Efficient tensor-network simulations of weakly-measured quantum circuits

2025/10/08 by Pereira, Darren, Banchi, Leonardo
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2510.07211

Abstract

We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the spatial direction. Applications of our algorithm include validating quantum computers (capable of mid-circuit measurements) in regimes of easy classical simulability, and studying generative-machine-learning applications, where sampling from complex stochastic processes is the main task. As a demonstration of our algorithm, we consider a (1+1)-dimensional brickwall circuit of Haar-random unitaries, interspersed with generalized single-qubit measurements of variable strength. We simulate the dynamics for tens to hundreds of qubits if the circuit exhibits area-law entanglement (under strong measurements), and tens of qubits if it exhibits volume-law entanglement (under weak measurements). We observe signatures of a measurement-induced phase transition between the two regimes as a function of measurement strength.

Citations

• Overcoming the entanglement barrier with sampled tensor networks
• Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
• Postselection-free experimental observation of the measurement-induced phase transition in circuits with universal gates
• Correlations, Spectra and Entanglement Transitions in Ensembles of Matrix Product States
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• Measurement-induced phase transitions by matrix product states scaling
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• Generative Learning of Continuous Data by Tensor Networks
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• Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
• The ITensor Software Library for Tensor Network Calculations
• Denoising Diffusion Probabilistic Models
• The density-matrix renormalization group in the age of matrix product states

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• Simulating and Sampling from Quantum Circuits with 2D Tensor Networks
• Learning Circuits with Infinite Tensor Networks