Locally purified density operators for noisy quantum circuits

2024/11/04 by Yuchen Guo, Shuo Yang · 2 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum many-body systems

paper · doi:10.1088/0256-307x/41/12/120302

openalex publication_date 2024/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/05

Abstract

Abstract Open quantum system simulations are essential for exploring novel quantum phenomena and evaluating noisy quantum circuits. In this Letter, we investigate whether mixed states generated from noisy quantum circuits can be efficiently represented by locally purified density operators (LPDOs). We map an LPDO of N qubits to a pure state of size 2 × N defined on a ladder and introduce a unified method for managing virtual and Kraus bonds. We numerically simulate noisy random quantum circuits with depths of up to d = 40 using fidelity and entanglement entropy as accuracy measures. The LPDO representation is effective in describing mixed states in both the quantum and classical regions; however, it encounters significant challenges at the quantum-classical critical point, restricting its applicability to the quantum region. In contrast, matrix product operators (MPO) successfully characterize the entanglement trend throughout the simulation, while the truncation in MPOs breaks the positivity condition required for a physical density matrix. This work advances our understanding of efficient mixed-state representations in open quantum systems and provides insights into the entanglement structure of noisy quantum circuits.

Citations

• Colloquium : Area laws for the entanglement entropy
• Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
• The density-matrix renormalization group in the age of matrix product states
• Dynamical quantum phase transitions: a review
• Quantum Computing in the NISQ era and beyond
• Quantum Computation and Quantum Information
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems

Cited by

• Noisy Monitored Quantum Circuits
• Locally Purified Maximally Mixed States At Scale: Entanglement Pruning and Symmetries

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