Peng-Fei Zhou

Ying Lu, Peng-Fei Zhou, Shao-Ming Fei et al.

The quantum instruction set (QIS) is defined as the quantum gates that are physically realizable by controlling the qubits in quantum hardware. Compiling quantum circuits into the product of the gates in a properly defined QIS is a fundamental step in quantum computing. We here propose the quantum variational instruction set (QuVIS) formed by flexibly designed multi-qubit gates for higher speed and accuracy of quantum computing. The controlling of qubits for realizing the gates in a QuVIS is variationally achieved using the fine-grained time optimization algorithm. Significant reductions in both the error accumulation and time cost are demonstrated in realizing the swaps of multiple qubits and quantum Fourier transformations, compared with the compiling by a standard QIS such as the quantum microinstruction set (QuMIS, formed by several one- and two-qubit gates including one-qubit rotations and controlled-NOT gates). With the same requirement on quantum hardware, the time cost for QuVIS is reduced to less than one half of that for QuMIS. Simultaneously, the error is suppressed algebraically as the depth of the compiled circuit is reduced. As a general compiling approach with high flexibility and efficiency, QuVIS can be defined for different quantum circuits and be adapted to the quantum hardware with different interactions.

Ying Lu, Peng-Fei Zhou, Qi-Xuan Fang et al.

Large language models (LLMs) are dominated by dense linear transformations, whose storage, memory and computational overheads hinder efficient adaptation and deployment while masking the functional impacts of structural simplification. Here we present Tensor Mixture (MixT), a general tensor-structured compression scheme that replaces targeted dense linear layers with natively executable mixtures of tensor operators. Operating directly on generic linear projections instead of model-specific components, MixT is potentially applicable across Transformer-based LLMs and other dense neural mappings. We evaluate MixT on Qwen3-8B and LLaMA2-7B under a unified recovery protocol, identifying a broad compressible regime in which MMLU accuracy is largely preserved before an abrupt transition at model-specific boundaries. This transition coincides with coordinated shifts in output entropy, prediction entropy and inter-layer geometry. At the LLaMA2-7B transition boundary, MixT reduces full-model parameters by 47.5\%, inference FLOPs by 37.1\%, training FLOPs by 52.1\% and peak inference memory by 60.4\%, demonstrating its practical potential for lower-cost LLM compression.

Yong Qing, Ke Li, Peng-Fei Zhou et al.

Neural network (NN) designed for challenging machine learning tasks is in general a highly nonlinear mapping that contains massive variational parameters. High complexity of NN, if unbounded or unconstrained, might unpredictably cause severe issues including \R{overfitting}, loss of generalization power, and unbearable cost of hardware. In this work, we propose a general compression scheme that significantly reduces the variational parameters of NN's, despite of their specific types (linear, convolutional, \textit{etc}), by encoding them to deep \R{automatically differentiable} tensor network (ADTN) that contains exponentially-fewer free parameters. Superior compression performance of our scheme is demonstrated on several widely-recognized NN's (FC-2, LeNet-5, AlextNet, ZFNet and VGG-16) and datasets (MNIST, CIFAR-10 and CIFAR-100). For instance, we compress two linear layers in VGG-16 with approximately $10^{7}$ parameters to two ADTN's with just 424 parameters, improving the testing accuracy on CIFAR-10 from $90.17\%$ to $91.74\%$. We argue that the deep structure of ADTN is an essential reason for the remarkable compression performance of ADTN, compared to existing compression schemes that are mainly based on tensor decompositions/factorization and shallow tensor networks. Our work suggests deep TN as an exceptionally efficient mathematical structure for representing the variational parameters of NN's, which exhibits superior compressibility over the commonly-used matrices and multi-way arrays.

Rui Hong, Peng-Fei Zhou, Bin Xi et al.

The hybridizations of machine learning and quantum physics have caused essential impacts to the methodology in both fields. Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation provided the eigenstate, by combining Metropolis sampling with deep neural network, which we dub as Metropolis potential neural network (MPNN). A loss function is proposed to explicitly involve the energy in the optimization for its accurate evaluation. Benchmarking on the harmonic oscillator and hydrogen atom, MPNN shows excellent accuracy and stability on predicting not just the potential to satisfy the Schrodinger equation, but also the eigen-energy. Our proposal could be potentially applied to the ab-initio simulations, and to inversely solving other partial differential equations in physics and beyond.

Ying Lu, Yue-Min Li, Peng-Fei Zhou et al.

State preparation is of fundamental importance in quantum physics, which can be realized by constructing the quantum circuit as a unitary that transforms the initial state to the target, or implementing a quantum control protocol to evolve to the target state with a designed Hamiltonian. In this work, we study the latter on quantum many-body systems by the time evolution with fixed couplings and variational magnetic fields. In specific, we consider to prepare the ground states of the Hamiltonians containing certain interactions that are missing in the Hamiltonians for the time evolution. An optimization method is proposed to optimize the magnetic fields by "fine-graining" the discretization of time, in order to gain high precision and stability. The back propagation technique is utilized to obtain the gradients of the fields against the logarithmic fidelity. Our method is tested on preparing the ground state of Heisenberg chain with the time evolution by the XY and Ising interactions, and its performance surpasses two baseline methods that use local and global optimization strategies, respectively. Our work can be applied and generalized to other quantum models such as those defined on higher dimensional lattices. It enlightens to reduce the complexity of the required interactions for implementing quantum control or other tasks in quantum information and computation by means of optimizing the magnetic fields.

Peng-Fei Zhou, Rui Hong, Shi-Ju Ran

Constructing quantum circuits for efficient state preparation belongs to the central topics in the field of quantum information and computation. As the number of qubits grows fast, methods to derive large-scale quantum circuits are strongly desired. In this work, we propose the automatically differentiable quantum circuit (ADQC) approach to efficiently prepare arbitrary quantum many-qubit states. A key ingredient is to introduce the latent gates whose decompositions give the unitary gates that form the quantum circuit. The circuit is optimized by updating the latent gates using back propagation to minimize the distance between the evolved and target states. Taking the ground states of quantum lattice models and random matrix product states as examples, with the number of qubits where processing the full coefficients is unlikely, ADQC obtains high fidelities with small numbers of layers $N_L \sim O(1)$. Superior accuracy is reached compared with the existing state-preparation approach based on the matrix product disentangler. The parameter complexity of MPS can be significantly reduced by ADQC with the compression ratio $r \sim O(10^{-3})$. Our work sheds light on the "intelligent construction" of quantum circuits for many-qubit systems by combining with the machine learning methods.