Divide-and-conquer verification method for noisy intermediate-scale quantum computation · arXivDesk
2109.14928Sep 30, 202117 pages, 7 figures, v3: Added a proof-of-principle experiment (Sec. IV) and improved Sec. V, Accepted for publication in Quantum
Divide-and-conquer verification method for noisy intermediate-scale quantum computation
Yuki Takeuchi, Yasuhiro Takahashi, Tomoyuki Morimae, Seiichiro Tani
Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity ⟨ψt∣ρ^out∣ψt⟩
Nearby in the stack
between an actual
n
-qubit output state
ρ^out
obtained from the noisy intermediate-scale quantum computation and the ideal output state (i.e., the target state)
∣ψt⟩
. Although the direct fidelity estimation method requires
O(2n)
copies of
ρ^out
on average, our method requires only
O(D3212D)
copies even in the worst case, where
D
is the denseness of
∣ψt⟩
. For logarithmic-depth quantum circuits on a sparse chip,
D
is at most
O(logn)
, and thus
O(D3212D)
is a polynomial in
n
. By using the IBM Manila 5-qubit chip, we also perform a proof-of-principle experiment to observe the practical performance of our method.