Method and apparatus for quantum holographic information processing

A system of encoding a quantum algorithm in an optical device, comprising:

• a controller for receiving an n by n unitary matrix operator representing the quantum algorithm, each row of the unitary matrix operator defining a superposition of n basis state vectors for transforming an input state into an output state;
• a recording stage operatively coupled to the controller for recording each row of the unitary matrix operator,
• wherein the controller causes the recording stage to selectively apply, to a volume holographic element having first and second opposing and substantially parallel faces, a combination of an ith one of n reference waves and a superposition of n signal waves defined by the superposition defined in an ith row of the unitary matrix operator,
• wherein the recording stage comprises optical components for generating the superposition of the n signal waves by directing a combination of plane waves selected from a first set of n plane waves lying on a first conical surface having a first half angle and that extends from a selected point on a first face of the volume holographic element and for generating the ith one of the n reference waves by directing a plane wave selected from a second set of n plane waves lying on a second conical surface concentric with the first conical surface and having a second half angle different than the first half angle and extending from the selected point.

A system for executing an n-dimensional quantum algorithm using an optical device, comprising:

• at least one volume holographic element having first and second opposing and substantially parallel faces and that, responsive to receiving at least one of n pre-defined superpositions of n pre-defined signal plane waves lying on a first conical surface having a first half angle, produces an output comprising at least one of n pre-defined reference plane waves lying on a second conical surface with a second half angle different than the first half angle, wherein each of the n pre-defined reference plane waves uniquely corresponds to each of the n pre-defined superpositions;
• an input stage optically coupled to the first face of the at least one volume holographic element and for generating at least one incident plane wave comprising at least one of the n-predefined superpositions;
• and
• a detector stage optically coupled to the second face of the at least one volume holographic element and for detecting an output intensity for the n pre-define reference waves responsive to the at least one incident plane wave.