arXiv subjects

Wen-Qiang Liu

Publications and source records attributed to Wen-Qiang Liu.

At least 19 recordsLinked to original sources

arXiv2026

Linear optical fan-out gates using fewer ancillary single photons with enhanced success probability

Photonic quantum gates are fundamental building blocks for a wide range of optical quantum information processing tasks. We propose an efficient linear-optical scheme for implementing a post-selected three-qubit fan-out gate (also known as a controlled-NOT-NOT gate) using only two ancillary single photons and linear optical elements. The scheme can be generalized to an $n$-qubit fan-out gate, requiring $(n-1)$ ancillary single photons and $(3n-3)$ polarizing beam splitters (PBSs), with a success probability of $\left(\frac{1}{4}\right)^{n-1}$. Compared to the standard gate decomposition approach, which requires $(2n-2)$ ancillary single photons, $(5n-5)$ PBSs, and yields a success probability of $\left(\frac{1}{8}\right)^{n-1}$. Our scheme significantly reduces the resource overhead and improves the success probability. We further evaluate the gate performance and demonstrate improved robustness compared to gate decomposition-based methods.

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arXiv2026

Heralded high-dimensional module-based quantum computation

Parity measurements have been explored as building blocks for preparing and discriminating entangled states, as well as for implementing quantum computation. We first develop two alternative high-dimensional generalized parity modules, and then propose a procedure for constructing high-dimensional generalized module-based controlled-NOT gate. The construction of module-based quantum computing introduced here is deterministic, heralded, insensitive to the dimensionality of the computing basis, and postselection technique is not required. The result shows that out of $(d-1)!$ generalized parity modules, only modules $ \mathcal{P}=(j\ominus i)\bmod d$ and $ \mathcal{P}=(j \oplus i)\bmod d$ can be used as building blocks for high-dimensional quantum computing. Furthermore, we proposed an optical nondestructive scheme for implementing generalized parity module through quantum nondemolition measurements, and the success of the parity module is heralded by photon-number-resolving detectors and single-photon detectors.

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arXiv2026

Enhancing Quantum Machine Learning with Anyons

The power of quantum computing and quantum machine learning relies on harnessing uniquely quantum phenomena as computational resources. While superposition, coherence and entanglement have been central to this effort, the role of particle exchange statistics remains largely unexplored. Here, we introduce a quantum kernel framework that unifies bosonic, fermionic, and anyonic (fractional) exchange statistics within a single learning paradigm. We study this family of kernels from three perspectives. At the representation level, Haar-averaged effective-dimension analysis shows that fractional exchange phases access feature-space directions inaccessible to the purely symmetric or antisymmetric limits. At the level of kernel geometry, the corresponding Gram matrices show greater separation from the distinguishable-particle baseline and reduced label-dependent model complexity. Finally, on learning benchmarks, anyonic kernels consistently outperform their bosonic and fermionic counterparts, with stronger target alignment and more favorable class geometry. Together, these findings show that exchange statistics reshape the structure and geometry of quantum feature space, leading to enhanced learning performance. Our work identifies particle exchange statistics as an overlooked computational ingredient for quantum machine learning and provides the first systematic comparison of quantum learning models across exchange phases.

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arXiv2026

Effective schemes for fusion of hyperentangled W states

Hyperentangled states are fascinating resources in quantum information processing as they can significantly increase the channel capacity and enhance noise resistance. We explore a hyperfusion mechanism to fuse one n photon hyper-W state and one m-photon hyper-W state into a large-scale (n+m-2)-photon hyper-W state. Another mechanism to fuse one n-photon hyper-W state, one m-photon hyper-$W$ state, and one $t$-photon hyper-W state into an (n+m+t-3)-photon hyper-W state is also proposed. These two hyperfusion mechanisms are constructed employing only polarizing beam splitters, balanced beam splitters, half-wave plates, single-photon detectors, and cross-Kerr nonlinearities. Conditional quantum gates, path couplers, and ancillary photons are not required in our constructions. Moreover, our fused $W$ states are hyperentangled in the polarization and spatial degrees of freedom of single-photon systems. The presence of only one garbage output state demonstrates that high efficiency can be achieved in our schemes.

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arXiv2026

Unambiguous arbitrary high-dimensional Bell states analyzer via indefinite causal order

High-dimensional quantum systems greatly outperform their two-dimensional counterparts in channel capacity, quantum complexity and efficiency, quantum communication security, etc. Bell-state analyzer (BSA) is a crucial prerequisite for a number of quantum communication protocols. We propose an approach for completely and deterministically distinguishing a set of arbitrary $d$-dimensional ($d \geq 3$) Bell states via indefinite causal order (ICO). In previous schemes, bit and phase information are discriminated in succession. Exploiting the gravitational ICO as the sole resource, we propose some high-dimensional BSA schemes. Independent of the dimensions, a set of generalized Bell states are completely and deterministically discriminated by adjusting the form of the embedded local single-qudit gates within ICO switch and measuring each qudit in the $\{|0\rangle, |1\rangle, \cdots, |d-1\rangle\}$ basis. Notably, in our high-dimensional BSA process, the indefinite causal structure is not consumed. Hence a completely nondestructive high-dimensional BSA can be achieved by iterating the indefinite causal structure process for two rounds.

