01870nas a2200181   4500000000100000000000100001008004100002100002000043700001400063700001600077700002200093700001800115700002200133245008900155856003700244490000800281520139900289       2022                            d1 aLudmila Botelho1 aAdam Glos1 aAkash Kundu1 aJaroslaw Miszczak1 aÖzlem Salehi1 aZoltán Zimborás00aError mitigation for variational quantum algorithms through mid-circuit measurements  uhttps://arxiv.org/abs/2108.109270 v1053 a<p>Noisy intermediate-scale quantum algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memory-consuming techniques for current quantum devices having at most hundreds or thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and W states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbert space. With this preknowledge, some errors can be detected during the evolution of the circuit, by filtering the states not obeying the pattern through postselection. In this paper, we present mid-circuit postselection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding. For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits. We demonstrate the effectiveness of the approach for the quantum alternating operator ansatz algorithm. Our method is particularly suitable for the currently available hardware, where measuring and resetting are possible, but classical conditional operators are not.</p>