A Universal Quantum Computer From Relativistic Motion

TL;DR

A lower bound on the channel fidelity is derived that shows the existence of parameter regimes in which all entangling operations are effectively unitary, despite the noise generated from the presence of a mediating quantum field.

Abstract

We present an explicit construction of a relativistic quantum computing architecture using a variational quantum circuit approach that is shown to allow for universal quantum computing. The variational quantum circuit consists of tunable single-qubit rotations and entangling gates that are implemented successively. The single qubit rotations are parameterized by the proper time intervals of the qubits' trajectories and can be tuned by varying their relativistic motion in spacetime. The entangling layer is mediated by a relativistic quantum field instead of through direct coupling between the qubits. Within this setting, we give a prescription for how to use quantum field-mediated entanglement and manipulation of the relativistic motion of qubits to obtain a universal gate set, for which compact non-perturbative expressions that are valid for general spacetimes are also obtained. We also derive a lower bound on the channel fidelity that shows the existence of parameter regimes in which all entangling operations are effectively unitary, despite the noise generated from the presence of a mediating quantum field. Finally, we consider an explicit implementation of the quantum Fourier transform with relativistic qubits.

Figures (2)

• Figure 1: The RVQC model. On the left we have an array of UDW qubits that each follow a worldline through spacetime. During the pictured time interval of the worldlines, all qubit trajectories are manipulated to set the qubit rotation angles. They then each interact with a scalar quantum field in the purple spacetime regions becoming entangled; this corresponds to applying one layer $\hat{U}_{\bm \theta}^{(\ell)}$ of the RVQC, which is shown in the lower blue circuit diagram. Layers are repeatedly applied and the output is measured after the final layer is applied, as in the top golden circuit diagram.
• Figure 2: The average fidelity (top) and loss (bottom) over 20 different training runs. One can see that the model quickly reaches a low/high loss/fidelity but takes some time to converge to the loss tolerance value, which is typical behaviour in similarly-sized QML problems. Each training run took a different total number of steps to converge, the lowest being 4717 and the highest being 30000. To do the plot averaging, we padded the values of all runs smaller than the longest one with their final converged value, which is akin to freezing the learning rate after convergence. Note that the top figure displays the average fidelity calculated every 100 training steps. The lighter, shaded regions are ± the standard deviation of the average fidelity/loss, which is calculated over the 20 different runs at the same time step.