May 27, 2025
Fault-tolerant compilation of quantum circuits using finite universal gate sets inherently leads to errors. For example, the Solovay-Kitaev algorithm can be used to decompose any single-qubit rotation into a sequence of H and T gates, which approximates the desired operation but introduces small unitary errors. When the decomposition accuracy is low, these unitary errors can bias the calculations. We develop a method which, in combination with Pauli twirling, enables unbiased estimation of expectation values of Hermitian observables. We analyze the conditions under which this technique can be effectively applied and demonstrate its utility in Hamiltonian simulation tasks involving large circuits.
The manuscript is now available on arXiv: https://arxiv.org/abs/2505.11486.