Density Matrix Simulation of 3 Qubit Quantum Error Correction Code*

Encoding logical qubits is the essential component for high performance quantum computer. Although 3-qubit bit-flip quantum error correction code cannot correct both bit-flip and phase-flip errors, it is a simple and small code because it employs cnot and toffoli gates without syndrome measurement and ancilla. This study examines how the accuracy of logical qubits is improved at the same computation time and how long the additional time is available for logical qubit gate operations. This density matrix model includes not only dephasing and relaxation process, but also gate and measurement errors. This simulation expected that the computation time of the logical qubits would be twice as long as the physical qubits with an accuracy of 95% if the entire time for quantum error correction is a hundredth of coherence time. The simulation results are compared with the IBM QX experiment as increasing the computation time for both physical and logical qubits.