Encoding One Logical Qubit Into Six Physical Qubits Speaker(s): Bilal Shaw
Abstract: We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary singlequbit error. Our first example is a degenerate sixqubit quantum errorcorrecting code. We explicitly provide the stabilizer generators, encoding circuits, codewords, logical Pauli operators, and logical CNOT operator for this code. We also show how to convert this code into a nontrivial subsystem code that saturates the subsystem Singleton bound. We then prove that a sixqubit code without entanglement assistance cannot simultaneously possess a CalderbankShorSteane (CSS) stabilizer and correct an arbitrary singlequbit error. A corollary of this result is that the Steane sevenqubit code is the smallest singleerror correcting CSS code. Our second example is the construction of a nondegenerate sixqubit CSS entanglementassisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary singlequbit error. The code we obtain is globally equivalent to the Steane sevenqubit code and thus corrects an arbitrary error on the receiver's half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary singlequbit error on the sender's side. We discuss the advantages and disadvantages for each of the two codes.
Date: 09/07/2008  4:00 pm
