arXiv subjects

Benchi Zhao

Publications and source records attributed to Benchi Zhao.

15 recordsLinked to original sources

arXiv2026

Virtual quantum neural networks

Quantum neural networks are a prominent model of quantum machine learning. Their training consists in the minimization of a given loss function over a parametrized family of quantum circuits, mathematically described by unitary operators, or, more generally, completely positive linear maps. In this work, we extend the notion of quantum neural network, using random sampling and classical data processing to enlarge the optimization space in a way that includes linear combinations of completely positive maps. Our extended model, called virtual quantum neural networks, leverages its enlarged optimization space to achieve increased expressivity and improved noise robustness. These benefits are illustrated in three representative tasks: quantum error mitigation, binary classification, and estimation of ground-state energies. Overall, virtual quantum neural networks offer a flexible learning paradigm that expands the space of achievable computations and strengthens the applications of near-term quantum hardware.

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arXiv2026

Causal-Class Hierarchies in Coherence-Constrained Channel Transformation

Higher-order quantum transformations allow multiple channel uses to be combined through different causal architectures, from parallel and fixed-order sequential networks to general higher-order processes. Whether this causal freedom improves channel transformation when the higher-order operation is also constrained by a resource theory remains largely unexplored. We study this question in the dynamical resource theory of coherence using a unified semidefinite-programming framework. For two qubit amplitude-damping channels and the identity target, we prove a strict causal hierarchy at every nontrivial damping strength under both maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC). In contrast, mixed-Pauli channels admit a common teleportation simulation that transfers the channel dependence to Bell-diagonal program states prepared in parallel. The remaining processing can then be absorbed into a single quantum operational, so parallel, fixed-order sequential, and general higher-order strategies achieve the same optimal error for any target. These results identify free program-state parallelisation as a structural obstruction to causal enhancement.

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arXiv2026

Universal quantum state purification under energy-preserving constraints

Pure quantum states are a fundamental resource for quantum information processing, but unavoidable noise degrades their purity and limits the performance of quantum tasks. Quantum state purification attempts to restore purity by jointly processing several noisy copies of an unknown state, typically in a probabilistic way. Whether purification is possible, and how much it can achieve, depends strongly on the set of operations that are physically allowed. In this work, we study universal purification under \textit{energy-preserving operations}, which cannot exchange energy with an external environment. We identify exactly when the energy-preserving constraint forbids any universal purification advantage, and we provide concrete examples in which an advantage available to unrestricted operations disappears under energy conservation. When energy-preserving purification remains possible, we determine its optimal fidelity and success probability and construct the corresponding protocols. The framework includes unrestricted purification as a special case and extends naturally to purification assisted by an external energy resource.

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arXiv2025

The communication power of indefinite causal order

Quantum theory is in principle compatible with scenarios where physical processes occur in an indefinite order, potentially yielding advantages in a broad range of information processing tasks. However, advantages in communication, the most basic form of information processing, have so far remained controversial and hard to prove. Here we provide a framework for assessing the role of causal order in communication, by comparing different causal structures under the constraint that the allowed operations must not generate signaling from signaling-incapable devices. Using this framework, we establish a clear-cut advantage of indefinite causal order, and, at the same time, we identify a series of fundamental limits to the communication power of causal structures in quantum mechanics. Notably, we find that a special form of indefinite causal order, obtained by coherently controlling the order of two processes, enhances the transmission of classical messages in a one-shot scenario, but no quantum operation with indefinite order can offer advantages over shared entanglement when asymptotically many uses of the same communication device are employed. Overall, our results unveil non-trivial relations between communication, causal order, entanglement, and no-signaling quantum processes.

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arXiv2025

Power and limitations of distributed quantum state purification

Quantum state purification protocols, which mitigate noise by converting multiple copies of noisy quantum states into fewer copies with a lower noise level, have applications in quantum communication and computation with imperfect devices. Here, we systematically study the task of state purification in distributed quantum systems, demanding that purification be achieved by local operations and classical communication (LOCC). We prove that, in the presence of depolarizing noise, no LOCC purification protocol starting from two copies can work blindly for all the states in three important sets: the set of all pure two-qubit states, the set of all two-qubit maximally entangled states, and the Bell basis. In stark contrast, we show that a targeted, single-state purification is always achievable in the presence of depolarizing noise, and we provide an explicit analytical LOCC protocol for every given two-qubit state. For arbitrary finite sets of pure states and arbitrary noise profiles, we develop an optimization-based algorithm that systematically designs LOCC purification protocols, and we demonstrate it through concrete examples. Overall, our results identify both fundamental limitations and practical noise reduction strategies for distributed quantum information processing.

