arXiv subjects

Chufan Lyu

Publications and source records attributed to Chufan Lyu.

9 recordsLinked to original sources

arXiv2026

Variational Quantum Dimension Reduction for Recurrent Quantum Models

Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large memory spaces, introducing redundancy and limiting scalability. Here, we introduce a \textit{variational quantum dimension reduction} framework that identifies and removes irrelevant memory degrees of freedom while preserving the recurrent dynamics of the target model. Our approach employs two parameterized quantum circuits: a decoupling unitary $V(\theta_1)$ that isolates the essential memory subspace; and a compressed recurrent unitary $\tilde{U}(\theta_2)$ that reconstructs the dynamics in the reduced space. The optimization is guided by a unified cost function combining decoupling fidelity and dynamical accuracy, evaluated using the \textit{Quantum Fidelity Divergence Rate} (QFDR), a metric that quantifies long-term fidelity per time step. Applied to a cyclic random walk model, our framework achieves up to three orders of magnitude smaller QFDR compared to variational matrix product state truncation, while requiring only trajectory samples rather than explicit state reconstructions. This establishes a scalable, data-driven paradigm for learning minimal recurrent quantum architectures, enabling variational circuit optimization and quantum process compression for near-term quantum devices.

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arXiv2024

MindSpore Quantum: A User-Friendly, High-Performance, and AI-Compatible Quantum Computing Framework

We introduce MindSpore Quantum, a pioneering hybrid quantum-classical framework with a primary focus on the design and implementation of noisy intermediate-scale quantum (NISQ) algorithms. Leveraging the robust support of MindSpore, an advanced open-source deep learning training/inference framework, MindSpore Quantum exhibits exceptional efficiency in the design and training of variational quantum algorithms on both CPU and GPU platforms, delivering remarkable performance. Furthermore, this framework places a strong emphasis on enhancing the operational efficiency of quantum algorithms when executed on real quantum hardware. This encompasses the development of algorithms for quantum circuit compilation and qubit mapping, crucial components for achieving optimal performance on quantum processors. In addition to the core framework, we introduce QuPack, a meticulously crafted quantum computing acceleration engine. QuPack significantly accelerates the simulation speed of MindSpore Quantum, particularly in variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and tensor network simulations, providing astonishing speed. This combination of cutting-edge technologies empowers researchers and practitioners to explore the frontiers of quantum computing with unprecedented efficiency and performance.

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arXiv2024

Variational simulation of higher-spin systems on qubit-based quantum simulators

Qubit-based quantum simulators naturally target two-level systems, whereas many quantum many-body problems are intrinsically $d$ level. Encodings from qudits to qubits then enlarge the Hilbert space and can introduce unphysical states that interfere with variational optimization. We formulate a variational framework for encoded $d$-level models that suppresses these illegitimate states with penalty terms and benchmark it for spin-1 and spin-3/2 bilinear-biquadratic Heisenberg chains. We compare binary encoding, which minimizes the qubit overhead, with symmetry encoding, which preserves the relevant spin symmetries and enables symmetry-conserving ans\"atze. Although binary encoding is more qubit efficient, its hardware-efficient ansatz is harder to train and less effective at exploiting conserved quantities. In contrast, symmetry encoding requires more qubits but reaches substantially higher fidelities, converges faster, and exhibits better trainability than the binary hardware-efficient ansatz. These results identify symmetry-preserving encodings as a practical route to simulating higher-spin models on existing qubit platforms.

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arXiv2023

Multi-Level Variational Spectroscopy using a Programmable Quantum Simulator

Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device. Variational quantum-classical algorithms have emerged as a promising approach for achieving such tasks on near-term quantum simulators, despite facing significant quantum and classical resource overheads. Here, we experimentally demonstrate multi-level variational spectroscopy for fundamental many-body Hamiltonians using a superconducting programmable digital quantum simulator. By exploiting symmetries, we effectively reduce circuit depth and optimization parameters allowing us to go beyond the ground state. Combined with the subspace search method, we achieve full spectroscopy for a 4-qubit Heisenberg spin chain, yielding an average deviation of 0.13 between experimental and theoretical energies, assuming unity coupling strength. Our method, when extended to 8-qubit Heisenberg and transverse-field Ising Hamiltonians, successfully determines the three lowest energy levels. In achieving the above, we introduce a circuit-agnostic waveform compilation method that enhances the robustness of our simulator against signal crosstalk. Our study highlights symmetry-assisted resource efficiency in variational quantum algorithms and lays the foundation for practical spectroscopy on near-term quantum simulators, with potential applications in quantum chemistry and condensed matter physics.

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arXiv2023

Variational quantum simulation of long-range interacting systems

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the performance. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology.

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arXiv2023

Symmetry enhanced variational quantum spin eigensolver

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

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arXiv2020

Accelerated variational algorithms for digital quantum simulation of many-body ground states

One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we first provide a quantitative comparison between the adiabatic and variational methods with respect to required quantum resources on digital quantum simulators, namely the depth of the circuit and the number of two-qubit quantum gates. Our results show that the variational methods are less demanding with respect to these resources. However, they need to be hybridized with a classical optimization which can converge slowly. Therefore, as the second result of the paper, we provide two different approaches for speeding the convergence of the classical optimizer by taking a good initial guess for the parameters of the variational circuit. We show that these approaches are applicable to a wide range of Hamiltonian and provide significant improvement in the optimization procedure.

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arXiv2020

Quantum locally linear embedding for nonlinear dimensionality reduction

Reducing the dimension of nonlinear data is crucial in data processing and visualization. The locally linear embedding algorithm (LLE) is specifically a representative nonlinear dimensionality reduction method with well maintaining the original manifold structure. In this paper, we present two implementations of the quantum locally linear embedding algorithm (QLLE) to perform the nonlinear dimensionality reduction on quantum devices. One implementation, the linear-algebra-based QLLE algorithm, utilizes quantum linear algebra subroutines to reduce the dimension of the given data. The other implementation, the variational quantum locally linear embedding algorithm (VQLLE) utilizes a variational hybrid quantum-classical procedure to acquire the low-dimensional data. The classical LLE algorithm requires polynomial time complexity of $N$, where $N$ is the global number of the original high-dimensional data. Compared with the classical LLE, the linear-algebra-based QLLE achieves quadratic speedup in the number and dimension of the given data. The VQLLE can be implemented on the near term quantum devices in two different designs. In addition, the numerical experiments are presented to demonstrate that the two implementations in our work can achieve the procedure of locally linear embedding.

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arXiv2020

Quantum transfer component analysis for domain adaptation

Domain adaptation, a crucial sub-field of transfer learning, aims to utilize known knowledge of one data set to accomplish tasks on another data set. In this paper, we perform one of the most representative domain adaptation algorithms, transfer component analysis (TCA), on quantum devices. Two different quantum implementations of this transfer learning algorithm; namely, the linear-algebra-based quantum TCA algorithm and the variational quantum TCA algorithm, are presented. The algorithmic complexity of the linear-algebra-based quantum TCA algorithm is $O(\mathrm{poly}(\log (n_{s} + n_{t})))$, where $n_{s}$ and $n_{t}$ are input sample size. Compared with the corresponding classical algorithm, the linear-algebra-based quantum TCA can be performed on a universal quantum computer with exponential speedup in the number of given samples. Finally, the variational quantum TCA algorithm based on a quantum-classical hybrid procedure, that can be implemented on the near term quantum devices, is proposed.

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