Efficient, high-speed two-photon logic gates at room temperature for general-purpose quantum information processing
A two-photon logic gate introduces a phase shift between two photons using a Q-switched cavity with some nonlinearity. The two-photon logic gate catches photons in and releases photons from de-coupled cavity modes in response to electronic or photonic control signals. This “catch-and-release” two-photon gate can be formed in semiconductor photonic integrated circuit (PIC) that operates at room temperature. When combined with sources, linear circuits, other logic gates, and detectors, it can be used to make a quantum computer with up to 1000 error-corrected logical qubits on a cm 2 PIC, with full qubit connectivity to avoid overhead. Two-qubit gate fidelity exceeding 99% is possible with near-term technology, and scaling beyond 99.9% is possible. Two-photon logic gates are also suitable for gate-based quantum digital computing and for analog quantum computing schemes, such as adiabatic quantum computing or quantum annealing.
1. A method of processing a photon wave packet including either one photon or two photons, the method comprising:
coupling the photon wave packet from an optical waveguide into a first resonant mode of an optical resonator comprising a nonlinear optical material, the first resonant mode being at a first resonance frequency;
nonlinearly coupling the photon wave packet, via at least one classical control field, from the first resonant mode of the optical resonator to a second resonant mode of the optical resonator that is de-coupled from the optical waveguide, the second resonant mode being at a second resonance frequency different than the first resonance frequency;
applying a 0 phase shift to the photon wave packet if the photon wave packet includes one photon or a π phase shift to the photon wave packet if the photon wave packet includes two photons;
nonlinearly coupling the photon wave packet, via the at least one classical control field, from the second resonant mode to the first resonant mode; and
coupling the photon wave packet from the optical resonator to the optical waveguide.
2. The method of claim 1 , wherein the method preserves a temporal shape of the photon wave packet.
3. The method of claim 1 , wherein coupling the photon wave packet from the optical waveguide into the first resonant mode occurs at a coupling rate greater than a full-width half-maximum of the photon wave packet.
4. The method of claim 1 , wherein the nonlinear optical material comprises a χ (2) material and nonlinearly coupling the photon wave packet from the first resonant mode to the second resonant mode comprises applying the at least one classical control field at a frequency equal to a frequency difference between the first resonance frequency and the second resonance frequency.
5. The method of claim 1 , wherein nonlinearly coupling the photon wave packet from the first resonant mode to the second resonant mode occurs via three-wave mixing.
6. The method of claim 1 , wherein the nonlinear optical material comprises a χ (3) material, the at least one classical control field comprises a first optical control field at a first frequency and a second optical control field at a second frequency, nonlinearly coupling the photon wave packet from the first resonant mode to the second resonant mode comprises coupling the first optical control field and the second optical control field into the optical resonator, and a frequency difference between the first frequency and the second frequency equals a frequency difference between the first resonance frequency and the second resonance frequency.
7. The method of claim 1 , wherein nonlinearly coupling the photon wave packet from the first resonant mode to the second resonant mode occurs via four-wave mixing.
8. The method of claim 1 , wherein applying the 0 phase shift to the photon wave packet if the photon wave packet includes one photon or the π phase shift to the photon wave packet if the photon wave packet includes two photons comprises generating a second harmonic of the photon wave packet in the second resonant mode.
9. The method of claim 1 , wherein applying the 0 phase shift to the photon wave packet if the photon wave packet includes one photon or the π phase shift to the photon wave packet if the photon wave packet includes two photons occurs via self-phase-modulation of the photon wave packet in the second resonant mode.
10. The method of claim 1 , wherein applying the 0 phase shift to the photon wave packet if the photon wave packet includes one photon or the π phase shift to the photon wave packet if the photon wave packet includes two photons comprises:
nonlinearly coupling the photon wave packet from the second resonant mode to a third resonant mode of the optical resonator that is resonant with a two-level emitter; and
absorbing and emitting the photon wave packet by the two-level emitter.
11. The method of claim 1 , wherein applying the 0 phase shift to the photon wave packet if the photon wave packet includes one photon or the π phase shift to the photon wave packet if the photon wave packet includes two photons comprises:
nonlinearly coupling the photon wave packet from the second resonant mode to a third resonant mode of the optical resonator in response to a control field; and
nonlinearly coupling the photon wave packet from the third resonant mode to a fourth resonant mode via second-harmonic generation.
12. A two-photon logic gate comprising:
a first optical waveguide;
a first nonlinear optical resonator evanescently coupled to the first optical waveguide and having a first coupled resonant mode coupled to the first optical waveguide and a first de-coupled resonant mode de-coupled from the first optical waveguide, wherein a resonant frequency of the first coupled resonant mode is different than a resonant frequency of the first de-coupled resonant mode;
a second optical waveguide;
a second nonlinear optical resonator evanescently coupled to the second optical waveguide and having a second coupled resonant mode coupled to the second optical waveguide and a second de-coupled resonant mode de-coupled from the second optical waveguide, wherein a resonant frequency of the second coupled resonant mode is different than a resonant frequency of the second de-coupled resonant mode; and
a beam splitter, having a first output coupled to the first optical waveguide and a second output coupled to the second optical waveguide, to couple a two-photon state into the first nonlinear optical resonator via the first optical waveguide or into the second nonlinear optical resonator via the second optical waveguide.
13. The two-photon logic gate of claim 12 , wherein the first nonlinear optical resonator comprises a first resonator having a first free spectral range (FSR) and a second resonator, optically coupled to the first resonator, having a second FSR equal to an integer multiple of the first FSR.
14. The two-photon logic gate of claim 13 , wherein the first resonator is a first ring resonator having a first diameter and the second resonator is a second ring resonator evanescently coupled to the first ring resonator and having a second diameter different than the first diameter.
15. The two-photon logic gate of claim 13 , wherein the first resonator is a first Fabry-Perot cavity having a first optical path length and the second resonator is a second Fabry-Perot cavity having a second optical path length different than the first optical path length.
16. The two-photon logic gate of claim 12 , wherein the first nonlinear optical resonator is configured to apply a phase shift of π to a photon wave packet with two photons.
17. The two-photon logic gate of claim 16 , wherein the first nonlinear optical resonator is configured to apply the phase shift to the photon wave packet via self-phase-modulation of photons in the first de-coupled resonant mode.
18. The two-photon logic gate of claim 16 , wherein the first nonlinear optical resonator is configured to apply the phase shift to the photon wave packet via second harmonic generation of photons in the first de-coupled resonant mode.
19. The two-photon logic gate of claim 16 , wherein the first nonlinear optical resonator comprises a two-level emitter configured to absorb and re-emit photons propagating in a resonant mode of the first nonlinear optical resonator.
20. The two-photon logic gate of claim 12 , further comprising:
a third optical waveguide; and
a third nonlinear optical resonator evanescently coupled to the third optical waveguide and having a third coupled resonant mode coupled to the third optical waveguide and a third de-coupled resonant mode de-coupled from the third optical waveguide.
21. A quantum information processor comprising the two-photon logic gate of claim 12 .
22. The quantum information processor of claim 21 , further comprising:
a network of Mach-Zehnder interferometers coupled to the two-photon logic gate.