A photonic gate is a fundamental building block in optical quantum computing and quantum information processing. Photonic gates are used to manipulate a quantum state encoded in photons and perform computations. Similarly to [quantum circuits – add link to entry!], photonic gates can be arranged in a linear optical circuit to implement complex algorithms.
Linear optical gates
At Quandela we essentially use linear optical gates. As indicated by their name, the latter act linearly on the creation and annihilation operators, as opposed to non-linear optical components. The creation and annihilation operators are operators that act on a state of light by creating or annihilating a photon. For instance, applying the creation operator onto a state with no photon |0>, gives a single-photon state |1>. If one considers a system made of two waveguides, each waveguide will have its own creation and annihilation operator (corresponding to the creation or annihilation of a photon in that specific waveguide). A beamsplitter is a linear –optical gate that takes two creation operators as input and can for instance return as output their sum and their difference.
Since a linear optical gate acting on two modes act linearly on the corresponding creation operators, it can be represented with a matrix.
Dual-rail encoding
Photonic gates can also have an interpretation in terms of operations on qubits if we encode a qubit in linear optics. Consider two waveguides. Imposing a photon to stay in these two waveguides gives a binary information that encodes a qubit: the photon being in the first mode encodes the qubit state |0> and the photon being in the second mode encodes the qubit state |1>. Then, any 2-mode linear optical gate applied on two modes encoding one qubit is equivalent to a 1-qubit gate. For instance, the beam splitter applies an X-rotation gate on the qubit.
Frequently-asked question on photonic gates
- Which photonic gates are the easiest to implement?
Linear-optical gates are the easiest to implement. The most common linear-optical gates are beamsplitters (which divide a light beam into two and then recombine it) and phase-shifters (which modify the phase of the electromagnetic wave associated with light).
- Is it possible to perform any arbitrary computation using only linear-optical gates?
Linear optics alone is not universal for quantum computing, but universality can be achieved by adding post-selection. In that case, photons are measured after being sent through an interferometer. The outcome of the measurement (e.g. in which waveguides the photons are measured at the end), tells us which operation has been applied on the quantum information. If the outcome does not correspond to the desired gate implementation, the results are thus discarded. For instance, the conditional phase-shift gate, which can implement a CZ gate between two qubits if applied on two modes encoding two |1> states, can only be implemented in a probabilistic manner, using post-selection.