Space-time qubits

TL;DR

This paper develops a framework for representing qubits using quantum field operators, explicitly incorporating space-time dependence, and demonstrates how to analyze simple quantum circuits within this field-theoretic approach.

Contribution

It introduces a novel algebraic formulation of qubits based on field operators, enabling space-time explicit modeling and potential for interacting qubit systems.

Findings

Constructed a qubit algebra from field creation and annihilation operators.

Demonstrated calculation of two-qubit circuit evolution in a field framework.

Showed the approach's potential for generalization to interacting, non-matched wavepackets.

Abstract

We construct a qubit algebra from field creation and annihilation operators acting on a global vacuum state. Particles to be used as qubits are created from the vacuum by a near-deterministic single particle source. Our formulation makes the space-time dependence of the qubits explicit, preparing the way for quantum computation within a field framework. The method can be generalized to deal with interacting qubits whose wavepackets are not perfectly matched to each other. We give an example of how to calculate the Heisenberg evolution of a simple two-qubit circuit, taking expectation values in the field vacuum state.