Researchers Map Qubit States To Probability Distributions In Phase Space

Edward Jiang of ICFO, Institute of Photonic Sciences, Timothy Heightman of ICFO, Institute of Photonic Sciences, and Marcin Płodzień of Uniwersytet Jagielloński have developed a new framework for simulating quantum circuits by representing N-qubit states as probability distributions on a 2N-dimensional manifold. The researchers parameterize unitary gates as “normalizing flows” between these distributions, creating a new path for quantum circuit simulation using generative models. Evaluations on three quantum circuit families demonstrate the method’s accuracy exceeds that of current neural network methods, particularly as system sizes increase.

Phase Space Representation of Multi-Qubit States

This framework, detailed in recent work, maps the complex state of multiple qubits onto a more manageable, classically-understandable space, potentially simplifying simulations. The team’s method defines these distributions using the Q function, ensuring a positive probability distribution across the (S^2)^N manifold, a characteristic important for interpretation. Normalizing flows, originally developed for generative modeling, are employed to transform one probability distribution into another, effectively modeling the action of a quantum gate on the qubit state.