# Parallel Quantum Computing Emulation

## TL;DR

This paper introduces a parallel emulation method for quantum computing using classical analog signals, enabling larger quantum states to be simulated efficiently across multiple signals and encoding schemes.

## Contribution

It presents a novel approach to extend classical analog signal-based quantum emulation to multiple parallel signals, increasing the size of simulatable quantum states.

## Key findings

- Enables larger quantum states to be emulated with the same gate time.
- Supports operations on qubits encoded in frequency, spatial, or time domains.
- Provides methods for gate operations between different encoding schemes.

## Abstract

Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary operations on a finite-dimensional Hilbert space, are not unique to quantum systems but may be found in certain classical systems as well. Previously, it has been shown that one can represent an arbitrary multi-qubit quantum state in terms of classical analog signals using nested quadrature amplitude modulated signals. Furthermore, using digitally controlled analog electronics one may manipulate these signals to perform quantum gate operations and thereby execute quantum algorithms. The computational capacity of a single signal is, however, limited by the required bandwidth, which scales exponentially with the number of qubits when represented using frequency-based encoding. To overcome this limitation, we introduce a method to extend this approach to multiple parallel signals. Doing so allows a larger quantum state to be emulated with the same gate time required for processing frequency-encoded signals. In the proposed representation, each doubling of the number of signals corresponds to an additional qubit in the spatial domain. Single quit gate operations are similarly extended so as to operate on qubits represented using either frequency-based or spatial encoding schemes. Furthermore, we describe a method to perform gate operations between pairs of qubits represented using frequency or spatial encoding or between frequency-based and spatially encoded qubits. Finally, we describe how this approach may be extended to represent qubits in the time domain as well.