Photonic Quantum Computing

TL;DR

It is possible to combine both DV and CV in a hybrid CV-DV fashion to overcome the limitations of either approach to achieve scalable universal photonic quantum computation.

Abstract

Photonic quantum computation refers to quantum computation that uses photons as the physical system for doing the quantum computation. The field is largely divided between discrete-variable (DV) and continuous-variable (CV) photonic quantum computation. In the former, quantum information is represented by one or more modal properties (e.g. polarisation) that take on distinct values from a finite set. Quantum information is processed via operations on these modal properties (e.g. waveplates in the case of polarisation), and eventually measured using single-photon detectors. In CV photonic quantum computation, quantum information is represented by properties of the electromagnetic field that take on any value in an interval (e.g. position). Both CV and DV implementations have been realized experimentally; each has a unique set of challenges that need to be overcome to achieve scalable universal photonic quantum computation. It is possible to combine both DV and CV in a hybrid CV-DV fashion to overcome the limitations of either approach.

Figures (17)

• Figure 1: A single qubit state is any point on the sphere labelled by two coordinates $\theta,\phi$. This is called the Bloch sphere. If the logical qubits are encoded using two orthogonal polarisation states, this is called the Poincaré sphere. For example $|0\rangle_L=|H\rangle, |1\rangle_L=|V\rangle$.
• Figure 2: A polarising beamsplitter has two input ports labelled by a wave vector. It reflects vertically- polarised photons and transmits horizontally-polarised photons.
• Figure 3: A pictorial 'phase-space' to capture features of a minimum uncertainty state (a) coherent state (b) squeezed state.
• Figure 4: An optical realisation of a single qubit gate in an optical fibre (or waveguide) using dual-rail encoding. Synchronous transform-limited single-photon pulses can be injected into either. The relative phase difference is given by $\phi$. Single-photon detectors sample the probability distributions for detection at the upper detector or lower detector.
• Figure 5: The probability distribution for $|\tilde{0}\rangle$ (left) and $|\tilde{1}\rangle$ (right ) in the diagonal representation of $X_1=a+a^\dagger$ with $r=1.2, \ \tilde{\Delta}=0.01$ and $|\psi_0\rangle$ has been chosen to be a squeezed state with variance in $X_1$ given by $e^{2r}$.