Divide-and-conquer verification method for noisy intermediate-scale quantum computation
Divide-and-conquer verification method for noisy intermediate-scale quantum computation
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DOI：
10.22331/q-2022-07-07-758
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发表时间：
2021-09
期刊：
影响因子：
6.4
通讯作者：
Yuki Takeuchi;Y. Takahashi;T. Morimae;S. Tani
中科院分区：
文献类型：
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作者：
Yuki Takeuchi;Y. Takahashi;T. Morimae;S. Tani
在一个稀疏量子计算芯片上，几个有噪声的中等规模的量子计算可以被视为对数深度量子电路，其中两个量子比特门只能直接应用于一些量子比特对。在本文中，我们提出了一种有效地验证这种有噪声的中等规模量子计算的方法。为此，我们首先刻画了关于钻石范数的小规模量子操作。然后利用这些刻画的量子运算，我们估计了⟨ψt|ρ^out|ψt⟩与理想输出态(即目标态)|ρtψ之间的保真度。虽然直接保真度估计方法平均需要O(2n)个ρ^Out副本，但即使在最坏的情况下，我们的方法也只需要O(D3212D)个副本，其中D是|ψt⟩的稠密性。对于稀疏芯片上的对数深度量子电路，D至多为O(Logn)，因此O(D3212D)是n中的多项式。我们还利用IBM Manila 5量子位芯片进行了原理证明实验，以观察该方法的实际性能。
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⟩ 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.