arXiv subjects

Zhong-Xia Shang

Publications and source records attributed to Zhong-Xia Shang.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Gibbs State Preparation via Relative Decoding: From Fast-Mixing Sources to Broader Target Classes

Provable guarantees for preparing quantum Gibbs states, such as rapid mixing or gapped coherent preparation paths, are known only for restricted Hamiltonian families and usually must be re-derived for each new family. Building on homomorphic polynomial transduction, a generalization of decoded quantum interferometry (DQI) and Hamiltonian DQI (HDQI), we show how relative decoding transfers such a guarantee from a source Hamiltonian $H_A$ to a target $H_B$. Writing each Hamiltonian as a sum of $m$ Pauli terms, the subsets of terms whose product is proportional to the identity, its relations, form a binary linear code, $K_A$ for the source and $K_B$ for the target, with the Pauli-label matrix as parity-check matrix as in DQI. Starting from the canonical thermofield double (TFD) of $H_A$, a Bell transform, a reversible label map, and a coherent decoder for the quotient code $K_B/K_A$ prepare an approximate TFD of $H_B$, and hence its Gibbs state. Because this decoder only resolves target relations absent from the source, the reachable inverse temperature is set by the relative distance $d_{\rm rel}$, the fewest terms in any such relation. It can far exceed the ordinary distance $d_{\rm ord}$, the fewest terms in any target relation, which bounds the uniform exact decoding radius of DQI and HDQI. We show that linear $d_{\rm rel}$ with efficient decoding at linear radius certifies a constant inverse temperature. As an example, starting from a nearest-neighbor spin chain whose TFD is known to be preparable at every finite temperature, a sparse classical parity-check matrix yields bounded-degree, geometrically nonlocal, noncommuting targets with $d_{\rm ord}=3$ and $d_{\rm rel}=Θ(m)$. To our knowledge, this gives a new class of efficiently preparable TFDs.

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arXiv2026

Hamiltonian dynamics from pure dissipation

The fundamental difference between closed and open quantum dynamics lies in their environmental interaction: closed systems are perfectly isolated and evolve reversibly under unitary Hamiltonian dynamics, whereas open systems continuously couple to an external bath, resulting in irreversible dissipation and information loss. In this work, we show internal Hamiltonian dynamics can be "faked`` via external pure dissipation, i.e., Lindbladians without a coherent Hamiltonian part. More concretely, we show that, in a GKSL representation with zero explicit Hamiltonian term but nontraceless jump operators, bounded-norm dissipative generators can approximate Hamiltonian dynamics within $ε$ error in diamond norm using $\mathcal{O}(t^2/ε)$ evolution time. We further prove that for time-independent dynamics this $\mathcal{O}(t^2/ε)$ scaling is in the worst case, necessary and optimal from a geometric perspective, which captures the fundamental decoherence cost for catching up with the speed of Hamiltonian dynamics. Our construction leads to various implications, including the BQP-completeness of purely dissipative dynamics even before reaching approximate equilibrium, a Zeno-adjacent state-independent freezing effect, the no super-quadratic fast-forwarding theorem of a class of purely dissipative dynamics, and reducing Lindbladian simulation cost via gauge changing.

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arXiv2026

Optimal Tolerant Testing of Lindbladian Dissipation

Quantifying dissipation is essential for controlling quantum noise and characterizing open-system dynamics. In practical experimental settings, residual noise may still persist despite efforts to suppress it, making it important to determine whether the dissipative strength remains within a prescribed tolerance threshold. We study this question for an unknown, time-independent Lindblad generator with bounded strength, where the jump operators are local but with unrestricted overlap, using only memoryless forward-evolution access. The task is to distinguish dissipative strength of at most $\varepsilon_1$ from strength of at least $\varepsilon_2$, for $0 \leq \varepsilon_1 < \varepsilon_2$, measured in the canonical dissipator's normalized Frobenius norm. We give an algorithm that solves this task in total evolution time $O(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$ for all nontrivial thresholds, with constant success probability, and provide a matching lower bound $Ω(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$ that establishes optimality even for adaptive protocols. This extends dissipation testing to the tolerant setting and eliminates the bounded-degree requirement, making the framework applicable to a broader range of experimentally relevant settings.

