Symmetries, States, and Measurements: Decoherence and Complexity in a Nonlinear Kerr System

Decoherence––the process by which quantum superpositions become probabilistic mixtures––occurs when information about the state of a quantum system leaks into an environment. In this talk, we study the competition between decoherence and quantum complexity in a toy model, and discuss its implications for computation in the era of Noisy Intermediate Scale Quantum (NISQ) devices. Our toy model is a single Bosonic mode evolving under the nonlinear Kerr interaction. This is a structure generating process: for the closed Kerr system, an initial coherent state evolves into a kitten state (the higher order generalization of the Schrödinger cat state) exhibiting both negativity and sub-Planckian features in the quantum state’s Wigner function. However, only certain measurements are sensitive to the quantum features of the kitten states, with the measurement expectation values connected to the states by their shared symmetry of the cyclic group Z_n. Introducing weak decoherence, the quantum nature of these expectation values disappears and is replaced with semiclassical behavior well-described by the Truncated Wigner Approximation. We also find that these expectation values are calculable with decreased computational cost for stronger decoherence, and discuss the implications of this for NISQ-era quantum computation.

At the end of this talk we will also briefly revisit the question of describing decoherence more generally. We will introduce the measurement theory formalism of continuous weak measurement, which provides a less-conventional, state-independent framework for studying decoherence and complexity in NISQ-era devices.