Quantum Error Correction: Applications and implementations

Rohan Timmaraju

Quantum Computing is a computing framework that takes advantage of unique quantum mechanical properties (such as superposition and entanglement) to perform calculations and implement algorithms that could offer exponential speed-ups over classical computing. However, in physical implementations of such quantum computers, qubits – the fundamental components of these systems – can accumulate errors that must be accounted for. In order to mitigate these errors, various quantum error correction (QEC) codes have been developed, including the repetition code and surface codes. In this experiment I implement and evaluate three types of QEC codes on the Qiskit simulator to compare their efficacy and applicability in correcting for different kinds of errors. I hypothesize that surface codes, with their more effective design and range of correction methods, should perform the best with much lower error thresholds and resultant logical error rates. The results support the hypothesis and suggest that surface codes are a viable method of implementing scalable error correction in quantum computers.

Masahito Hayashi

Akshaya Jayashankar, Prabha Mandayam

Jingfu Zhang, Raymond Laflamme, Dieter Suter

Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single-qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single-qubit errors, and measure the fidelity of the encoded logical gate operations.

Yaakov S. Weinstein

Fault-tolerant protocol assumes the application of error correction after every quantum gate. However, correcting errors is costly in terms of time and number of qubits. Here we demonstrate that quantum error correction (QEC) can be applied significantly less often with only a minimal loss of fidelity. This is done by simulating the implementation of 50 encoded, single-qubit, quantum gates within the [[7,1,3]] QEC code in a noisy, nonequiprobable Pauli error environment with QEC being applied at different intervals. We find that applying QEC after every gate is rarely optimal and even applying QEC only once after all 50 gates sacrifices only a slight amount of fidelity with the benefit of 50-fold saving of resources. In addition, we find that in cases where bit-flip errors are dominant, it is best not to apply QEC at all.

Daniel A. Lidar, Todd A. Brun