gain-to-damping ratio. Furthermore, we demonstrate full synchronization and partial synchronization between two groups of TLS with different natural frequencies. This work establishes ensemble of TLS as a remarkable system for understanding spontaneous quantum synchronization.

quant-ph↗

arXiv2025

Fluctuation-guided adaptive random compiler for Hamiltonian simulation

Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the deterministic Trotter-Suzuki sequence. However, its fixed sampling distribution does not adapt to the dynamics of the system, limiting its accuracy. In this work, we propose a fluctuation-guided adaptive algorithm that adaptively updates sampling probabilities based on fluctuations of Hamiltonian terms to achieve higher simulation fidelity. Remarkably, the protocol renders an intuitive physical understanding: Hamiltonian terms with greater sensitivity to the state evolution should be prioritized during sampling. The overload of measuring fluctuations necessary for updating the sampling probability is affordable, and can be further largely reduced by classical shadows. We demonstrate the effectiveness of the method with numeral simulations across discrete-variable, continuous-variable and hybrid-variable systems.

quant-ph↗

arXiv2025

Exploring critical states of the quantum Rabi model via Hamiltonian variational ans\"atze

Characterizing quantum critical states towards the thermodynamic limit is essential for understanding phases of matter. The power of quantum simulators for preparing the critical states relies crucially on the structure of quantum circuits and in return provides new insight into the critical states. Here, we explore the critical states of the quantum Rabi model~(QRM) by preparing them variationally with Hamiltonian variational ans\"atze~(HVA), in which the intricated interplay among different quantum fluctuations can be parameterized at different levels. We find that the required circuit depth scales linearly with the effective system size, suggesting that HVA can efficiently capture the behavior of critical states of QRM towards the thermodynamic limit. Moreover, we reveal that HVA gradually squeeze the initial state to the target critical state, with a number of blocks increasing only linearly with the effective system size. Our work suggests variational quantum algorithm as a new probe for the complicated critical states.

quant-ph↗

arXiv2025

Public-Key Quantum Authentication and Digital Signature Schemes Based on the QMA-Complete Problem

We propose a quantum authentication and digital signature protocol whose security is founded on the Quantum Merlin Arthur~(QMA)-completeness of the consistency of local density matrices. The protocol functions as a true public-key cryptography system, where the public key is a set of local density matrices generated from the private key, a global quantum state. This construction uniquely eliminates the need for trusted third parties, pre-shared secrets, or authenticated classical channels for public key distribution, making a significant departure from symmetric protocols like quantum key distribution. We provide a rigorous security analysis, proving the scheme's unforgeability against adaptive chosen-message attacks by quantum adversaries. The proof proceeds by a formal reduction, demonstrating that a successful forgery would imply an efficient quantum algorithm for the QMA-complete Consistency of Quantum Marginal Problem~(QMP). We further analyze the efficiency of verification using partial quantum state tomography, establishing the protocol's theoretical robustness and outlining a path towards practical implementation

quant-ph↗

arXiv2025

Adaptive random compiler for Hamiltonian simulation

Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application probabilities based on the strengths of Hamiltonian terms, as measured by the trace norm. However, relying solely on the trace norm to define sampling distributions may not be optimal, especially for continuous-variable and hybrid-variable systems involving unbounded operators, where quantifying Hamiltonian strengths is challenging. In this work, we propose an adaptive randomized compilation algorithm that dynamically updates sampling weights via low-order moment measurements of Hamiltonian terms, assigning higher probabilities to terms with greater uncertainty. This approach improves accuracy without significantly increasing gate counts and extends randomized compilation to continuous-variable and hybrid-variable systems by addressing the difficulties in characterizing the strengths of unbounded Hamiltonian terms. Numerical simulations demonstrate the effectiveness of our method.

quant-ph↗

arXiv2025

Variational Quantum Algorithm for Solving the Liouvillian Gap

In open quantum systems, the Liouvillian gap characterizes the relaxation time toward the steady state. However, accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator. In this work, we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap. By utilizing the Choi-Jamiokowski isomorphism, we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian. Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence. Moreover, to address scenarios with degenerate steady states, we introduce an iterative energy-offset scanning technique. Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths. These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.

quant-ph↗

arXiv2025

Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators

Quantum operator scrambling describes the spreading of local operators into the whole system in the picture of Heisenberg evolution, which is often quantified by the operator size growth. Here we propose a measure of quantum operator scrambling via Holevo information of operators, by taking its capacity to distinguish operator information locally. We show that the operator size is closely related to a special kind of Holevo information of operators. Moreover, we propose a feasible protocol for measuring Holevo information of operators on digital quantum simulators based on random states. \textcolor{black}{For the mixed-field Ising model,} our numerical simulations show that the integrable system can be told apart from the chaotic system by measuring the spatial-temporal patterns of Holevo information. Furthermore, we find that error mitigation is required to restore the time-oscillation behavior of Holevo information for the integrable system, a crucial feature distinct from the chaotic one. Our work provides a new perspective to understand the information scrambling and quantum chaos from aspects of Holevo information of operators.

