No-go theorem for passive single-rail linear optical quantum computing

TL;DR

This paper proves that universal quantum computing with single-rail photons using only passive optical elements is impossible, guiding future design strategies for optical quantum computers.

Contribution

It establishes a no-go theorem showing passive linear optics cannot achieve universal quantum computation with single-rail photons.

Findings

Photon bunching cannot be passively suppressed.

Passive optical elements alone are insufficient for universal quantum computing.

The result guides future optical quantum computer design.

Abstract

Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.