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arXiv2026

From Simple Sources to Quantum Advantage: Homomorphic Polynomial Transduction via Relative Decoding

Decoded quantum interferometry (DQI) and its Hamiltonian extension (HDQI) prepare states whose amplitudes are low-degree polynomials of an objective, using Fourier transforms and coherent decoding. We recast this approach as quantum state transduction through algebra homomorphisms. We transfer an efficiently preparable operator state of a degree-$D$ polynomial in a source Hamiltonian $H_A$ to the corresponding polynomial state of a target Hamiltonian $H_B=π(H_A)$, where $π$ is a unital $*$-homomorphism between the finite-dimensional source and target $C^*$-algebras. The transduction uses operator Fourier transforms and relative decoding to recover source operators rather than individual term-selection labels. The relative distance $d_{\mathrm{rel}}$ is the first degree at which source and target traces disagree. We prove that $2D<d_{\mathrm{rel}}$ is equivalent to preserving all inner products between degree-$D$ polynomials. Moreover, $d_{\mathrm{rel}}\ge d_{\mathrm{ord}}$, where $d_{\mathrm{ord}}$ is the ordinary distance used in (H)DQI, and we give families with $d_{\mathrm{ord}}=O(1)$ but $d_{\mathrm{rel}}=Θ(n)$ and efficient decoders. Our framework replaces the complicated pilot state preparation by the more modular task of preparing a source polynomial state. DQI and HDQI arise as relation-free special cases. The framework accommodates nonuniform coefficients and noncommuting interactions and extends to fermionic, qudit, and bosonic systems, with applications to approximate optimization and Gibbs sampling. As evidence of advantages, for a nonlinear pairwise variant of optimal polynomial intersection where constant $d_{\mathrm{ord}}$ limits DQI-style preparations, relative decoding yields an ideal quantum score of 0.643 versus 0.606 for the best tested classical heuristic, a gap exceeding 3 percentage points.

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arXiv2026

A Simple Quantum Linear-System Solver via Dissipation

Dissipation has been recently demonstrated as a powerful primitive for designing quantum algorithms. We apply this viewpoint directly to linear-system solving, $Ax=b$. We construct a simple purely dissipative Lindbladian whose unique fixed point encodes the linear-system solution. We prove dimension-independent trace-distance mixing in $Θ(κ^2\log(1/\eps))$ time. We then show how to run this Lindbladian on digital quantum computers via collective block encoding and Lindbladian simulation, resulting in an $O\!\left(κ^2\log(1/\eps) \frac{\log(κ/\eps)}{\log\log(κ/\eps)}\right)$ query complexity for both $U_A$, the block encoding of $A$, and $U_b$, the $|b\rangle$ state preparation unitary.

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arXiv2026

Exponential Lindbladian fast forwarding and exponential amplification of certain Gibbs state properties

Fast-forwarding refers to the ability to simulate a system of time $t$ using significantly fewer than $t$ queries or circuit depth. While various Hamiltonian systems are known to circumvent the no fast-forwarding theorem, analogous results for dissipative dynamics, governed by Lindbladians, remain largely unexplored. We first present a quantum algorithm for simulating purely dissipative Lindbladians with unitary jump operators, achieving additive query complexity $\mathcal{O}\left(t + \log(\varepsilon^{-1})\right)$ up to error~$\varepsilon$, improving previous algorithms. When the jump operators have certain structures (i.e., block-diagonal Paulis), the algorithm can be modified to achieve exponential fast-forwarding, attaining circuit depth $\mathcal{O}\left(\log\left(t + \log(\varepsilon^{-1})\right)\right)$, while preserving query complexity via parallel access. Using these fast-forwarding techniques, we develop a quantum algorithm for estimating Gibbs state properties of the form $\langle ψ_1 | e^{-β(H + I)} | ψ_2 \rangle$, up to additive error $ε$, with $H$ the Hamiltonian and $β$ the inverse temperature. For input states exhibiting certain coherence conditions -- e.g.,~$\langle 0|^{\otimes n} e^{-β(H + I)} |+\rangle^{\otimes n}$ -- our method achieves exponential improvement in complexity (measured by circuit depth), $\mathcal{O} (2^{-n/2} ε^{-1} \log β),$ compared to the quantum singular value transformation-based approach, with complexity $\tilde{\mathcal{O}} (ε^{-1} \sqrtβ )$. We show how to apply this exponential improvement to applications such as the ground state overlap testing and amplitude estimation. For general $| ψ_1 \rangle$ and $| ψ_2 \rangle$, we also show how the level of improvement is changed with the coherence resource in $| ψ_1 \rangle$ and $| ψ_2 \rangle$.