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arXiv2026

Practical implementation of arbitrary nonlocal controlled-unitary gate via indefinite causal order

Quantum gate teleportation enables the implementation of nonlocal quantum operations without direct interactions between distant nodes. We propose an efficient protocol for implementing arbitrary controlled-unitary (CU) gates acting on two spatially separated parties via indefinite causal order (ICO). By establishing a maximally entanglement between two remote nodes and coherently superposing orders of single-qubit gates, our protocol circumvents the drawback of complex local two-qubit operations. This ICO-based approach enables full programmability of CU gates by adjusting the inherent single-qubit operations, offering advantages over conventional fixed causal-order methods in terms of reduced circuit complexity and improved experimental flexibility. Furthermore, we develop an optical construction to implement the polarization CU gate using a stable and reciprocal Sagnac interferometer. Our work establishes a practical framework for scalable distributed quantum computation with flexible operations.

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arXiv2026

Remote state preparation of single-partite high-dimensional states in complex Hilbert spaces

High-dimensional quantum systems offer a new playground for quantum information applications due to their remarkable advantages such as higher capacity and noise resistance. We propose potentially practical schemes for remotely preparing four- and eight-level equatorial states in complex Hilbert spaces exactly by identifying a set of orthogonal measurement bases. In these minimal-resource-consuming schemes, both pre-shared maximally and non-maximally entangled states are taken into account. The three-, five-, six-, and seven-level equatorial states in complex Hilbert spaces can also be obtained by adjusting the parameters of the desired states. The evaluations indicate that our high-dimensional RSP schemes might be possible with current technology. The collection operations, necessary for our high-dimensional RSP schemes via partially entangled channels, can be avoided by encoding the computational basis in the spatial modes of single-photon systems.

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arXiv2026

Efficient and deterministic high-dimensional controlled-swap gates on hybrid linear optical systems with high fidelity

Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom ($d$-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only $d$ PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.

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arXiv2025

Deterministic generation of multi-qubit entangled states among distant parties using indefinite causal order

Quantum entanglement plays an irreplaceable role in various remote quantum information processing tasks. Here we present protocols for generating deterministic and heralded $N$-qubit entangled states across multiple network nodes. By utilizing a pre-shared maximally entangled state and single-qubit operations within an indefinite causal order framework, the multi-qubit entangled state between distant parties can be generated deterministically. The complex entangled state measurements and multiple pre-shared entangled states, are essential in conventional entanglement swapping technique, but are not required in our approach. This greatly reduces the complexity of the quantum circuit and makes it more experimentally feasible. Furthermore, we develop optical architectures to implement these protocols by encoding qubits in polarization degree of freedom. The results indicate that our protocols significantly improve the efficiency of long-distance entanglement generation and provide a practical framework for establishing large-scale quantum networks.

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arXiv2023

Experimental realization of universal high-dimensional quantum gates with ultra-high fidelity and efficiency

Qudit, a high-dimensional quantum system, provides a larger Hilbert space to process the quantum information and has shown remarkable advantages over the qubit counterparts. It is a great challenge to realize the high fidelity universal quantum gates with qudits. Here we theoretically propose and experimentally demonstrate a set of universal quantum gates for a single optical qudit with four dimensions (including the generalized Pauli $X_4$ gate, Pauli $Z_4$ gate, and all of their integer powers), which are encoded in the polarization-spatial degree of freedom without multiple unstable cascaded interferometers. Furthermore, we also realize the controlled-$X_4$ gate and all of its integer powers. We have achieved both the ultra-high average gate fidelity $99.73\%$ and efficiency $99.47\%$, which are above the the error threshold for fault-tolerant quantum computation. Our work paves a way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.

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arXiv2023

Efficiently simulating the work distribution of multiple identical bosons with boson sampling

Boson sampling has been theoretically proposed and experimentally demonstrated to show quantum computational advantages. However, it still lacks the deep understanding of the practical applications of boson sampling. Here we propose that boson sampling can be used to efficiently simulate the work distribution of multiple identical bosons. We link the work distribution to boson sampling and numerically calculate the transition amplitude matrix between the single-boson eigenstates in a one-dimensional quantum piston system, and then map the matrix to a linear optical network of boson sampling. The work distribution can be efficiently simulated by the output probabilities of boson sampling using the method of the grouped probability estimation. The scheme requires at most a polynomial number of the samples and the optical elements. Our work opens up a new path towards the calculation of complex quantum work distribution using only photons and linear optics.

