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Synthesizing arbitrary quantum states in a superconducting resonator

Abstract

The superposition principle is a fundamental tenet of quantum mechanics. It allows a quantum system to be ‘in two places at the same time’, because the quantum state of a physical system can simultaneously include measurably different physical states. The preparation and use of such superposed states forms the basis of quantum computation and simulation1. The creation of complex superpositions in harmonic systems (such as the motional state of trapped ions2, microwave resonators3,4,5 or optical cavities6) has presented a significant challenge because it cannot be achieved with classical control signals. Here we demonstrate the preparation and measurement of arbitrary quantum states in an electromagnetic resonator, superposing states with different numbers of photons in a completely controlled and deterministic manner. We synthesize the states using a superconducting phase qubit to phase-coherently pump photons into the resonator, making use of an algorithm7 that generalizes a previously demonstrated method of generating photon number (Fock) states in a resonator8. We completely characterize the resonator quantum state using Wigner tomography, which is equivalent to measuring the resonator’s full density matrix.

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Figure 1: Circuit diagram and one photon Rabi-swap oscillations between qubit and resonator.
Figure 2: Sequence to synthesize an arbitrary resonator state.
Figure 3: Wigner tomography of superpositions of resonator Fock states |0〉 + | N 〉.
Figure 4: Wigner tomography of the states |0〉 + e ik π/8 |3〉 + |6〉 for five values of phase k = 0 to 4.

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Acknowledgements

Devices were made at the UCSB Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network. We thank M. Geller for discussions. This work was supported by IARPA (grant W911NF-04-1-0204) and by the NSF (grant CCF-0507227).

Author Contributions M.H. performed the experiments and analysed the data. H.W. improved the resonator design and fabricated the sample. J.M.M. and E.L. designed the custom electronics and M.H. developed the calibrations for it. M.A. and M.N. provided software infrastructure. All authors contributed to the fabrication process, qubit design or experimental set-up. M.H., J.M.M. and A.N.C. conceived the experiment and co-wrote the paper.

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Correspondence to A. N. Cleland.

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Hofheinz, M., Wang, H., Ansmann, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009). https://doi.org/10.1038/nature08005

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