Classical Analog Emulation of Quantum Circuits via Time-Averaged Dynamic States

Abstract

Classical analog hardware that emulates quantum circuits at the gate level offers a route to benchmarking, prototyping, and teaching quantum algorithms. We introduce wavebits, classical wave analogs of qubits whose amplitudes are carried by physical oscillatory signals, and show that any nonseparable N-qubit state can be encoded in 2N narrowband signals that remain locally separable at every instant. The nonseparable correlations are recovered at readout by time-averaged demodulation over auxiliary carrier frequencies, referred to as nonseparability channels. We prove that any two-qubit gate unravels into the time-averaged tensor product of two local time-varying operators, and that arbitrary circuits are emulated with a base-frequency count scaling linearly with the number of entangling layers, independent of qubit number. The exponential cost of the 2^N-dimensional state reappears at readout and in the averaging time of deep circuits, not during circuit execution, as quantified by an analytic error bound that also serves as a hardware design rule. A mixed-signal prototype emulates Bell state generation, controlled-NOT gates, phase kickback, and Bloch-sphere rotations with fidelities above 0.98, and numerical benchmarks against exact state vectors validate the scheme for up to six qubits. The architecture is directly implementable in acoustic, photonic, and mixed-signal platforms.