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Calculating unknown eigenvalues with a quantum algorithm



A quantum algorithm solves computational tasks using fewer physical resources than the best-known classical algorithm. Of most interest are those for which an exponential reduction is achieved. The key example is the phase estimation algorithm, which provides the quantum speedup in Shor's factoring algorithm and quantum simulation algorithms. To date, fully quantum experiments of this type have demonstrated only the read-out stage of quantum algorithms, but not the steps in which input data is read in and processed to calculate the final quantum state. Indeed, knowing the answer beforehand was essential. We present a photonic demonstration of a full quantum algorithm—the iterative phase estimation algorithm (IPEA)—without knowing the answer in advance. This result suggests practical applications of the phase estimation algorithm, including quantum simulations and quantum metrology in the near term, and factoring in the long term.

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Figure 1: The phase estimation algorithm.
Figure 2: Optical implementation of the phase estimation algorithm.
Figure 3: Phase estimation data for 12 different Us.
Figure 4: Using the phase estimation algorithm to generate the eigenstates of U.


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The authors thank P.J. Shadbolt for writing the quantum process tomography code and J.C.F. Matthews, A. Peruzzo, G.J. Pryde and P. Zhang for helpful discussions. This work was supported by the Engineering and Physical Sciences Research Council (EPSRC), the European Research Council (ERC), PHORBITECH, Quantum Interfaces, Sensors, and Communication based on Entanglement (QESSENCE) and the Centre for Nanoscience and Quantum Information (NSQI). J.O'B. acknowledges a Royal Society Wolfson Merit Award.

Author information




The theory was developed by X.-Q.Z. and T.C.R. The theory was mapped to the experimental circuit by X.-Q.Z., P.K., T.C.R. and J.O.B. Experiments were performed by X.-Q.Z. and P.K. Data were analysed by X.-Q.Z., P.K., T.C.R. and J.O.B. The manuscript was written by X.-Q.Z., P.K., T.C.R. and J.O.B. The project was supervised by X.-Q.Z. and J.O.B.

Corresponding author

Correspondence to Jeremy L. O'Brien.

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The authors declare no competing financial interests.

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Zhou, XQ., Kalasuwan, P., Ralph, T. et al. Calculating unknown eigenvalues with a quantum algorithm. Nature Photon 7, 223–228 (2013).

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