arXiv subjects

Yuchen Pang

Publications and source records attributed to Yuchen Pang.

4 recordsLinked to original sources

arXiv2025

Simulating Clifford Circuits with Gaussian Elimination

Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still show important quantum effects such as entanglement. In this work, we present an algorithm that simulates Clifford circuits by performing Gaussian elimination on a modified adjacency matrix derived from the circuit structure. Our work builds on an ZX-calculus tensor network representation of Clifford circuits that reduces to quantum graph states. We give a concise formula of amplitudes of graph states based on the LDL decomposition of matrices over GF(2), and use it to get efficient algorithms for strong and weak simulation of Clifford circuits using tree-decomposition-based fast LDL algorithm. The complexity of our algorithm matches the state of art for weak graph state simulation and improves the state of art for strong graph state simulation by taking advantage of Strassen-like fast matrix multiplication. Our algorithm is also efficient when computing many amplitudes or samples of a Clifford circuit. Further, our amplitudes formula provides a new characterization of locally Clifford equivalent graph states as well as an efficient protocol to learn graph states with low-rank adjacency matrices.

quant-ph↗

arXiv2025

Autoregressive pairwise Graphical Models efficiently find ground state representations of stoquastic Hamiltonians

We introduce Autoregressive Graphical Models (AGMs) as an Ansatz for modeling the ground states of stoquastic Hamiltonians. Exact learning of these models for smaller systems show the dominance of the pairwise terms in the autoregressive decomposition, which informs our modeling choices when the Ansatz is used to find representations for ground states of larger systems. We find that simple AGMs with pairwise energy functions trained using first-order stochastic gradient methods often outperform more complex non-linear models trained using the more expensive stochastic reconfiguration method. We also test our models on Hamiltonians with frustration and observe that the simpler linear model used here shows faster convergence to the variational minimum in a resource-limited setting.

quant-ph↗

arXiv2020

The Potential of Quantum Annealing for Rapid Solution Structure Identification

The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. A meticulous comparison to a variety of algorithms spanning both complete and local search suggests that quantum annealing's performance on the proposed optimization tasks is distinct. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches.

math.OC↗

arXiv2020

Efficient 2D Tensor Network Simulation of Quantum Systems

Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States (PEPS) are well-suited for key classes of physical systems and quantum circuits. However, direct contraction of PEPS networks has exponential cost, while approximate algorithms require computations with large tensors. We propose new scalable algorithms and software abstractions for PEPS-based methods, accelerating the bottleneck operation of contraction and refactorization of a tensor subnetwork. We employ randomized SVD with an implicit matrix to reduce cost and memory footprint asymptotically. Further, we develop a distributed-memory PEPS library and study accuracy and efficiency of alternative algorithms for PEPS contraction and evolution on the Stampede2 supercomputer. We also simulate a popular near-term quantum algorithm, the Variational Quantum Eigensolver (VQE), and benchmark Imaginary Time Evolution (ITE), which compute ground states of Hamiltonians.

cs.DC↗