Divideandconquer verification method for noisy intermediatescale quantum computation
Abstract
Several noisy intermediatescale quantum computations can be regarded as logarithmicdepth quantum circuits on a sparse quantum computing chip, where twoqubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediatescale quantum computation. To this end, we first characterize smallscale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langle\psi_t\hat{\rho}_{\rm out}\psi_t\rangle$ between an actual $n$qubit output state $\hat{\rho}_{\rm out}$ obtained from the noisy intermediatescale quantum computation and the ideal output state (i.e., the target state) $\psi_t\rangle$. Although the direct fidelity estimation method requires $O(2^n)$ copies of $\hat{\rho}_{\rm out}$ on average, our method requires only $O(D^32^{12D})$ copies even in the worst case, where $D$ is the denseness of $\psi_t\rangle$. For logarithmicdepth quantum circuits on a sparse chip, $D$ is at most $O(\log{n})$, and thus $O(D^32^{12D})$ is a polynomial in $n$. By using the IBM Manila 5qubit chip, we also perform a proofofprinciple experiment to observe the practical performance of our method.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.14928
 Bibcode:
 2021arXiv210914928T
 Keywords:

 Quantum Physics
 EPrint:
 17 pages, 7 figures, v3: Added a proofofprinciple experiment (Sec. IV) and improved Sec. V, Accepted for publication in Quantum