arXiv subjects

Chunlin Yang

Publications and source records attributed to Chunlin Yang.

4 recordsLinked to original sources

arXiv2025

Quantum separability criteria from bipartite systems to multipartite systems based on generalized Bloch representation

Quantum entanglement serves as a fundamental resource in quantum information theory. This paper presents a comprehensive framework of separability criteria for detecting bipartite and multipartite entanglements. We construct a novel parameterized extended correlation tensor via the generalized Bloch representation under an arbitrary orthogonal basis, which improves the performance of entanglement detection. Moreover, we employ the generalized matrix unfolding to generalize the extended correlation tensor construction to multipartite systems, obtaining separability criteria for multipartite entanglement. Detailed examples demonstrate that our separability criteria exhibit enhanced capability in detecting entanglement.

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arXiv2025

Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems

Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for solving the GEPs in non-Hermitian systems. The algorithm transforms the generalized eigenvalue problem into a process of searching for unitary transformation matrices. We demonstrate a method for evaluating both the loss function and its gradients on near-term quantum devices. We validate numerically the algorithm's performance through simulations, and demonstrate its application to GEPs in ocean acoustics. The algorithm's robustness is further confirmed through noise simulations.

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arXiv2025

Binary Tree Block Encoding of Classical Matrix

Block-encoding is a critical subroutine in quantum computing, enabling the transformation of classical data into a matrix representation within a quantum circuit. The resource trade-offs in simulating a block-encoding can be quantified by the circuit size, the normalization factor, and the time and space complexity of parameter computation. Previous studies have primarily focused either on the time and memory complexity of computing the parameters, or on the circuit size and normalization factor in isolation, often neglecting the balance between these trade-offs. In early fault-tolerant quantum computers, the number of qubits is limited. For a classical matrix of size $2^{n}\times 2^{n}$, our approach not only improves the time of decoupling unitary for block-encoding with time complexity $\mathcal{O}(n2^{2n})$ and memory complexity $\Theta(2^{2n})$ using only a few ancilla qubits, but also demonstrates superior resource trade-offs. Our proposed block-encoding protocol is named Binary Tree Block-encoding (\texttt{BITBLE}). Under the benchmark, \textit{size metric}, defined by the product of the number of gates and the normalization factor, numerical experiments demonstrate the improvement of both resource trade-off and classical computing time efficiency of the \texttt{BITBLE} protocol. The algorithms are all open-source.

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arXiv2024

Dictionary-based Block Encoding of Sparse Matrices with Low Subnormalization and Circuit Depth

Block encoding severs as an important data input model in quantum algorithms, enabling quantum computers to simulate non-unitary operators effectively. In this paper, we propose an efficient block-encoding protocol for sparse matrices based on a novel data structure, called the dictionary data structure, which classifies all non-zero elements according to their values and indices. Non-zero elements with the same values, lacking common column and row indices, belong to the same classification in our block-encoding protocol's dictionary. When compiled into the \{\rm U(2), CNOT\} gate set, the protocol queries a $2^n \times 2^n$ sparse matrix with $s$ non-zero elements at a circuit depth of $\mathcal{O}(\log(ns))$, utilizing $\mathcal{O}(n^2s)$ ancillary qubits. This offers an exponential improvement in circuit depth relative to the number of system qubits, compared to existing methods~\cite{clader2022quantum,zhang2024circuit} with a circuit depth of $\mathcal{O}(n)$. Moreover, in our protocol, the subnormalization, a scaled factor that influences the measurement probability of ancillary qubits, is minimized to $\sum_{l=0}^{s_0}\vert A_l\vert$, where $s_0$ denotes the number of classifications in the dictionary and $A_l$ represents the value of the $l$-th classification. Furthermore, we show that our protocol connects to linear combinations of unitaries (LCU) and the sparse access input model (SAIM). To demonstrate the practical utility of our approach, we provide several applications, including Laplacian matrices in graph problems and discrete differential operators.

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