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arXiv2025

Dynamic LOCC Circuits for Automated Entanglement Manipulation

Due to the limited qubit number of quantum devices, distributed quantum computing is considered a promising pathway to overcome this constraint. In this paradigm, multiple quantum processors are interconnected to form a cohesive computational network, and the most natural set of free operations is local operations and classical communication (LOCC). However, designing a practical LOCC protocol for a particular task has been a tough problem. In this work, we propose a general and flexible framework called dynamic LOCCNet (DLOCCNet) to simulate and design LOCC protocols. We demonstrate its effectiveness in two key applications: entanglement distillation and distributed state discrimination. The protocols designed by DLOCCNet, in contrast to conventional ones, can solve larger-sized problems with reduced training time, making the framework a practical and scalable tool for current quantum devices. This work advances our understanding of the capabilities and limitations of LOCC while providing a powerful methodology for protocol design.

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arXiv2024

Variational quantum Hamiltonian engineering

The Hamiltonian of a quantum system is represented in terms of operators corresponding to the kinetic and potential energies of the system. The expectation value of a Hamiltonian and Hamiltonian simulation are two of the most fundamental tasks in quantum computation. The overheads for realizing the two tasks are determined by the Pauli norm of Hamiltonian, which sums over all the absolute values of Pauli coefficients. In this work, we propose a variational quantum algorithm (VQA) called variational quantum Hamiltonian engineering (VQHE) to minimize the Pauli norm of Hamiltonian, such that the overhead for executing expectation value estimation and Hamiltonian simulation can be reduced. First, we develop a theory to encode the Pauli norm optimization problem into the vector L1-norm minimization problem. Then we devise an appropriate cost function and utilize the parameterized quantum circuits (PQC) to minimize the cost function. We also conduct numerical experiments to reduce the Pauli norm of the Ising Hamiltonian and molecules' Hamiltonian to show the efficiency of the proposed VQHE.

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arXiv2024

Retrieving non-linear features from noisy quantum states

Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation, and predicting non-linear features from quantum states. But in reality, inevitable quantum noise prevents us from accessing the desired value. In this paper, we address this issue by systematically analyzing the feasibility and efficiency of extracting high-order moments from noisy states. We first show that there exists a quantum protocol capable of accomplishing this task if and only if the underlying noise channel is invertible. We then establish a method for deriving protocols that attain optimal sample complexity using quantum operations and classical post-processing only. Our protocols, in contrast to conventional ones, incur lower overheads and avoid sampling different quantum operations due to a novel technique called observable shift, making the protocols strong candidates for practical usage on current quantum devices. The proposed method also indicates the power of entangled protocols in retrieving high-order information, whereas in the existing methods, entanglement does not help. We further construct the protocol for large quantum systems to retrieve the depolarizing channels, making the proposed method scalable. Our work contributes to a deeper understanding of how quantum noise could affect high-order information extraction and provides guidance on how to tackle it.

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arXiv2024

Probabilistic channel simulation using coherence

Channel simulation using coherence, which refers to realizing a target channel with coherent states and free operations, is a fundamental problem in the quantum resource theory of coherence. The limitations of the accuracy of deterministic channel simulation motivate us to consider the more general probabilistic framework. In this paper, we develop the framework for probabilistic channel simulation using coherence with free operations. When the chosen set of free operations is the maximally incoherent operations, we provide an efficiently computable semidefinite program (SDP) to calculate the maximal success probability and derive the analytic expression of success probability for some special cases. When the chosen set of free operations is the dephasing-covariant incoherent operations (DIO), we show that if the target channel is not a resource nonactivating channel, then one cannot simulate it exactly both deterministically and probabilistically. The SDP for maximal success probability of simulating a channel by DIO is also given correspondingly.

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arXiv2023

Power of quantum measurement in simulating unphysical operations

The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations according to classically determined probability distributions. In this work, we show that using quantum measurement instead leads to lower simulation costs for general Hermitian-preserving maps. Remarkably, we establish the equality between the simulation cost and the well-known diamond norm, thus closing a previously known gap and assigning diamond norm a universal operational meaning for all Hermitian-preserving maps. We demonstrate our method in two applications closely related to error mitigation and quantum machine learning, where it exhibits a favorable scaling. These findings highlight the power of quantum measurement in simulating unphysical operations, in which quantum interference is believed to play a vital role. Our work paves the way for more efficient sampling techniques and has the potential to be extended to more quantum information processing scenarios.

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arXiv2023

Near-term Efficient Quantum Algorithms for Entanglement Analysis

Entanglement plays a crucial role in quantum physics and is the key resource in quantum information processing. However, entanglement detection and quantification are believed to be hard due to the operational impracticality of existing methods. This work proposes three near-term efficient algorithms exploiting the hybrid quantum-classical technique to address this difficulty. The first algorithm finds the Schmidt decomposition--a powerful tool to analyze the properties and structure of entanglement--for bipartite pure states. While the logarithm negativity can be calculated from the Schmidt decomposition, we propose the second algorithm to estimate the logarithm negativity for bipartite pure states, where the width of the parameterized quantum circuits is further reduced. Finally, we generalize our framework for mixed states, leading to our third algorithm which detects entanglement on specific families of states, and determines disdillability in general. All three algorithms share a similar framework where the optimizations are accomplished by maximizing a cost function utilizing local parameterized quantum circuits, with better hardware efficiency and practicality compared to existing methods. The experimental implementation on Quantum Leaf using the IoP CAS superconducting quantum processor exhibits the validity and practicality of our methods for analyzing and quantifying entanglement on near-term quantum devices.

