Two-photon quantum photonic logic gates
Photonic controlled-phase gates that include a dipole emitter chirally coupled to a plurality of photonic qubit pairs in a waveguide are disclosed herein. Each photonic qubit pair includes a two-qubit state |xy , wherein the two-qubit state |xy comprises a combination of single-qubit states |0 and |1 , and may be |00 , |01 , |10 , and |11 . The dipole emitter is configured to interact with the single-qubit state |0 to impose a π phase shift, and the dipole emitter interacts with states |00 , |01 , and |10 to impose the π phase shift.
1. A photonic controlled-phase gate comprising a dipole emitter chirally coupled to a plurality of photonic qubit pairs in a photonic crystal waveguide, each photonic qubit pair comprising a two-qubit state |xy , wherein:
a. the two-qubit state |xy comprises a combination of single-qubit states |0 and |1 , the state selected from the group consisting of |00 , |01 , |10 , and | 11);
b. the dipole emitter is configured to interact with the single-qubit state |0 to impose a π phase shift; and
c. the dipole emitter interacts with states |00 , |01 , and |10 to impose the π phase shift;
wherein the photonic crystal waveguide comprises a glide plane structure and the dipole emitter is positioned at a chiral point of the photonic crystal waveguide.
2. The gate of claim 1 , wherein the dipole emitter is selected from a Rydberg atom, a quantum dot, a superconducting qubit, and an N-V defect state in a single-walled carbon nanotubes.
3. The gate of claim 2 , wherein the quantum dot is an InGaAs quantum dot.
4. The gate of claim 3 , wherein the dipole emitter is a circularly polarized dipole emitter chirally coupled to a circularly polarized electric field of the photonic crystal waveguide, wherein:
a. the single-qubit state | 0 comprises a photon with helicity σ + and transition frequency ω + and the single-qubit state |1 comprises a photon with helicity σ − and transition frequency ω + ; or
b. the single-qubit state |0 comprises a photon with helicity σ + and transition frequency ω + and the single-qubit state |1 comprises a photon with helicity σ + and transition frequency ω − .
5. The gate of claim 3 , wherein the dipole emitter is a horizontally linearly-polarized dipole emitter coupled to a horizontal/vertical linearly-polarized electric field of the chiral waveguide, wherein:
a. the single-qubit state |0 comprises a horizontally-polarized photon with transition frequency ω + and the single-qubit state |1 comprises a vertically-polarized photon with transition frequency ω + ; or
b. the dipole emitter comprises a horizontally linearly-polarized dipole emitter coupled to a horizontal/vertical linearly-polarized electric field of the chiral waveguide, the single-qubit state |0 comprises a horizontally-polarized photon with transition frequency ω + and the single-qubit state |1 comprises a horizontally-polarized photon with transition frequency ω − .
6. The gate of claim 1 , wherein the dipole emitter interacts with state |00 to form a photonic dimer.
7. A two-qubit photonic controlled-phase gate device, comprising a first and second chiral waveguide, each chiral waveguide containing first and second dipole emitters, respectively, wherein:
a. the first chiral waveguide is operatively coupled at opposite ends to a first input waveguide and a first output waveguide and the second chiral waveguide is operatively coupled at opposite ends to a second input waveguide and a second output waveguide;
b. the first input waveguide is operatively coupled to a first qubit source and the second input waveguide is operatively coupled to a second qubit source;
c. the first input waveguide and the second input waveguide are operatively coupled to an input beam combiner positioned between the first and second qubit sources and the first and second chiral waveguides;
d. the first output waveguide and the second output waveguides are further operatively coupled to first and second frequency domain modulators and first and second photodetectors at ends opposite the first and second chiral waveguides, respectively; and
e. the first and second dipole emitters are chirally coupled to a plurality of photonic qubit pairs produced by the first and second qubit sources, respectively, each photonic qubit pair comprising a two-qubit state |xy , wherein:
i. each two-qubit state |xy comprises a combination of single-qubit states |0 and |1 , the state selected from the group consisting of |00 , |01 , |10 , and |11 ;
ii. the dipole emitter is configured to interact with each single-qubit state |0 to impose a π phase shift; and
iii. the dipole emitter interacts with states |00 , |01 , and |10 to impose the π phase shift.
