Fidelities of Quantum ARQ Protocol Alexei Ashikhmin Bell Labs cal Automatic Repeat Request (ARQ) Protocol , von Neumann Measurement, Quantum Codes m Automatic Repeat Request (ARQ) Protocol m Errors m Enumerators ty of Quantum ARQ Protocol ntum Codes of Finite Lengths asymptotical Case (the code length from the paper “Quantum Error Detection”, by A. Ashikhmin,A. Barg, E. Knill re used in this talk
26
Embed
Fidelities of Quantum ARQ Protocol Alexei Ashikhmin Bell Labs Classical Automatic Repeat Request (ARQ) Protocol Qubits, von Neumann Measurement, Quantum.
The state (pure) of qubits is a vector Manipulating by qubits, we effectively manipulate by complex coefficients of As a result we obtain a significant (sometimes exponential) speed up qubits Qubits
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Fidelities of Quantum ARQ Protocol Alexei Ashikhmin
• Quantum Codes of Finite Lengths• The asymptotical Case (the code length )
Some results from the paper “Quantum Error Detection”, by A. Ashikhmin,A. Barg, E. Knill, and S. Litsyn are used in this talk
• is a parity check matrix of a code
• Compute syndrome
• If we detect an error
• If , but we have an undetected error
Classical ARQ Protocol
Noisy Channel
• The state (pure) of qubits is a vector
• Manipulating by qubits, we effectively manipulate by
complex coefficients of
• As a result we obtain a significant (sometimes exponential)
speed up
qubits
Qubits
• In this talk all complex vectors are assumed to be
normalized, i.e.
• All normalization factors are omitted to make notation short
• is projected on with probability
• is projected on with probability
• We know to which subspace was projected
von Neumann Measurementand orthogonal subspaces,
is the orthogonal projection on is the orthogonal projection on
1 2 k… k+1 n…
information qubitsin state
n1 2 …
quantum codewordin the state
unitary rotation
Quantum Codes
redundant qubitsin the ground states
is the code space
is the code rate
the joint state:
ARQ protocol: – We transmit a code state – Receive – Measure with respect to and – If the result of the measurement belongs
to we ask to repeat transmission – Otherwise we use
Quantum ARQ Protocol
is fidelity
If is close to 1 we can use
Conditional Fidelity
The conditional fidelity is the average value ofunder the condition that is projected on
Recall that the probability that is projected on is equal to
Quantum ARQ Protocol
• Quantum computer is unavoidably vulnerable to errors
• Any quantum system is not completely isolated from the environment
• Uncertainty principle – we can not simultaneously reduce: – laser intensity and phase fluctuations – magnetic and electric fields fluctuations – momentum and position of an ion
• The probability of spontaneous emission is always greater than 0
• Leakage error – electron moves to a third level of energy