Gauge-Fixing Quantum Density Operators At Scale

Abstract

We provide theory, algorithms, and simulations of non-equilibrium quantum systems using a one-dimensional (1D) completely-positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product state's orthogonality center, to additionally store positive classical mixture correlations, the MP$\rho$ factorization naturally emerges. In this work we analytically and numerically examine the virtual freedoms associated with the representation of quantum density operators. Using this augmented perspective, we simplify algorithms in certain limits to integrate the canonical form's master equation dynamics. This enables us to quickly evolve under the dynamics of two-body quantum channels without resorting to optimization-based methods. In addition to this technical advance, we also scale-up numerical examples and discuss implications for accurately modeling hardware architectures and predicting their performance. This includes an example of the quantum to classical transition of informationally leaky, i.e., decohering, qubits. In this setting, due to loss from environmental interactions, non-local complex coherence correlations are converted into global incoherent classical statistical mixture correlations. Lastly, the representation of both global and local correlations is discussed. We expect this work to have applications in additional non-equilibrium settings, beyond qubit engineering.

accepted version, 14 pages, 10 figures

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The ITensor Software Library for Tensor Network Calculations
• A positive tensor network approach for simulating open quantum many-body systems
• Quantum fidelity measures for mixed states
• Isometric Tensor Network States in Two Dimensions
• Purifications of multipartite states: limitations and constructive methods
• Separability transitions in topological states induced by local decoherence
• Simulating Noisy Quantum Circuits with Matrix Product Density Operators
• A tree tensor network approach to simulating Shor's algorithm
• Optimal Tree Tensor Network Operators for Tensor Network Simulations: Applications to Open Quantum Systems
• Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators
• Tensor network noise characterization for near-term quantum computers
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Optimized trajectory unraveling for classical simulation of noisy quantum dynamics

Cited by in corpus (1)

• Locally Purified Maximally Mixed States At Scale: Entanglement Pruning and Symmetries