Quantum Convolutional Coding Techniques

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Quantum Convolutional Coding Techniques

• Mark M. Wilde

Communication Sciences Institute, Ming Hsieh
Department of Electrical Engineering, University
of Southern California, Los Angeles, California
90089
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What is a qubit?
A qubit is a quantum system with two degrees of
freedom.
Examples
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What are qubits good for?
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Tell me more about a qubit
Measurement projects the qubit
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What can I do to a qubit?
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What can I do to two qubits?
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What is Quantum Entanglement?
Quantum entanglement is the resource that fuels a
quantum computer or a quantum communication
network.
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Quantum Information and Noise
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Can We Correct Quantum Errors?
What to do?
Classical codes learn about errors by measuring
bits
BUT
Measuring a quantum state destroys its quantum
information.
What to do?
Classical codes do not accumulate small errors
over time because classical errors are discrete
BUT
Quantum errors are continuous and small errors
may build up over time.
What to do?
Classical Error Correction copies classical
information to protect it
BUT
No-Cloning Theorem prohibits general copying of
quantum information.
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Shors Solution

• Use extra ancilla qubits for redundancy

• Perform particular measurements that learn only
  about errors

• Measurement projects the encoded qubits and
  effectively digitizes the errors.

Shor, PRA 52, pp. R2493-R2496 (1995).
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Shor Code
Perform measurements that learn only about errors
Encode qubits with ancillas
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Our Research _at_
Novel forms of Quantum Error Correction
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Entanglement-Assisted Quantum Error Correction
Brun et al., Science 314, 436-439 (2006).
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Classical Convolutional Coding
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Quantum Convolutional Coding
Ollivier and Tillich, PRL 91, 177902
(2003). Forney et al., IEEE Trans. Inf. Theory
53, 865-880 (2007).
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Entanglement-Assisted Quantum Convolutional Coding
Wilde and Brun, In preparation (2007).
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Advantages of EAQCC
Can produce an EAQCC from two arbitrary classical
binary convolutional codes
The rate and error-correcting properties of the
classical codes translate to the
EAQCC.(high-performance classical codes gt
high-performance quantum codes)
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EAQCC Example 1
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Infinite-Depth Operations
Implements 1/(1D)
Implements 1/(1DD3)
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EAQCC Example 2
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Block Entanglement Distillation
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Convolutional Entanglement Distillation
Wilde et al., arXiv0708.3699 (2007).
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Conclusion

• Quantum computing and quantum communication are
  the future of computing and communication
• Quantum error correction is the way to make
  quantum computing and communication practical
• Quantum error correction also leads to private
  classical communication
• There is still much to explore in these areas
  (QEC07_at_USC)