Noisy gates and gate fidelities

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 to perform operations like superposition and entanglement. However, in current quantum computers those gate operations are still prone to error. One type of error that can occur is the to think of noise affects our quantum circuits in a way...

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Explore apply one gate first and see how it Apply a sequence of gates that will lead you to a well known state (e.g. apply a long sequence of X gates that will lead you to either end up in north or south pole)

Each operation introduces a slight error. So the more operations, the more polluted the overall outcome becomes overrotation. Also, the more operations we need to perform on our qubits the harder it is to see the actual output.

Gate errors occur when errors are introduced during the application of quantum gates, which are the basic building blocks of quantum circuits. These errors can occur due to imperfections in the physical hardware, such as imprecise control over the qubits or external noise affecting the gates. These errors can cause the qubits' state to move to an unexpected position on the Bloch sphere, leading to errors in calculations. With imperfect gates, the more operations that are applied within a circuit, the less accurate the overall result gets. The accuracy of a single gate is typically express 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. 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 performance of quantum hardware, as it directly affects the reliability of quantum computations.

Errors during measurement

Errors can also occur while reading out the state of a qubit. Such readout errors will cause the measurement result to flip (e.g. reading out a \(\ket{0}\) instead of a \(\ket{1}\)). This can happen due to the physical limitations of the measurement devices or due to external noise interfering during measurement.

Decoherence

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Prepare the qubit below in the \(\ket{1}\) state by applying an X gate and wait.

energy decay

What best describes your observation?

Imperfect operations are one source for errors. However, noise within a quantum computer can come from various sources, such as the environment, imperfect hardware components, and even the way the algorithm is executed. The natural process that occurs as qubits interact with their environment is called decoherence. Essentially, when a qubit is measured or interacts with other particles, its state becomes entangled with the state of those other particles, leading to a loss of coherence. This can cause the qubit to deviate from its expected position on the Bloch sphere. This can lead to unprecise or unexpected results.

Understanding the different sources of noise is crucial for mitigating errors and developing more powerful and reliable quantum computers. The different sources of noise can combine and interact in complex ways, making it difficult to eliminate noise entirely in current quantum computing hardware. As a result, researchers are developing techniques to mitigate the effects of noise and improve the reliability of quantum computations.

In future chapters you will be able to explore ways to model, understand and circumvent these kinds of errors.