Multi-qubit Clifford Randomized Benchmarking

Motivations

The primary motivation behind the development of multi-qubit Clifford Randomized Benchmarking was to generalize the single-qubit randomized benchmarking (RB) protocol to systems comprising multiple qubits. This extended protocol was introduced in 2010 by E. Magesan et al. [1].

Protocol

The protocol utilizes the multi-qubit Clifford group \(C_n\). For each sequence length \(l\), Clifford gates are uniformly and efficiently sampled from \(C_n\) [2]. The single and two-qubit gates depth of the resulting quantum circuit associated with each element in \(C_n\) grows as \(O(n^2 / \log(n))\). The inverse unitary \(R\) is efficiently computed from the sequence [3], and a final unitary \(P\) consists of a uniformly random Pauli gate. The success metric is the probability of observing the Identity. It is estimated for the different lengths \(l\) and used to fit the exponential decay function.

Quantum circuit associated to the multi-qubits clifford randomized benchmarking protocol

Limitations

One limitation identified by the community concerns the depth scaling associated with implementing each gate in the Clifford group \(C_n\). As the number of qubits increases, the implementation becomes increasingly challenging, and circuit fidelity tends to degrade rapidly in the presence of noise. The output fidelity of the quantum circuit also strongly depends on the compilation process used to map each Clifford gate to the gate set natively used by the quantum computer. Inefficiencies or suboptimal strategies in this step can significantly impact the benchmarking results.

References

  1. [1]E. Magesan, J. M. Gambetta, and J. Emerson, “Scalable and robust randomized benchmarking of quantum processes,” Physical review letters, vol. 106, no. 18, p. 180504, 2011.
  2. [2]R. Koenig and J. A. Smolin, “How to efficiently select an arbitrary Clifford group element,” Journal of Mathematical Physics, vol. 55, no. 12, Dec. 2014, doi: 10.1063/1.4903507. [Online]. Available at: http://dx.doi.org/10.1063/1.4903507
  3. [3]D. Gottesman, Stabilizer codes and quantum error correction. California Institute of Technology, 1997.

Page last modification: 2025-05-28 12:12 Multi-qubit Clifford Randomized Benchmarking

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