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arXiv2026

Bra-ket entanglement, an indicator bridging entanglement, magic, and coherence

Understanding the intricate interplay between distinct quantum resources is a fundamental prerequisite for rigorously characterizing the boundary between classical and quantum technologies. Among the vast landscape of quantum resources, entanglement, magic, and coherence have arguably attracted the most intense investigation. However, while universally recognized as the core drivers of quantum advantage, our understanding of their structural interplay remains fragmented and compartmentalized. In this work, we introduce an indicator called {\em bra-ket entanglement} (BKE) defined in the operator vectorization space to bridge all three quantum resources. Specifically, we show that BKE governs a resource dependence transition in the generation of entanglement: in the low-BKE regime, the growth of entanglement is dominated by coherence, largely independent of magic. However, as BKE increases, the dependence on coherence will gradually be replaced by a dependence on magic. Consequently, in the high-BKE regime, entanglement generation becomes dominated by magic, largely independent of coherence. These results are built on a series of new entropy-theoretic relations and are verified through numerical experiments. We also discuss implications of our results for the resource transitions in classical simulations of mixed states and marginal probabilities and for relating different classical simulation methods.

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arXiv2025

Fast-forwardable Lindbladians imply quantum phase estimation

Quantum phase estimation (QPE) and Lindbladian dynamics are both foundational in quantum information science and central to quantum algorithm design. In this work, we bridge these two concepts: certain simple Lindbladian processes can be adapted to perform QPE-type tasks. However, unlike QPE, which achieves Heisenberg-limit scaling, these Lindbladian evolutions are restricted to standard quantum limit complexity. This indicates that, different from Hamiltonian dynamics, the natural dissipative evolution speed of such Lindbladians does not saturate the fundamental quantum limit, thereby suggesting the potential for quadratic fast-forwarding. We confirm this by presenting a quantum algorithm that simulates these Lindbladians for time $t$ within an error $\varepsilon$ using $\mathcal{O}\left(\sqrt{t\log(\varepsilon^{-1})}\right)$ cost, whose mechanism is fundamentally different from the fast-forwarding examples of Hamiltonian dynamics. As a bonus, this fast-forwarded simulation naturally serves as a new Heisenberg-limit QPE algorithm. Therefore, our work explicitly bridges the standard quantum limit-Heisenberg limit transition to the fast-forwarding of dissipative dynamics. We also adopt our fast-forwarding algorithm for efficient Gibbs state preparation and demonstrate the counter-intuitive implication: the allowance of a quadratically accelerated decoherence effect under arbitrary Pauli noise.

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arXiv2025

Design nearly optimal quantum algorithm for linear differential equations via Lindbladians

Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary dynamics into intrinsically unitary quantum circuits. In this work, we propose a new quantum algorithm for solving ODEs by harnessing open quantum systems. Specifically, we propose a novel technique called non-diagonal density matrix encoding, which leverages the inherent non-unitary dynamics of Lindbladians to encode general linear ODEs into the non-diagonal blocks of density matrices. This framework enables us to design quantum algorithms with both theoretical simplicity and high performance. Combined with the state-of-the-art quantum Lindbladian simulation algorithms, our algorithm can outperform all existing quantum ODE algorithms and achieve near-optimal dependence on all parameters under a plausible input model. We also give applications of our algorithm including the Gibbs state preparations and the partition function estimations.

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arXiv2025

Entanglement-induced exponential advantage in amplitude estimation via state matrixization

Estimating quantum amplitude, or the overlap between two quantum states, is a fundamental task in quantum computing and underpins numerous quantum algorithms. In this work, we introduce a novel algorithmic framework for quantum amplitude estimation by transforming pure states into their matrix forms (Matrixization) and encoding them into non-diagonal blocks of density operators and diagonal blocks of unitary operators. Utilizing the construction details of state preparation circuits, we systematically reconstruct amplitude estimation algorithms within the novel matrixization framework through a technique known as channel block encoding. Compared with the standard approach, amplitude estimation through matrixization can have a different complexity that depends on the entanglement properties of the two quantum states. Specifically, our new algorithm can have exponentially smaller gate complexity when one of the two quantum states is prepared by a linear-depth quantum circuit that is below maximal entanglement under a certain bi-partition and the other state is maximally entangled. We later generalize this result to broader regimes and discuss implications. Our results demonstrate that the near-optimal performance of the standard amplitude estimation algorithm can be surpassed in specific cases.

