Photonic Qubits

Table of Contents

1. Introduction
2. What Are Photonic Qubits?
3. Quantum Properties of Light
4. Qubit Encodings in Photons
5. Polarization Encoding
6. Path Encoding
7. Time-Bin and Frequency Encoding
8. Advantages of Photonic Qubits
9. Challenges in Photonic Quantum Computing
10. Single-Photon Sources
11. Entangled Photon Pair Generation
12. Beam Splitters and Interference
13. Mach-Zehnder and Hong-Ou-Mandel Interference
14. Linear Optical Quantum Computing (LOQC)
15. Knill-Laflamme-Milburn (KLM) Scheme
16. Measurement-Based Quantum Computation
17. Quantum Gates with Photons
18. Quantum Teleportation with Photons
19. Quantum Repeaters and Photonic Networks
20. Integration on Photonic Chips
21. Quantum Key Distribution with Photons
22. Photonic Quantum Simulators
23. Commercial and Research Efforts
24. Scalability Prospects and Future Directions
25. Conclusion

1. Introduction

Photonic qubits use individual photons — the fundamental particles of light — to encode and process quantum information. Due to their low decoherence and ability to travel long distances, photons are ideal for quantum communication and emerging quantum computing architectures.

2. What Are Photonic Qubits?

Photonic qubits represent quantum information through light-based degrees of freedom. These systems can:

• Maintain quantum coherence for long durations
• Transmit information across optical fibers or free space
• Be manipulated using passive and active optical components

3. Quantum Properties of Light

Key quantum features enabling computation with photons:

• Superposition of polarization, path, or time-bin states
• Entanglement between photons
• Indistinguishability and interference

4. Qubit Encodings in Photons

Information is typically encoded in:

• Polarization states: \( |H\rangle, |V\rangle \)
• Spatial modes (path): two distinct paths
• Time-bin or frequency: early vs late photon arrival or different frequencies

5. Polarization Encoding

Implemented using:

• Wave plates
• Polarizing beam splitters
• Single-photon detectors

6. Path Encoding

A single photon split between two spatial modes:
\[
|0\rangle = \text{Path A}, \quad |1\rangle = \text{Path B}
\]

Controlled using beam splitters, mirrors, and phase shifters.

7. Time-Bin and Frequency Encoding

Time-bin encoding:

• Use early and late pulses to define \( |0\rangle \) and \( |1\rangle \)
• Maintains robustness in long-distance communication

Frequency encoding:

• Use two frequencies of a single photon as basis states

8. Advantages of Photonic Qubits

• Room temperature operation
• High-speed communication
• Long coherence times
• Compatibility with optical fibers and photonic chips

9. Challenges in Photonic Quantum Computing

• Difficulty in creating deterministic photon-photon interactions
• Low efficiency of photon generation and detection
• Need for probabilistic gates and post-selection in LOQC

10. Single-Photon Sources

Essential for scalable quantum optics:

• Spontaneous parametric down-conversion (SPDC)
• Quantum dots
• Defect centers in diamond

Ideal source must be:

• On-demand
• Bright
• Indistinguishable photons

11. Entangled Photon Pair Generation

Produced via:

• Type-II SPDC in nonlinear crystals
• Waveguide-integrated SPDC
• Quantum dot cascade emission

Used in teleportation, QKD, and multi-photon entanglement.

12. Beam Splitters and Interference

Beam splitters are core components:

• Enable superposition and interference
• Facilitate entanglement and measurement-based gates

13. Mach-Zehnder and Hong-Ou-Mandel Interference

Hong-Ou-Mandel effect:

• Two identical photons entering a beam splitter will “bunch” into the same output port:
  \[
  |1\rangle_A |1\rangle_B \rightarrow \frac{1}{\sqrt{2}}(|2\rangle_C |0\rangle_D + |0\rangle_C |2\rangle_D)
  \]

Used to test indistinguishability and create entanglement.

14. Linear Optical Quantum Computing (LOQC)

Computing with photons using only:

• Beam splitters
• Phase shifters
• Photon detectors
• Feed-forward logic

Pioneered by the Knill-Laflamme-Milburn (KLM) protocol.

15. Knill-Laflamme-Milburn (KLM) Scheme

• Uses ancilla photons and projective measurements
• Enables universal quantum computation
• But probabilistic and resource-intensive

16. Measurement-Based Quantum Computation

Also known as cluster-state computing:

• Create large entangled states (cluster states)
• Perform computation by adaptive measurements

Well-suited for photonic platforms due to ease of entanglement distribution.

17. Quantum Gates with Photons

• Hadamard, Z, X gates via waveplates and interferometers
• Controlled-Z or CNOT gates via entanglement and post-selection
• Nonlinear media may offer future deterministic gates

18. Quantum Teleportation with Photons

Photons are ideal carriers for teleportation:

• Source generates entangled pair
• Bell-state measurement collapses system
• Receiver applies Pauli operation

19. Quantum Repeaters and Photonic Networks

Used to extend quantum communication over long distances:

• Quantum repeaters correct losses
• Entanglement swapping and memory interfaces needed for scalability

20. Integration on Photonic Chips

Efforts to miniaturize optics:

• Silicon photonics and lithium niobate platforms
• Integrated sources, modulators, and detectors
• Compact, scalable, and stable architectures

21. Quantum Key Distribution with Photons

Backbone of modern QKD systems:

• BB84, E91, and decoy-state protocols use photon polarization or phase
• Secured by quantum no-cloning and disturbance detection

22. Photonic Quantum Simulators

Used to simulate physical phenomena:

• Boson sampling
• Molecular energy spectra
• Quantum walks and topological effects

23. Commercial and Research Efforts

• Xanadu (Canada): Borealis photonic processor
• PsiQuantum: Silicon photonic quantum computer
• Toshiba, ID Quantique: QKD hardware
• Multiple university-led efforts on integrated optics

24. Scalability Prospects and Future Directions

• Deterministic photon sources
• Quantum error correction with bosonic codes
• On-chip nonlinear optics
• Fusion with telecom infrastructure

25. Conclusion

Photonic qubits offer unique advantages in transmission, coherence, and room-temperature operation. Though challenges remain in deterministic interaction and scalability, advances in integrated optics and quantum photonics are paving the way toward scalable, networked, and secure quantum systems. Photons will undoubtedly play a key role in the future of both quantum computing and communication.