  Encoding One Logical Qubit Into Six Physical Qubits  Recording
Details  Scientific Areas:  PIRSA Number:    We discuss two
methods to encode one qubit into six physical qubits. Each of
our two examples corrects an arbitrary single-qubit error. Our
first example is a degenerate six-qubit quantum error-correcting
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 non-trivial subsystem code that saturates the subsystem
Singleton bound. We then prove that a six-qubit code without
entanglement assistance cannot simultaneously possess a
Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary
single-qubit error. A corollary of this result is that the
Steane seven-qubit code is the smallest single-error correcting
CSS code. Our second example is the construction of a non-
degenerate six-qubit CSS entanglement-assisted code. This code
uses one bit of entanglement (a