![]() ![]() Observation of quantum interference between separated mechanical oscillator wave packets. Quantum harmonic oscillator state synthesis by reservoir engineering. Error analysis for encoding a qubit in an oscillator. WKB and Berry Phase 171–188 (Wiley-VCH, Berlin, 2005). Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion. C., Brickman, K.-A., Deslauriers, L., Lee, P. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Implementing a universal gate set on a logical qubit encoded in an oscillator. Mathematical Foundations of Quantum Mechanics (Princeton Univ. Hybrid discrete- and continuous-variable quantum information. Sequential modular position and momentum measurements of a trapped ion mechanical oscillator. Encoding qubits into oscillators with atomic ensembles and squeezed light. Encoding a qubit into a cavity mode in circuit QED using phase estimation. All-optical generation of states for “encoding a qubit in an oscillator”. Continuous variable encoding by ponderomotive interaction. Preparing encoded states in an oscillator. Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman–Kitaev–Preskill codes. Performance and structure of single-mode bosonic codes. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. New class of quantum error-correcting codes for a bosonic mode. Bosonic quantum codes for amplitude damping. The code states also have direct applications in quantum sensing, allowing simultaneous measurement of small displacements in both position and momentum 14, 15.Ĭhuang, I. This control method opens a route for exploring continuous variable error correction as well as hybrid quantum information schemes using both discrete and continuous variables 13. For Pauli gates we reach process fidelities of about 97 per cent, whereas for continuous rotations we use gate teleportation and achieve fidelities of approximately 89 per cent. Also, we demonstrate a universal logical single-qubit gate set, which we analyse using process tomography. We prepare and reconstruct logical states with an average squared fidelity of 87.3 ± 0.7 per cent. Here we demonstrate such an encoded qubit using a superposition of displaced squeezed states of the harmonic motion of a single trapped 40Ca + ion, controlling and measuring the mechanical oscillator through coupling to an ancillary internal-state qubit 12. Various proposals have been made for realizing approximations to such states, but these have thus far remained out of reach 7, 8, 9, 10, 11. In such a system, a powerful encoding has been devised based on periodically spaced superpositions of position eigenstates 4, 5, 6. Such encoded qubits are commonly based on arrays of many physical qubits, but can also be realized using a single higher-dimensional quantum system, such as a harmonic oscillator 1, 2, 3. The stable operation of quantum computers will rely on error correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. ![]()
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