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arXiv2023

Information recoverability of noisy quantum states

Extracting classical information from quantum systems is an essential step of many quantum algorithms. However, this information could be corrupted as the systems are prone to quantum noises, and its distortion under quantum dynamics has not been adequately investigated. In this work, we introduce a systematic framework to study how well we can retrieve information from noisy quantum states. Given a noisy quantum channel, we fully characterize the range of recoverable classical information. This condition allows a natural measure quantifying the information recoverability of a channel. Moreover, we resolve the minimum information retrieving cost, which, along with the corresponding optimal protocol, is efficiently computable by semidefinite programming. As applications, we establish the limits on the information retrieving cost for practical quantum noises and employ the corresponding protocols to mitigate errors in ground state energy estimation. Our work gives the first full characterization of information recoverability of noisy quantum states from the recoverable range to the recovering cost, revealing the ultimate limit of probabilistic error cancellation.

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arXiv2023

Optimal quantum dataset for learning a unitary transformation

Unitary transformations formulate the time evolution of quantum states. How to learn a unitary transformation efficiently is a fundamental problem in quantum machine learning. The most natural and leading strategy is to train a quantum machine learning model based on a quantum dataset. Although the presence of more training data results in better models, using too much data reduces the efficiency of training. In this work, we solve the problem on the minimum size of sufficient quantum datasets for learning a unitary transformation exactly, which reveals the power and limitation of quantum data. First, we prove that the minimum size of a dataset with pure states is $2^n$ for learning an $n$-qubit unitary transformation. To fully explore the capability of quantum data, we introduce a practical quantum dataset consisting of $n+1$ elementary tensor product states that are sufficient for exact training. The main idea is to simplify the structure utilizing decoupling, which leads to an exponential improvement in the size of the datasets with pure states. Furthermore, we show that the size of the quantum dataset with mixed states can be reduced to a constant, which yields an optimal quantum dataset for learning a unitary. We showcase the applications of our results in oracle compiling and Hamiltonian simulation. Notably, to accurately simulate a 3-qubit one-dimensional nearest-neighbor Heisenberg model, our circuit only uses $96$ elementary quantum gates, which is significantly less than $4080$ gates in the circuit constructed by the Trotter-Suzuki product formula.

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arXiv2022

Quantum algorithms for estimating quantum entropies

The von Neumann and quantum Rényi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum query model that prepares the purification of the input state, have been established in the literature. {However, constructing such a model is almost as hard as state tomography.} In this paper, we propose quantum algorithms to estimate the von Neumann and quantum $α$-Rényi entropies of an $n$-qubit quantum state $ρ$ using independent copies of the input state. We also show how to efficiently construct the quantum circuits for {quantum entropy estimation} using primitive single/two-qubit gates. We prove that the number of required copies scales polynomially in $1/ε$ and $1/Λ$, where $ε$ denotes the additive precision and $Λ$ denotes the lower bound on all non-zero eigenvalues. Notably, our method outperforms previous methods in the aspect of practicality since it does not require any quantum query oracles, which are usually necessary for previous methods. Furthermore, we conduct experiments to show the efficacy of our algorithms to single-qubit states and study the noise robustness. We also discuss the applications to some quantum states of practical interest as well as some meaningful tasks such as quantum Gibbs state preparation and entanglement estimation.

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arXiv2021

Practical distributed quantum information processing with LOCCNet

Distributed quantum information processing is essential for building quantum networks and enabling more extensive quantum computations. In this regime, several spatially separated parties share a multipartite quantum system, and the most natural set of operations is Local Operations and Classical Communication (LOCC). As a pivotal part in quantum information theory and practice, LOCC has led to many vital protocols such as quantum teleportation. However, designing practical LOCC protocols is challenging due to LOCC's intractable structure and limitations set by near-term quantum devices. Here we introduce LOCCNet, a machine learning framework facilitating protocol design and optimization for distributed quantum information processing tasks. As applications, we explore various quantum information tasks such as entanglement distillation, quantum state discrimination, and quantum channel simulation. We discover protocols with evident improvements, in particular, for entanglement distillation with quantum states of interest in quantum information. Our approach opens up new opportunities for exploring entanglement and its applications with machine learning, which will potentially sharpen our understanding of the power and limitations of LOCC. An implementation of LOCCNet is available in Paddle Quantum, a quantum machine learning Python package based on PaddlePaddle deep learning platform.

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