Quantum Volume in Action

What does QV really mean?

I’m working on a three-qubit circuit for a paper, so I can’t show the actual circuit just yet, but the key information about it is that all three qubits are connected. Two-qubit CNOT operations are performed between the first and second qubits, the first and third qubits, and the second and third qubits. Look at qubits 0, 1, and 2 in the connectivity diagram above, as well as qubits 2, 3, and 4. That’s what I need.

Introduction

On a quantum computing simulator, connectivity is no problem; every qubit is magically connected to every other qubit. On real hardware however, this is far from the case. If two qubits need to be connected that are not connected, their quantum states need to be moved around via SWAP operations until their states are on connected qubits.

If you want to perform a CNOT operation on qubits 0 and 3 in the above connectivity diagram, for example, either qubits 0 and 2 need to be swapped or qubits 2 and 3 need to be swapped. The SWAP operation, however, depending on how physically far apart two qubits are, requires a minimum of three CNOT operations.

And there’s the problem. Single-qubit operations introduce errors; that’s beyond the scope of this article. CNOTs introduce even more errors; that’s also beyond the scope of this article. And, SWAP operations, therefore, introduce at least three CNOTs' worth of errors. Keep in mind that three CNOTs is the absolute minimum required per SWAP, and that…