Functional quantum computing: An optical approach

Recent theoretical investigations treat quantum computations as functions, quantum processes which operate on other quantum processes, rather than circuits. Much attention has been given to the $N$-switch function which takes $N$ black-box quantum operators as input, coherently permutes their ordering, and applies the result to a target quantum state. This is something which cannot be equivalently done using a quantum circuit. Here, we propose an all-optical system design which implements coherent operator permutation for an arbitrary number of input operators.

Figure 1

(a) A quantum circuit diagram which implements 2-switch using two copies of each operator. (b) A functional circuit diagram of 2-switch showing a superposition of two possible connections (solid and dashed) made by quantum controlled movable wires. Arrows illustrate the direction of information flow.

Figure 2

A schematic for the quantum switch. Cross-phase modulation, caused by a pump pulse multiplexed in and out of a fiber loop, alters the quantum signal interference within a nonlinear optical loop mirror, thereby coherently controlling whether an input signal exits from output 1 or output 2.

Figure 3

(a) A network of $N-1$ quantum switches which multiplexes an input photonic signal from the $x_0$ spatial mode into one of $N$ spatial modes. (b) A network of $N-1$ quantum switches which demultiplexes $N$ spatial modes of a photonic signal into a single spatial mode ($x_0$).

Figure 4

An optical device which simulates $N$-switch using $2N-2$ quantum switches and $N$ physical quantum operators. Because the behavior of the quantum switches is governed by a predetermined pattern of optical control pulses, the time at which a photonic signal is input to the device can be mapped to an order in which the photon passes through the quantum operators.

Figure 5

Experimental design for measuring the commutativity of two operators.