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arXiv2024

Pauli quantum computing: $I$ as $|0\rangle$ and $X$ as $|1\rangle$

We propose a new quantum computing formalism named Pauli quantum computing. In this formalism, we use the Pauli basis $I$ and $X$ on the non-diagonal blocks of density matrices to encode information and treat them as the computational basis $|0\rangle$ and $|1\rangle$ in standard quantum computing. There are significant differences between Pauli quantum computing and standard quantum computing from the achievable operations to the meaning of measurements, resulting in novel features and comparative advantages for certain tasks. We will give three examples in particular. First, we show how to design Lindbladians to realize imaginary time evolutions and prepare stabilizer ground states in Pauli quantum computing. These stabilizer states can characterize the coherence in the steady subspace of Lindbladians. Second, for quantum amplitudes of the form $\langle +|^{\otimes n}U|0\rangle^{\otimes n}$ with $U$ composed of $\{H,S,T,\text{CNOT}\}$, as long as the number of Hadamard gates in the unitary circuit $U$ is sub-linear $\mathit{o}(n)$, the gate (time) complexity of estimating such amplitudes using Pauli quantum computing formalism can be exponentially reduced compared with the standard formalism ($\mathcal{O}(ε^{-1})$ to $\mathcal{O}(2^{-(n-\mathit{o}(n))/2}ε^{-1})$). Third, given access to a searching oracle under the Pauli encoding picture manifested as a quantum channel, which mimics the phase oracle in Grover's algorithm, the searching problem can be solved with $\mathcal{O}(n)$ scaling for the query complexity and $\mathcal{O}(\text{poly}(n))$ scaling for the time complexity. While so, how to construct such an oracle is highly non-trivial and unlikely efficient due to the hardness of the problem.

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arXiv2024

A polynomial-time dissipation-based quantum algorithm for solving the ground states of a class of classically hard Hamiltonians

In this work, we give a polynomial-time quantum algorithm for solving the ground states of a class of classically hard Hamiltonians. The mechanism of the exponential speedup that appeared in our algorithm comes from dissipation in open quantum systems. To utilize the dissipation, we introduce a new idea of treating vectorized density matrices as pure states, which we call the vectorization picture. By doing so, the Lindblad master equation (LME) becomes a Schrödinger equation with non-Hermitian Hamiltonian. The steady state of the LME, therefore, corresponds to the ground states of a special class of Hamiltonians. The runtime of the LME has no dependence on the overlap between the initial state and the ground state. For the input part, given a Hamiltonian, under plausible assumptions, we give a polynomial-time classical procedure to judge and solve whether there exists LME with the desired steady state. For the output part, we propose a novel measurement strategy to extract information about the ground state from the original steady density matrix. We show that the Hamiltonians that can be efficiently solved by our algorithms contain classically hard instances assuming $\text{P}\neq \text{BQP}$. We also discuss possible exponential complexity separations between our algorithm and previous quantum algorithms without using the vectorization picture.

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arXiv2024

Unconditionally decoherence-free quantum error mitigation by density matrix vectorization

Fighting against noise is crucial for NISQ devices to demonstrate practical quantum applications. In this work, we give a new paradigm of quantum error mitigation based on the vectorization of density matrices. Different from the ideas of existing quantum error mitigation methods that try to distill noiseless information from noisy quantum states, our proposal directly changes the way of encoding information and maps the density matrices of noisy quantum states to noiseless pure states, which is realized by a novel and NISQ-friendly measurement protocol and a classical post-processing procedure. Our protocol requires no knowledge of the noise model, no ability to tune the noise strength, and no ancilla qubits for complicated controlled unitaries. Under our encoding, NISQ devices are always preparing pure quantum states which are highly desired resources for variational quantum algorithms to have good performance in many tasks. We show how this protocol can be well-fitted into variational quantum algorithms. We give several concrete ansatz constructions that are suitable for our proposal and do theoretical analysis on the sampling complexity, the expressibility, and the trainability. We also give a discussion on how this protocol is influenced by large noise and how it can be well combined with other quantum error mitigation protocols. The effectiveness of our proposal is demonstrated by various numerical experiments.

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arXiv2024

Hermitian-preserving ansatz and variational open quantum eigensolver

We propose a new variational quantum algorithm named Variational Open Quantum Eigensolver (VOQE) for solving steady states of open quantum systems described by either Lindblad master equations or non-Hermitian Hamiltonians. In VOQE, density matrices of mixed states are represented by pure states in doubled Hilbert space. We give a framework for building circuit ansatz which we call the Hermitian-preserving ansatz (HPA) to restrict the searching space. We also give a method to efficiently measure the operators' expectation values by post-selection measurements. We show the workflow of VOQE on solving steady states of the LMEs of the driven XXZ model and implement VOQE to solve the spectrum of the non-Hermitian Hamiltonians of the Ising spin chain in an imaginary field.

