Spiking neuromorphic chip learns entangled quantum states

Abstract

Neuromorphic systems are designed to emulate certain structural and dynamical properties of biological neuronal networks, with the aim of inheriting the brain's functional performance and energy efficiency in artificial-intelligence applications [1,2]. Among the platforms existing today, the spike-based BrainScaleS system stands out by realizing fast analog dynamics which can boost computationally expensive tasks [3]. Here we use the latest BrainScaleS generation [4] for the algorithm-free simulation of quantum systems, thereby opening up an entirely new application space for these devices. This requires an appropriate spike-based representation of quantum states and an associated training method for imprinting a desired target state onto the network. We employ a representation of quantum states using probability distributions [5,6], enabling the use of a Bayesian sampling framework for spiking neurons [7]. For training, we developed a Hebbian learning scheme that explicitly exploits the inherent speed of the substrate, which enables us to realize a variety of network topologies. We encoded maximally entangled states of up to four qubits and observed fidelities that imply genuine N -partite entanglement. In particular, the encoding of entangled pure and mixed two-qubit states reaches a quality that allows the observation of Bell correlations, thus demonstrating that non-classical features of quantum systems can be captured by spiking neural dynamics. Our work establishes an intriguing connection between quantum systems and classical spiking networks, and demonstrates the feasibility of simulating quantum systems with neuromorphic hardware.

Formulation and Emulation of Quantum-Inspired Dynamical Systems With Classical Analog Circuits

“…Other recent work has shown that quantum spin-based Ising systems, including probability distributions corresponding to those seen in quantum entanglement, can be learned and emulated by networks of leaky integrateand-fire spiking neurons on VLSI chips. These implementations effectively architect positive operator-valued measures (Czischek et al, 2021). Our work is complementary and consistent with such work since we effectively architect linear, nonspiking classical analog quadrature oscillator circuits to represent phase.…”

Variational learning of quantum ground states on spiking neuromorphic hardware

“…Due to the physical implementation the emulation becomes inherently parallel, rendering the sampling speed independent of the network size. We note that neuromorphic hardware has recently been used to represent entangled quantum states using a mapping of general mixed quantum states to a probabilisitic representation and training the system to represent a given state by approximating its corresponding probability distribution [19]. Here, instead, we directly encode the wave function of pure quantum states and use this approach for variational ground state search through minimization of the quantum system's total energy (Fig.…”