Quality of operations and qubits

As we have seen in the foundations module, the fundamental building blocks of quantum algorithms are quantum gates. These gates are responsible for manipulating the quantum states of qubits. One of the reasons why the results of running the Bernstein-Vazirani-Algorithm on a real quantum computer differed from the ideal output was that noise can cause errors during quantum gate operations.

Each operation introduces a slight error. These errors can occur due to imperfections in the physical hardware, such as imprecise control over the qubits or external noise affecting the gates. They can cause the qubits' state to move to an unexpected position on the Bloch sphere, leading to errors in calculations. The more operations that are applied within a circuit, the less accurate the overall result gets. To get a sense of the overall quality of the operations of a quantum computer, the accuracy of a single gate is typically expressed with gate fidelity.

Gate fidelity is a measure of how accurately a quantum gate performs its intended operation. It represents the similarity between the ideal (desired) operation of a quantum gate and the actual operation performed by a physical implementation of that gate. This might occur because quantum gates operate on an analog basis. Therefore, a rotation intended to be exactly 90° could actually end up being slightly off, for example, 92° or 89° instead.

A high-fidelity gate will produce states very close to the ideal output states. Output states produced by low-fidelity gates will be significantly different from the ideal ones. Gate fidelity is an important metric for evaluating the quality of quantum hardware, as it directly affects the reliability of quantum computations.

The gate fidelities of the current quantum computers are typically in the range of 95-99.99%. However, achieving a higher gate fidelity is essential for realizing the true potential of quantum computing.

Errors can also occur when no operations is performed or while reading out the state of a qubit. Such readout errors will cause the measurement result to flip (e.g. reading out a $|0\rangle$ instead of a $|1\rangle$).