Quantum gates that correct their own (quantum) errors

Alexei Kitaev

Yaakov S. Weinstein, Sidney Buchbinder

We apply single ‘logical’ qubit Clifford gates to states encoded in the [7,1,3] quantum error correction code in a nonequiprobable Pauli matrix error environment. The gates we analyze are the NOT, Phase, and Hadamard gates. We calculate accuracy measures of the applied gates by determining output state and logical gate fidelities. The latter is determined from the logical gate -matrix. In addition, we apply perfect and noisy quantum error correction to the output state of the Clifford gate. Perfect error correction allows the determination of whether errors that occurred during the gate are ‘correctable’. Noisy error correction gives an idea of what can be expected in a realistic quantum computation.

Wen-Long Ma, Philip Reinhold, Serge Rosenblum +2 more

Chungheon Baek, Tomohiro Ostuka, Seigo Tarucha +1 more

Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such limits, but imperfect gate operations introduce errors to the correction procedure as well. The additional gate operations required due to the physical layout of qubits exacerbate the situation. Here, we use density-matrix simulations to investigate the performance change of logical qubits according to quantum error correction codes and qubit layouts and the expected performance of logical qubits with gate operation time and gate error rates. Considering current qubit technology, the small quantum error correction codes are chosen. Assuming 0.1% gate error probability, a logical qubit encoded by a 5-qubit quantum error correction code is expected to have a fidelity 0.25 higher than its physical counterpart.

Serge Rosenblum, Philip Reinhold, Wen-Long Ma +3 more

Ritajit Majumdar, Saikat Basu, Priyanka Mukhopadhyay +1 more

Descriptions of quantum algorithms, communication etc. protocols assume the existence of closed quantum system. However, real life quantum systems are open and are highly sensitive to errors. Hence error correction is of utmost importance if quantum computation is to be carried out in reality. Ideally, an error correction block should be placed after every gate operation in a quantum circuit. This increases the overhead and reduced the speedup of the quantum circuit. Moreover, the error correction blocks themselves may induce errors as the gates used for error correction may be noisy. In this paper, we have proposed a procedure to trace error probability due to noisy gates and decoherence in quantum circuit and place an error correcting block only when the error probability exceeds a certain threshold. This procedure shows a drastic reduction in the required number of error correcting blocks. Furthermore, we have considered concatenated codes with tile structure layout lattice architecture[25][21],[24] and SWAP gate based qubit transport mechanism. Tracing errors in higher levels of concatenation shows that, in most cases, after 1 or 2 levels of concatenation, the number of QECC blocks required become static. However, since the gate count increases with increasing concatenation, the percentage saving in gate count is considerably high.