# Can we somehow relate quantum volume with the total number of gates present in a circuit which the machine can succesfully run without large errors

Let's say I have a circuit which contains x number of gates and a machine with quantum volume y, Can I relate x and y somehow to determine if the circuit can be succesfully run on the machine without a lot of noise.

Quantum volume is a metric designed to quantify the performance and capabilities of a quantum computer. It encompasses various factors like gate fidelity, connectivity, coherence time, and others to provide a measure of the quantum computer's overall capability to run complex algorithms successfully.

Relating Quantum Volume with Circuit Gates:

While quantum volume inherently measures the maximum achievable circuit size (combination of width and depth) with low error rates, it doesn't directly equate to the total number of gates a machine can handle. Here’s why:

1. Error Rates and Noise:

The number of gates a quantum computer can execute is closely related to error rates and noise. If a quantum volume test identifies a certain circuit size that meets a predefined error threshold, this circuit size is indicative of the complexity the quantum computer can manage. This complexity correlates to the total number of gates, but it's not a direct measure.

2. Circuit Design and Structure:

Quantum volume circuits are designed to test a range of factors like entanglement, connectivity, and gate fidelity across all qubits. A machine might successfully execute many gates if they're simple or low-depth, but quantum volume considers more complex and high-depth circuits that test the boundaries of what the system can handle.

3. Empirical Nature:

Since quantum volume is determined empirically through a standardized process, it inherently accounts for factors like gate types, coherence times, crosstalk, and more. It’s an aggregate measure rather than an explicit count of the number of gates that can be executed.

In summary, quantum volume can offer an indication of a quantum computer's capacity to run circuits of a certain width and depth without large errors. However, this metric does not explicitly translate to the total number of gates. It provides a benchmark for evaluating quantum computer performance in terms of successful execution of a variety of complex quantum circuits, encompassing a broader scope than merely counting gates.