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arXiv2024

Boson sampling enhanced quantum chemistry

In this work, we give a hybrid quantum-classical algorithm for solving electronic structure problems of molecules using only linear quantum optical systems. The variational ansatz we proposed is a hybrid of non-interacting Boson dynamics and classical computational chemistry methods, specifically, the Hartree-Fock method and the Configuration Interaction method. The Boson part is built by a linear optical interferometer which is easier to realize compared with the well-known Unitary Coupled Cluster (UCC) ansatz composed of quantum gates in conventional VQE and the classical part is merely classical processing acting on the Hamiltonian. We called such ansatzes Boson Sampling-Classic (BS-C). The appearance of permanents in the Boson part has its physical intuition to provide different kinds of resources from commonly used single-, double-, and higher-excitations in classical methods and the UCC ansatz to exploring chemical quantum states. Such resources can help enhance the accuracy of methods used in the classical parts. We give a scalable hybrid homodyne and photon number measurement procedure for evaluating the energy value which has intrinsic abilities to mitigate photon loss errors and discuss the extra measurement cost induced by the no Pauli exclusion principle for Bosons with its solutions. To demonstrate our proposal, we run numerical experiments on several molecules and obtain their potential energy curves reaching chemical accuracy.

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arXiv2024

Realization of fractional quantum Hall state with interacting photons

Fractional quantum Hall (FQH) states, known for their robust topological order and the emergence of non-Abelian anyons, have captured significant interest due to the appealing applications in fault-tolerant quantum computing. Bottom-up approach on an engineered quantum platform will provide opportunities to operate FQH states without external magnetic field and enhance local and coherent manipulation of these exotic states. Here we demonstrate a lattice version of photon FQH state using a programmable on-chip platform based on photon blockade and engineering gauge fields on a novel two-dimensional circuit quantum electrodynamics (QED) system. We first observe the effective photon Lorentz force and butterfly spectrum in the artificial gauge field, a prerequisite for FQH states. After adiabatic assembly of Laughlin FQH wavefunction of 1/2 filling factor from localized photons, we observe strong density correlation and chiral topological flow among the FQH photons. We then verify the unique features of FQH states in response to external fields, including the incompressibility of generating quasiparticles and the smoking-gun signature of fractional quantum Hall conductivity. Our work represents a significant advance in the bottom-up creation and manipulation of novel strongly correlated topological quantum matter composed of photons and opens up possibilities for fault-tolerant quantum information devices.

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arXiv2023

Schrödinger-Heisenberg Variational Quantum Algorithms

Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics. However, the extremely high accuracy needed to surpass classical computers poses a critical demand to the circuit depth, which is severely limited by the non-negligible gate infidelity, currently around 0.1-1%. Here, by incorporating a virtual Heisenberg circuit, which acts effectively on the measurement observables, to a real shallow Schrödinger circuit, which is implemented realistically on the quantum hardware, we propose a paradigm of Schrödinger-Heisenberg variational quantum algorithms to resolve this problem. We choose a Clifford virtual circuit, whose effect on the Hamiltonian can be efficiently and classically implemented according to the Gottesman-Knill theorem. Yet, it greatly enlarges the state expressivity, realizing much larger unitary t-designs. Our method enables accurate quantum simulation and computation that otherwise is only achievable with much deeper and more accurate circuits conventionally. This has been verified in our numerical experiments for a better approximation of random states and a higher-fidelity solution to the ground state energy of the XXZ model. Together with effective quantum error mitigation, our work paves the way for realizing accurate quantum computing algorithms with near-term quantum devices.

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arXiv2022

Quantum design for advanced qubits: plasmonium

The increasingly complex quantum electronic circuits with a number of coupled quantum degrees of freedom will become intractable to be simulated on classical computers, and requires quantum computers for an efficient simulation. In turn, it will be a central concept in quantum-aided design for next-generation quantum processors. Here, we demonstrate variational quantum eigensolvers to simulate superconducting quantum circuits with varying parameters covering a plasmon-transition regime, which reveals an advanced post-transmon qubit, "plasmonium". We fabricate this new qubit and demonstrate that it exhibits not only high single- and two-qubit gate fidelities (99.85(1)% and 99.58(3)%, respectively), but also a shrinking (by 60%) physical size and larger (by 50%) anharmonicity than the transmon, which can bring a number of advantages for scaling up multi-qubit devices. Our work opens the way to designing advanced quantum processors using existing quantum computing resources.

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