Optical ising-model solver using quantum annealing

1. An optical circuit for solving Ising-model using quantum annealing comprising:

a plurality of optical input ports for receiving a plurality of single photons, respectively;

a first plurality of optical programmable beam splitters for splitting the plurality of single photons, respectively to generate a first plurality of split photons;

a plurality of optical switches for selecting the first plurality of split photons or output photons output from respective optical output ports of the optical circuit, respectively to generate a plurality of selected photons;

a second plurality of optical programmable beam splitters for splitting the plurality of selected photons, respectively to generate a second plurality of split photons;

a first plurality of optical linear photon shifting devices for phase shifting of the second plurality of split photons, respectively to generate a first plurality of phase shifted photons;

a third plurality of optical programmable beam splitters for splitting the first plurality of phase shifted photons, respectively to generate a third plurality of split photons;

a second plurality of optical linear photon shifting devices for phase shifting of the third plurality of split photons, respectively to generate a second plurality of phase shifted photons; and

a plurality of optical cross-phase modulators for implementing a quadratic portion of the Ising-model, wherein outputs of the plurality of optical cross-phase modulators are switched by the plurality of optical switches to respective inputs of the second plurality of optical programmable beam splitters or to respective inputs of the optical output ports to be output from the optical circuit, respectively.

2. The optical circuit of claim 1 , wherein plurality of single photons are generated by single-photon source are either in a “1” state or a “0” state.

3. The optical circuit of claim 1 , wherein first, second and third plurality of optical programmable beam splitters are programmable by thermal tuners.

4. The optical circuit of claim 1 , further comprising a counter for keeping track of the number of iterations of the optical circuit and deciding which of the two inputs each of the plurality of the optical switches selects.

5. The optical circuit of claim 1 , wherein each of the first plurality of optical linear photon shifting devices implement a same constant phase shift.

6. The optical circuit of claim 1 , wherein the second plurality of optical linear photon shifting devices implement a phase shift Φ m, i according to

ϕ

m

,

i

=

B

i

⁢

Tk

⁢

⁢

π

m

2

where B i is the number of constraints that a bit i is contained in, m is the number of first plurality of split photons, k is a particular piece of the spit photons and T is the time period in which the Ising-model is adiabatically tuned.

7. The optical circuit of claim 1 , wherein each of the plurality of optical cross-phase modulators performs a phase shift proportional to the number of photons in each mode of said each cross-phase modulator.

8. The optical circuit of claim 1 , wherein each of the plurality of optical cross-phase modulators imparts a phase to a state in each photon mode that depends on the number of photons in each photon mode.

9. A method implemented by an optical circuit for solving Ising-model using quantum annealing with encoded photonic qubits, the method comprising:

discretizing a continuous time-dependent Hamiltonian function over an evolution time period T, into a plurality of portions, each portion being smaller than the continuous time-dependent Hamiltonian function, wherein each portion is time independent;

implementing each of said portions with a non-linear optical medium to generate a portion of a solution of the Ising Hamiltonian problem, by mapping the evolution time period to a spatial extent within the non-linear optical medium, wherein the non-linear optical medium encodes each photonic qubit into two modes that share a single photon by using dual-rail-encoding; and

iterating the discretizing and implementation over each said portions to output the all solution of the Ising Hamiltonian problem.

10. The method of claim 9 , wherein the Hamiltonian function is discretized into said portions, using a Trotter approximation.

11. The method of claim 9 , wherein the mapping sends a qubit zero into an optical state where the single photon is in a first mode and a qubit one to an optical state where the single photon is in a second mode.