Parallel Quantum Computing Emulation

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.arXiv:1908.06445v1 [quant-ph]

Emulation of Quantum Algorithms Using CMOS Analog Circuits

“…Consequently, the same circuit corresponds to a total of 11 qubits when utilized in analog quantum emulation which is promising. Additionally, qubits can be designed not only in the spatial domain but also in the temporal and spectral domains [14], reducing circuit size and facilitating an increase in the number of qubits. Furthermore, the continuous progress in technology is leading to advancements in 3-nm technologies which would allow us to design more qubits in the same space achieving a qubit count and quantum volume as high as 20-25.…”

“…[12] and [13] a theoretical framework for analog signals-based quantum emulation was proposed with a numerical simulation of the Deutsch-Jozsa algorithm [11], and in Ref. [14] they proposed techniques for improving hardware resource utilization but without a hardware demonstration.…”

Quantum Algorithms With Controlled Hodgkin-Huxley Neurons

“…One of the first researches on the classical emulation of a quantum computation focused mostly on electronic signals has been done in (La Cour et al, 2016), where the classical signals of bounded durations and amplitudes have been used to represent the Hilbert space structure of a multi-qubit quantum state. Later on, the authors extended their model for the case of parallel computations (La Cour et al, 2018).…”

Improving performance of an analog electronic device using quantum error correction

“…The choice was arbitrary, and other configurations give similar results. For more information regarding the time domain encoding scheme and the corresponding gate operations see [31]. The general workflow of the experiments is detailed in the flowchart in figure 3.…”