Addressable quantum gates

TL;DR

This paper extends the quantum circuit model to include addressable, superposition-capable wiring, enabling explicit representation of indefinite causal orders and analyzing the constraints of name anonymity.

Contribution

It introduces a new model for quantum circuits with addressable wiring and characterizes the structure of nameblind quantum evolutions.

Findings

Successfully models indefinite causal orders like the quantum switch.

Characterizes the structure of nameblind matrices in the extended model.

Shows quantum evolutions can act non-trivially on address labels.

Abstract

We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing indefinite causal orders and making their geometrical layout explicit: we express the quantum switch and the polarizing beam-splitter within the model. In this context, our main contribution is a full characterization of the anonymity constraints. Indeed, the names used as addresses should not matter beyond the wiring they describe, i.e. quantum evolutions should commute with "renamings". We show that these quantum evolutions can still act non-trivially upon the names. We specify the structure of "nameblind" matrices.