Non-fault-tolerantTgates for the [7,1,3] quantum error-correction code

Abstract

We simulate the implementation of a $T$ gate, or $\frac{\ensuremath{\pi}}{8}$ 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 procedure 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.