1,297 research outputs found
Quantum divide-and-conquer anchoring for separable non-negative matrix factorization
© 2018 International Joint Conferences on Artificial Intelligence. All right reserved. It is NP-complete to find non-negative factors W and H with fixed rank r from a non-negative matrix X by minimizing ||X − WHτ||2F. Although the separability assumption (all data points are in the conical hull of the extreme rows) enables polynomial-time algorithms, the computational cost is not affordable for big data. This paper investigates how the power of quantum computation can be capitalized to solve the non-negative matrix factorization with the separability assumption (SNMF) by devising a quantum algorithm based on the divide-and-conquer anchoring (DCA) scheme [Zhou et al., 2013]. The design of quantum DCA (QDCA) is challenging. In the divide step, the random projections in DCA is completed by a quantum algorithm for linear operations, which achieves the exponential speedup. We then devise a heuristic post-selection procedure which extracts the information of anchors stored in the quantum states efficiently. Under a plausible assumption, QDCA performs efficiently, achieves the quantum speedup, and is beneficial for high dimensional problems
Divide-and-conquer verification method for noisy intermediate-scale quantum computation
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 between an actual -qubit output state obtained from the noisy intermediate-scale quantum computation and the
ideal output state (i.e., the target state) . Although the
direct fidelity estimation method requires copies of on average, our method requires only copies even in the
worst case, where is the denseness of . For
logarithmic-depth quantum circuits on a sparse chip, is at most
, and thus is a polynomial in . By using the IBM
Manila 5-qubit chip, we also perform a proof-of-principle experiment to observe
the practical performance of our method.Comment: 17 pages, 7 figures, v3: Added a proof-of-principle experiment (Sec.
IV) and improved Sec. V, Accepted for publication in Quantu
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