Linear Optical Quantum Computing -Rishabh Sahu
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.
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 1 16 .
Quantum Teleportation Fix Proposed by Gottesman and Chuang, 1999 Introduction Bell Measurement |𝜓> |𝜙> |𝜓>
Quantum Teleportation Fix Several identities:
Quantum Teleportation Fix | 𝜓 1 > | 𝜙 1 > CZ|𝜓> | 𝜙 2 > | 𝜓 2 >
Quantum Teleportation Fix | 𝜓 1 > | 𝜙 1 > CZ|𝜓> | 𝜙 2 > | 𝜓 2 >
Quantum Teleportation Fix | 𝜓 1 > | 𝜙 1 > CZ|𝜓> | 𝜙 2 > | 𝜓 2 >
Quantum Teleportation Fix | 𝜓 1 > | 𝜙 1 > CZ|𝜓> | 𝜙 2 > | 𝜓 2 >
Quantum Teleportation Fix | 𝜓 1 > | 𝜙 1 > CZ|𝜓> | 𝜙 2 > | 𝜓 2 >
Quantum Teleportation Fix | 𝜓 1 > | 𝜙 1 > Offline System CZ|𝜓> | 𝜙 2 > | 𝜓 2 >
Quantum Teleportation using Linear Optics Dual-Rail bit Entangled Resource 𝐸 1 : 𝑃 𝐸 1 +𝑃 𝐸 2 = 1 2 𝐸 2 :
Quantum Teleportation using Linear Optics QFT |𝜓> Mode 1 |𝜓> Mode 2 Entangled Resource
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
Experimental Realization?
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