Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems

Abstract

This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto a state-space manifold having reduced dimensionality and possessing a Kahler potential of multi-linear form. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given, and methods for quantum state optimization by Dantzig selection are given.

104 pages, 13 figures, 2 tables

References in corpus (23)

• The density-matrix renormalization group
• Sparsity and Incoherence in Compressive Sampling
• High-sensitivity diamond magnetometer with nanoscale resolution
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Time-dependent density functional theory: Past, present, and future
• Classical simulation of quantum many-body systems with a tree tensor network
• Scanning magnetic field microscope with a diamond single-spin sensor
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Ground state fidelity from tensor network representations
• Entanglement renormalization and topological order
• Variational quantum Monte Carlo simulations with tensor-network states
• Classical simulation versus universality in measurement based quantum computation
• Quantum MERA Channels
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Rejoinder: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Solution of large scale nuclear structure problems by wave function factorization
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Discussion: The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Discussion: The Dantzig selector: statistical estimation when $p$ is much larger than $n$
• Phase space contraction and quantum operations

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