8. The gate of claim 7 , wherein the first and second chiral waveguides are selected from a photonic crystal waveguide, a nanobeam waveguide, and a chiral waveguide.
9. The gate of claim 8 , wherein the photonic crystal waveguide comprises a glide plane structure and the dipole emitter is positioned at a chiral point of the photonic crystal waveguide.
10. The gate of claim 9 , wherein the dipole emitter is selected from a Rydberg atom, a quantum dot, a superconducting qubit, and an N-V defect state in a single-walled carbon nanotubes.
11. The gate of claim 10 , wherein the quantum dot is an InGaAs quantum dot.
12. The gate of claim 11 , wherein the dipole emitter is a circularly polarized dipole emitter chirally coupled to a circularly polarized electric field of the photonic crystal waveguide, wherein:
a. the single-qubit state | 0 comprises a photon with helicity σ + and transition frequency ω + and the single-qubit state |1 comprises a photon with helicity σ − and transition frequency ω + ; or
b. the single-qubit state |0 comprises a photon with helicity σ + and transition frequency ω + and the single-qubit state |1 comprises a photon with helicity σ + and transition frequency ω − .
13. The gate of claim 11 , wherein the dipole emitter is a horizontally linearly-polarized dipole emitter coupled to a horizontal/vertical linearly-polarized electric field of the chiral waveguide, wherein:
a. the single-qubit state |0 comprises a horizontally-polarized photon with transition frequency ω + and the single-qubit state |1 comprises a vertically-polarized photon with transition frequency ω + ; or
b. the dipole emitter is a horizontally linearly-polarized dipole emitter coupled to a horizontal/vertical linearly-polarized electric field of the chiral waveguide, the single-qubit state |0 comprises a horizontally-polarized photon with transition frequency ω + and the single-qubit state |1 comprises a horizontally-polarized photon with transition frequency ω − .
14. The gate of claim 7 , wherein the dipole emitter interacts with state |00 to form a photonic dimer.
15. The gate of claim 7 , wherein at least one of the first and second photodetectors comprises a superconducting wire detector, the superconducting wire detector configured to specifically detect photonic qubit pairs with the two-qubit state |00 .
16. A two-qubit photonic controlled-phase gate device comprising:
a. a first waveguide comprising a first input port, a first exit port, and a first controlled-phase gate optically coupled to the first waveguide between the first input port and the first exit port; and
b. a second waveguide comprising a second input port, a second exit port, and a second controlled-phase gate optically coupled to the second waveguide between the second input port and the second exit port, wherein:
i. the first and second input ports are configured to receive a first and second photonic qubit, each photonic qubit comprising one of single-qubit states |0 and |1 ;
ii. the first and second input ports are optically coupled by a first 50:50 coupler and the first and second exit ports are optically coupled by a second 50:50 coupler;
iii. the first 50:50 coupler is configured to transform the single-qubit states of the first and second photonic qubits to produce first and second two-qubit states selected from |00 , |01 , |10 , and |11 ;
iv. each of the first and second controlled-phase gates comprises a dipole emitter chirally coupled to the plurality of photonic qubits in a gate waveguide, the dipole emitter configured to interact with the single-qubit state |0 ; and
v. each dipole emitter interacts with two-qubit states |00 , |01 , and |10 to impose a π phase shift.
17. The gate device of claim 16 , wherein the single-qubit states of the first and second photonic qubits entering the first and second input ports respectively are transformed into third and fourth photonic qubits exiting the first and second exit ports with single-qubit states as expressed in the table:
First/Second Input Ports
First/Second Exit Ports
|1 |1
|1 |1
|0 |1
−|0 |1
|1 |0
−|1 |0
|0 |0
−|0 |0
wherein a (−) sign denotes the π phase shift.