1. Linear Optical Quantum Computing
-Rishabh Sahu

2. Summary Qubits: (Dual-rail bits) |1> |0> |0> |1> |0>
Single bit unitary transformation are trivial.
Two-bit gates are challenge as photons don’t interact.

3. Two-qubit CZ gate | 𝜙 1 > CZ| 𝜙 1 > 𝜋 4 − 𝜋 4 | 𝜙 2 >
Control
Target CZ
|0>
|0,0>
|1>
|0,1>
|1,0>
-|1,1>
CZ| 𝜙 1 >
𝜋 4
− 𝜋 4
| 𝜙 2 >
Success probability is

4. Quantum Teleportation Fix
Proposed by Gottesman and Chuang, 1999
Introduction
Bell Measurement
|𝜓>
|𝜙>
|𝜓>

5. Quantum Teleportation Fix
Several identities:

6. Quantum Teleportation Fix
| 𝜓 1 >
| 𝜙 1 >
CZ|𝜓>
| 𝜙 2 >
| 𝜓 2 >

7. Quantum Teleportation Fix
| 𝜓 1 >
| 𝜙 1 >
CZ|𝜓>
| 𝜙 2 >
| 𝜓 2 >

8. Quantum Teleportation Fix
| 𝜓 1 >
| 𝜙 1 >
CZ|𝜓>
| 𝜙 2 >
| 𝜓 2 >

9. Quantum Teleportation Fix
| 𝜓 1 >
| 𝜙 1 >
CZ|𝜓>
| 𝜙 2 >
| 𝜓 2 >

10. Quantum Teleportation Fix
| 𝜓 1 >
| 𝜙 1 >
CZ|𝜓>
| 𝜙 2 >
| 𝜓 2 >

11. Quantum Teleportation Fix
| 𝜓 1 >
| 𝜙 1 >
Offline System
CZ|𝜓>
| 𝜙 2 >
| 𝜓 2 >

12. Quantum Teleportation using Linear Optics
Dual-Rail bit
Entangled Resource
𝐸 1 :
𝑃 𝐸 1 +𝑃 𝐸 2 = 1 2
𝐸 2 :

13. Quantum Teleportation using Linear Optics
QFT
|𝜓>
Mode 1
|𝜓>
Mode 2
Entangled Resource

14. Quantum Teleportation using Linear Optics
Measurement
Output
Mode
Probability
Total probability of success = 2/3 (for 3-dimensional system)
For a n-dimensional system, success probability =1− 1 𝑛

15. Experimental Realization?

16. Thank You