Encoding One Logical Qubit Into Six Physical Qubits
| dc.creator | Shaw, Bilal | |
| dc.creator | Wilde, Mark M. | |
| dc.creator | Oreshkov, Ognyan | |
| dc.creator | Kremsky, Isaac | |
| dc.creator | Lidar, Daniel A. | |
| dc.date | 2008-03-10 | |
| dc.date | 2008-08-12 | |
| dc.date.accessioned | 2026-07-07T09:55:48Z | |
| dc.date.available | 2026-07-07T09:55:48Z | |
| dc.description | 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 circuit, 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 (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit 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 single-qubit error on the sender's side. We discuss the advantages and disadvantages for each of the two codes. | |
| dc.description | 13 pages, 3 figures, 4 tables | |
| dc.identifier | https://arxiv.org/abs/0803.1495 | |
| dc.identifier | http://arxiv.org/abs/0803.1495 | |
| dc.identifier | Physical Review A 78, 012337 (2008) | |
| dc.identifier | doi:10.1103/PhysRevA.78.012337 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166755 | |
| dc.subject | Quantum Physics | |
| dc.title | Encoding One Logical Qubit Into Six Physical Qubits | |
| dc.type | text |