n-Qubit Operations on Sphere and Queueing Scaling Limits for Programmable Quantum Computer

TL;DR

This paper explores the mathematical rules for n-qubit operations on a sphere and derives scaling limits for queueing systems in programmable quantum computers, providing insights into performance and design under different traffic regimes.

Contribution

It introduces a novel framework for modeling n-qubit operations on a sphere and derives new scaling limits for quantum computer queueing systems under multiple traffic regimes.

Findings

Derived reflecting Gaussian random fields as scaling limits.

Analyzed performance balancing in fixed qubit regimes.

Explored qubit number scaling for quantum computer design.

Abstract

We study n-qubit operation rules on (n+1)-sphere with the target to help developing a (photon or other technique) based programmable quantum computer. In the meanwhile, we derive the scaling limits (called reflecting Gaussian random fields on a (n+1)-sphere) for n-qubit quantum computer based queueing systems under two different heavy traffic regimes. The queueing systems are with multiple classes of users and batch quantum random walks over the $(n+1)$-sphere as arrival inputs. In the first regime, the qubit number $n$ is fixed and the scaling is in terms of both time and space. Under this regime, performance modeling during deriving the scaling limit in terms of balancing the arrival and service rates under first-in first-out and work conserving service policy is conducted. In the second regime, besides the time and space scaling parameters, the qubit number $n$ itself is also considered as a varying scaling parameter with the additional aim to find a suitable number of qubits for the design of a quantum computer. This regime is in contrast to the well-known Halfin-Whitt regime.