quant-ph↗

arXiv2024

The Spectral Amplitude Principle for Dynamics of Quantum Neural Networks

The mechanism governing the training dynamics of Quantum Neural Networks (QNNs) remains under-explored. In classical Deep Neural Networks (DNNs), training is dominated by "Spectral Bias," i.e. prioritizing learning low-frequency components and struggle for high-frequency details. In this work, we theoretically and empirically identify a distinct mechanism in QNNs, which we term Spectral Amplitude Priority. By analyzing the frequency-domain gradients and residual dynamics via the Quantum Neural Tangent Kernel (QNTK), we prove that QNN training is governed primarily by the magnitude of spectral components rather than their frequency indices. Consequently, QNNs can efficiently capture high-frequency functions-provided they have significant amplitude-thereby overcoming the inherent limitations of their classical counterparts. We validate this principle on both synthetic high-frequency functions and quantum-advantage tasks. The results show that QNNs significantly outperform DNNs in high-frequency tasks, offering an explanation for QNNs' superior expressivity in complex spectral landscapes.

quant-ph↗

arXiv2024

Variational quantum simulation of ground states and thermal states for lattice gauge theory with multi-objective optimization

Variational quantum algorithms provide feasible approaches for simulating quantum systems and are applied widely. For lattice gauge theory, however, variational quantum simulation faces a challenge as local gauge invariance enforces a constraint on the physical Hilbert space. In this paper, we incorporate multi-objective optimization for variational quantum simulation of lattice gauge theory at zero and finite temperatures. By setting energy or free energy of the system and penalty for enforcing the local gauge invariance as two objectives, the multi-objective optimization can self-adjust the proper weighting for two objectives and thus faithfully simulate the gauge theory in the physical Hilbert space. Specifically, we propose variational quantum eigensolver and variational quantum thermalizer for preparing the ground states and thermal states of lattice gauge theory, respectively. We demonstrate the quantum algorithms for a $Z_2$ lattice gauge theory with spinless fermion in one dimension. With numeral simulations, the multi-objective optimization shows that minimizing energy~(free energy) and enforcing the local gauge invariance can be achieved simultaneously at zero temperature~(finite temperature). The multi-objective optimization suggests a feasible ingredient for quantum simulation of complicated physical systems on near-term quantum devices.

quant-ph↗

arXiv2024

Determining non-Hermitian parent Hamiltonian from a single eigenstate

A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For non-Hermitian systems, it is natural to expect that determining the Hamiltonian requires a pair of both left and right eigenstates. Here, we observe that it can be sufficient to determine a non-Hermitian Hamiltonian from a single right or left eigenstate. Our approach is based on the quantum covariance matrix, where the solution of Hamiltonian corresponds to the complex null vector. Our scheme favours non-Hermitian Hamiltonian learning on experimental quantum systems, as only the right eigenstates there can be accessed. Furthermore, we use numerical simulations to examine the effects of measurement errors and show the stability of our scheme.

quant-ph↗

arXiv2024

Quantum coupon collector with mixed-state encoding

The coupon collector is a prototypical model for evaluating the number of samples for identifying a set. By superposing all elements in the set as a pure quantum state, a quantum version of the coupon collector aims to learn the state, which is shown to reduce the sample complexity. Here we propose a quantum coupon collector by encoding the set into a mixed state, where the information of missing elements are labelled with Pauli strings. Remarkably, the encoded mixed state has no quantum entangled state and is easy to prepare. With such mixed-state encoding, it can be efficient to learn the set by performing Bell measurements on two copies and then extracting the missing element by solving a series of equations obtained from the measurements. Our protocol further reduces the sample complexity from $O(n)$ in the case of pure-state encoding to $O(\log n)$ when the missing element is one, where $n$ is the number of elements in the set. The mixed-state encoding scheme provides a new avenue for quantum learning and enlarges the realm for exploring quantum advantages.

quant-ph↗

arXiv2024

Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points

Dual-unitary quantum circuits can provide analytic spatiotemporal correlation functions of local operators from transfer matrices, enriching our understanding of quantum dynamics with exact solutions. Nevertheless, a full understanding is still lacking as the case of a non-diagonalizable transfer matrix with exceptional points has less been investigated. In this paper, we give an inverse approach for constructing dual-unitary quantum circuits with exceptional points in the transfer matrices, by establishing relations between transfer matrices and local unitary gates. As a consequence of the coalesce of eigenvectors, the correlation functions exhibit a polynomial modified exponential decay, which is significantly different from pure exponential decay, especially at early stages. Moreover, we point out that the Hamiltonian evolution of a kicked XXZ spin chain can be approximately mapped to a dual-unitary circuit with exceptional points by Trotter decomposition. Finally, we investigate the dynamics approaching and at exceptional points, showing that behaviors of correlation functions are distinct by Laplace transformation.

quant-ph↗

arXiv2024

Simulating Parton Fragmentation on Quantum Computers

Parton fragmentation functions (FFs) are indispensable for understanding processes of hadron production ubiquitously existing in high-energy collisions, but their first principle determination has never been realized due to the insurmountable difficulties in encoding their operator definition using traditional lattice methodology. We propose a framework that makes a first step for evaluating FFs utilizing quantum computing methodology. The key element is to construct a semi-inclusive hadron operator for filtering out hadrons of desired types in a collection of particles encoded in the quantum state. We illustrate the framework by elaborating on the Nambu-Jona-Lasinio model with numeral simulations. Remarkably, We show that the semi-inclusive hadron operator can be constructed efficiently with a variational quantum algorithm. Moreover, we develop error mitigation techniques tailed for accurately calculating the FFs in the presence of quantum noises. Our work opens a new avenue for investigating QCD hadronization on near-term quantum computers.

hep-ph↗