M ar 2 01 3 Non-Fault Tolerant T-Gates for the [ 7 , 1 , 3 ] Quantum Error Correction Code

We simulate the implementation of a T -gate, or π 8 -gate, for a [7,1,3] encoded logical qubit in a nonequiprobable error environment. We demonstrate that the use of certain non-fault tolerant methods in the implementation may nevertheless enable reliable quantum computation while reducing basic resource consumption. Reliability is determined by calculating gate fidelities for the one-qubit logical gate. Specifically, we show that despite using a non-fault tolerant procedures in constructing a logical zero ancilla to implement the T -gate the gate fidelity of the logical gate, after perfect error correction, has no first order error terms. Meaning, any errors that may have occurred during implementation are ‘correctable’ and fault tolerance may still be achieved.