arXiv subjects

Langyu Li

Publications and source records attributed to Langyu Li.

4 recordsLinked to original sources

arXiv2026

Adaptive controllable architecture of analog Ising machine

As a quantum-inspired, non-traditional analog solver architecture, the analog Ising machine (AIM) has emerged as a distinctive computational paradigm to address the rapidly growing demand for computational power. However, the mathematical understanding of its principles, as well as the optimization of its solution speed and accuracy, remain unclear. In this work, we for the first time systematically discuss multiple implementations of AIM and establish a unified mathematical formulation. On this basis, by treating the binarization constraint of AIM (such as injection locking) as a Lagrange multiplier in optimization theory and combining it with a Lyapunov analysis from dynamical systems theory, an analytical framework for evaluating solution speed and accuracy is constructed, and further demonstrate that conventional AIMs possess a theoretical performance upper bound. Subsequently, by elevating the binarization constraint to a control variable, we propose the controllable analog Ising machine (CAIM), which integrates control Lyapunov functions and momentum-based optimization algorithms to realize adaptive sampling-feedback control, thereby surpassing the performance limits of conventional AIMs. In a proof-of-concept CAIM demonstration implemented using an FPGA-controlled LC-oscillator Ising machine, CAIM achieves a twofold speedup and a 7\% improvement in accuracy over AIM on a 50-node all-to-all weighted MaxCut problem, validating both the effectiveness and interpretability of the proposed theoretical framework.

quant-ph↗

arXiv2024

Principal Trotter Observation Error with Truncated Commutators

Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or average$-$case scenarios. In this work, we consider the simulation error under a fixed observable. Under a fixed observable, errors that commute with this observable become less important. To illustrate this point, we define the observation error as the expectation under the observable and provide a commutativity$-$based upper bound using the Baker$-$Campbell$-$Hausdorff formula. For highly commuting observables, the simulation error indicated by this upper bound can be significantly compressed. In the experiment with the Heisenberg model, the observation bound compresses the Trotter number by nearly half compared to recent commutator bounds. Additionally, we found that the evolution sequence significantly affects the observation error. By utilizing a simulated annealing algorithm, we designed a sequence optimization algorithm, achieving further compression of the Trotter number. The experiment on the hydrogen molecule Hamiltonian demonstrates that optimizing the sequence can lead to nearly half the reduction in the Trotter number.

quant-ph↗

arXiv2024

Parallel Ising Annealer via Gradient-based Hamiltonian Monte Carlo

Ising annealer is a promising quantum-inspired computing architecture for combinatorial optimization problems. In this paper, we introduce an Ising annealer based on the Hamiltonian Monte Carlo, which updates the variables of all dimensions in parallel. The main innovation is the fusion of an approximate gradient-based approach into the Ising annealer which introduces significant acceleration and allows a portable and scalable implementation on the commercial FPGA. Comprehensive simulation and hardware experiments show that the proposed Ising annealer has promising performance and scalability on all types of benchmark problems when compared to other Ising annealers including the state-of-the-art hardware. In particular, we have built a prototype annealer which solves Ising problems of both integer and fraction coefficients with up to 200 spins on a single low-cost FPGA board, whose performance is demonstrated to be better than the state-of-the-art quantum hardware D-Wave 2000Q and similar to the expensive coherent Ising machine. The sub-linear scalability of the annealer signifies its potential in solving challenging combinatorial optimization problems and evaluating the advantage of quantum hardware.

quant-ph↗

arXiv2023

Fast Numerical Solver of Ising Optimization Problems via Pruning and Domain Selection

Quantum annealers, coherent Ising machines and digital Ising machines for solving quantum-inspired optimization problems have been developing rapidly due to their near-term applications. The numerical solvers of the digital Ising machines are based on traditional computing devices. In this work, we propose a fast and efficient solver for the Ising optimization problems. The algorithm consists of a pruning method that exploits the graph information of the Ising model to reduce the computational complexity, and a domain selection method which introduces significant acceleration by relaxing the discrete feasible domain into a continuous one to incorporate the efficient gradient descent method. The experiment results show that our solver can be an order of magnitude faster than the classical solver, and at least two times faster than the quantum-inspired annealers including the simulated quantum annealing on the benchmark problems. With more relaxed requirements on hardware and lower cost than quantum annealing, the proposed solver has the potential for near-term application in solving challenging optimization problems as well as serving as a benchmark for evaluating the advantage of quantum devices.

quant-ph↗