# Gate Fidelity

Gate Fidelity

The term gate fidelity in quantum computing usually refers to the accuracy of quantum operations. In other words, it is a measure of how close an operation gets during execution to the operation it is intended to do. When a quantum gate operation is applied, there is a calculated ideal result, as well as an actual result from real hardware. The fidelity, therefore, is a measure of how close those two results are.

If the target quantum computer does not provide the average gate fidelity as a metric, the process of modeling gate fidelity can be simplified as:

1. Prepare a quantum state.
2. Apply the selected quantum gate to that quantum state.
3. Mathematically, or with a simulator, calculate the ideal result.
4. Use the target quantum computer to calculate the actual result.
5. Use the ideal result and the actual result to calculate the fidelity.

It is worth noting that practical quantum computing is going to require extremely high gate fidelities. They will need to be comparable to what is expected – and taken for granted – from classical computers. The low fidelities of today’s hardware contribute to the significance of ongoing research into Quantum Error Correction (QEC) and fault tolerance.

## What is Gate Fidelity?

As is the case with all things “quantum,” there is no standardized definition of the term “gate fidelity.” Therefore, there are variations of the definition that do not directly refer to accuracy.

One alternate definition, for example, involves distinguishability. For example, the resultant quantum states could be labeled F = 1, which means that they are identical, or they could be labeled F = 0, which means that they can be distinguished perfectly. The best possible result, of course, would be F = 1, indicating that the actual result is identical to the ideal result.

Some of the answers to a Stack Exchange Quantum Computing question “What does quantum gate fidelity mean?” suggest another variation of the definition. Instead of calculating an ideal result at all, two identical quantum states would be prepared, and then the same gate operation would be applied to both. Instead of showing the accuracy of the operation, therefore, comparing the results of both operations would demonstrate the consistency of applying the gate. The fidelity, in that sense, would be a measure of the gate’s deviation.

A question on EntangledQuery asks “How to Understand Gate Fidelity,” and has answers comparable to if the question had been asked on Stack Exchange. One answer, in particular, is worth noting, as it includes the mathematics of calculating fidelity, however it is defined. The answerer, JackSong, included references for the answer.

## Challenges in Achieving High Gate Fidelity

Achieving a high gate fidelity in quantum computing is a considerable engineering challenge. There are several factors that could negatively affect gate fidelity, including:

• Implementing the gates, whether with laser pulses or microwave pulses or by other means, could simply be flawed somewhere.
• The control systems, and the classical logic that governs them, could introduce errors into the compilation process, resulting in improperly configured pulses.
• The target qubits could be negatively affected by unwanted interactions with neighboring qubits or by operations being performed on those neighboring qubits.
• One or both target qubits, if manufactured, could be particularly error prone and suffer errors even in the absence of gate operations.

Even if a gate operation could be implemented perfectly, and even if the issues above wouldn’t affect the target qubit(s), environmental noise could still be responsible for introducing errors. So, the operation itself wouldn’t be directly responsible for the error, but the average gate fidelity would still suffer. That’s quite a challenge.

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