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arXiv2023

Optimal synthesis of general multi-qutrit quantum computation

Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in multi-valued quantum computation. We first propose a new recursive Cartan decomposition of semi-simple unitary Lie group $U(3^n)$ (arbitrary $n$-qutrit gate). Note that the decomposition completely decomposes an n-qutrit gate into local and non-local operations. We design an explicit quantum circuit for implementing arbitrary two-qutrit gates, and the cost of our construction is 21 generalized controlled X (GCX) and controlled increment (CINC) gates less than the earlier best result of 26 GGXs. Moreover, we extend the program to the $n$-qutrit system, and the quantum circuit of generic $n$-qutrit gates contained $\frac{41}{96}\cdot3^{2n}-4\cdot3^{n-1}-(\frac{n^2}{2}+\frac{n}{4}-\frac{29}{32})$ GGXs and CINCs is presented. Such asymptotically optimal structure is the best known result so far.

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arXiv2023

Experimentally demonstrating indefinite causal order algorithms to solve the generalized Deutsch's problem

Deutsch's algorithm is the first quantum algorithm to show the advantage over the classical algorithm. Here we generalize Deutsch's problem to $n$ functions and propose a new quantum algorithm with indefinite causal order to solve this problem. The new algorithm not only reduces the number of queries to the black-box by half over the classical algorithm, but also significantly reduces the number of required quantum gates over the Deutsch's algorithm. We experimentally demonstrate the algorithm in a stable Sagnac loop interferometer with common path, which overcomes the obstacles of both phase instability and low fidelity of Mach-Zehnder interferometer. The experimental results have shown both an ultra-high and robust success probability $\sim 99.7\%$. Our work opens up a new path towards solving the practical problems with indefinite casual order quantum circuits.

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arXiv2023

Practically Enhanced Hyperentanglement Concentration for Polarization-spatial Hyperentangled Bell States with Linear Optics and Common Single-photon Detectors

Hyperentanglement, defined as the simultaneous entanglement in several independent degrees of freedom (DOFs) of a quantum system, is a fascinating resource in quantum information processing with its outstanding merits. Here we propose heralded hyperentanglement concentration protocols (hyper-ECPs) to concentrate an unknown partially less polarization-spatial hyperentangled Bell state with available linear optics and common single-photon detectors. By introducing time-delay DOFs, the schemes are highly efficient in that the success of the scheme can be accurately heralded by the detection signatures, and postselection techniques or photon-number-resolving detectors, necessary for previous experiments, are not required. Additionally, our linear optical architectures allow certain states, where concentration fails, to be recyclable, and a trick makes the success probabilities of our schemes higher than those of previous linear optical hyper-ECPs.

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arXiv2023

Heralded and high-efficient entanglement concentrations based on linear optics assisted by time-delay degree of freedom

Entanglement concentration is a critical technique to prevent degraded fidelity and security in long-distance quantum communication. We propose novel practical entanglement concentration protocols (ECPs) for less-entangled Bell and Greenberger-Horne-Zeilinger states with unknown parameters by solely using simple linear optics. We avoid the need for the post-selection principles or photon-number-resolving detector to identify the parity-check measurement completely by orchestrating auxiliary time degree of freedom, and the success of ECPs is exactly heralded by the detection signatures without destroying the incident qubits. Additionally, the outting incident photons kept are in the maximally entangled or the less-entangled state, and the success probability can be increased by recycling the latter. The heralded and the basic linear optical elements make our practical ECPs are accessible to experimental investigation with current technology.

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arXiv2022

Linear optical universal quantum gates with higher success probabilities

Universal quantum gates lie at the heart of designing quantum computer. We construct two compact quantum circuits to implement post-selected controlled-phase-flip (CPF) gate and Toffoli gate with linear optics assisted by one and two single photons, respectively. The current existing maximum success probability of 1/4 for linear optical CPF gate is achieved by resorting to an ancillary single photon rather than an entangled photon pair or two single photons. Remarkably, our Toffoli gate is accomplished with current maximum success probability of 1/30 without using additional entangled photon pairs and the standard decomposition-based approach. Linear optical implementations of the presented two universal gates are feasible under current technology and provide a potential application in large-scale optical quantum computing.

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arXiv2022

Deterministic and complete hyperentangled Bell states analysis assisted by frequency and time interval degrees of freedom

Hyperentangled Bell states analysis (HBSA) is an essential building block for certain hyper-parallel quantum information processing. We propose a complete and deterministic HBSA scheme encoded in spatial and polarization degrees of freedom (DOFs) of two-photon system assisted by a fixed frequency-based entanglement and a time interval DOF. The parity information the spatial-based and polarization-based hyper-entanglement can be distinguished by the distinct time intervals of the photon pairs, and the phase information can be distinguished by the detection signature. Compared with previous schemes, the number of the auxiliary entanglements is reduced from two to one by introducing time interval DOF. Moreover, the additional frequency and time interval DOFs suffer less from the collective channel noise.

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arXiv2022

Collective unitary evolution with linear optics by Cartan decomposition

Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based on the results of decomposition, we design two compact architectures to deterministically implement arbitrary two-qubit polarization-spatial and spatial-polarization collective unitary operations, respectively. The involved linear optical elements are reduced from 25 to 20 and 21 to 20, respectively. Moreover, the parameterized quantum computation can be flexibly manipulated by wave plates and phase shifters. As an application, we construct the specific quantum circuits to realize two-dimensional quantum walk and quantum Fourier transformation. Our schemes are simple and feasible with the current technology.

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