Direct Randomized Benchmarking

Motivations

• A single gate of a Clifford group \(\mathbb{C}_n\) requires \(O(n^2 / \log(n))\) one and two-qubit gates, which leads to relatively deep circuits for a large number of qubits. Hence, CRB cannot be evaluated on a large number of qubits as the fidelity becomes vanishingly small.
• Provide the ability to benchmark custom gate sets other than the clifford group (e.g. the native gate set of a quantum computer).

Protocol

• A random n-qubit stabilizer state is created to form \(\rho_0\).
• Each gate is build from the user’s probability distribution \(\mu\) (e.g. each layer \(g_i\) having \(1/4\) probability of having a single CNOT, with the rest composed of random single-qubit rotations). The group should be able to generate gates of the \(\mathbb{C}_n\) Clifford group.
• The ending gate project the state of a random computational basis state.
• The success metric is the probability of observing the final bitstring \(b\). The success probability strongly depends on the distribution \(\mu\) and on the compiler. All these informations should be reported together.

Limitations

• Stabilizer initialization and measurement implementations still require \(O(n^2 / \log(n))\) gates.
• The protocol is not scalable as it requires to emulate the output of the quantum circuit to define the bitstring \(b\).

Litterature: [1], [2]

Implementations:

References

1. [1]T. J. Proctor, A. Carignan-Dugas, K. Rudinger, E. Nielsen, R. Blume-Kohout, and K. Young, “Direct randomized benchmarking for multiqubit devices,” Physical review letters, vol. 123, no. 3, p. 030503, 2019.
2. [2]A. M. Polloreno, A. Carignan-Dugas, J. Hines, R. Blume-Kohout, K. Young, and T. Proctor, “A theory of direct randomized benchmarking,” arXiv preprint arXiv:2302.13853, 2023.