Editing Quantum Volume Estimation (section)

==Properties==

* '''Figure of merit''': Quantum Volume
* Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting tool chains are expected to have higher quantum volumes
* The protocol can be implemented with any universal programmable quantum computing device. Quantum volume is architecture-independent, and can be applied to any system that is capable of running quantum circuits.
* The method used to compute the heavy outputs from the ideal output distribution of the model circuit scales exponentially with the width <math>m</math>.
* Ideally, the probability of observing a heavy output would be estimated using all of the qubits of a large device, but NISQ devices have appreciable error rates, so we begin with small model circuits and progress to larger ones.
* The quantum volume treats the width and depth of a model circuit with equal importance and measures the largest square shaped (i.e., <math>m = d</math>) model circuit a quantum computer can implement successfully on average.
* Given a model circuit <math>U</math>, a circuit-to-circuit transpiler finds an implementation <math>U'</math> for the target system such that <math>1- F_{avg}(U, U') \leq \epsilon \ll 1</math>
* There are two possible paths for increasing the quantum volume, which is given by the numerical simulations for given connectivity. The first path is to prioritize improving the gate fidelity above other operations. This
sets the roadmap for device performance to focus on the errors that limit gate performance, such as coherence and
calibration errors. The second path stems from the observation that, for these devices and this metric, circuit
optimization is becoming important.