Coding and Correcting Circuits for Two-Quantum Errors

Eesa Nikahd, Naser Mohammadzadeh, Zahra Shirmohammadi

One of the most important challenges in constructing large-scale quantum computers is handling the high error rates in quantum systems. Using error correction codes and frequently applying error correction on qubits is a common approach to compete with this challenge. Quantum error analysis techniques are required to compare the effectiveness of error correction codes and also to efficiently insert the error correction procedures (ECPs) in a quantum circuit. However, most existing assessment approaches are either inaccurate and inefficient or are slow and time-consuming. To address these problems, in this paper, a fast analytical approach is proposed that analyzes errors and smartly inserts ECPs into a quantum circuit and finally estimates the failure probability of the circuit. The approach is also able to estimate the pseudo-threshold of quantum error correction codes. Experimental results show that the proposed method improves the number of ECPs and the latency of the circuit encoded by the Steane’s [[7, 1, 3]] code on average by about 52.6% and 29.4% for the one-level one and by about 79.4% and 48.5% for the two-level concatenated code respectively compared with a related method in the literature. Moreover, the proposed method takes only a few seconds to run on even our relatively large benchmark circuits.

Kalyanapuram Rangachari Parthasarathy

Hong Tan

Using quantum XOR gate and Hadamard gate,we design the quantum circuit for Shor quantum error correction code.Furthermore,we propose two schemes of error correction and according quantum circuits of these schemes.

Kalyanapuram Rangachari Parthasarathy

Samuel L. Braunstein, John A. Smolin

An efficient coding circuit is given for the perfect quantum-error correction of a single quantum bit (qubit) against arbitrary one-qubit errors within a five-qubit code. The circuit presented employs a double ``classical'' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. Another circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary one-qubit errors. In addition, the performances of two error-correction schemes, one based on the quantum Zeno effect and the other using standard methods, are compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase diffusion.