We propose a quantum feedback scheme for the preparation and protection of photon-number states of light trapped in a high-Q microwave cavity. A quantum nondemolition measurement of the cavity field ...provides information on the photon-number distribution. The feedback loop is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number. The efficiency and reliability of the closed-loop state stabilization is assessed by quantum Monte Carlo simulations. We show that, in realistic experimental conditions, the Fock states are efficiently produced and protected against decoherence.
A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, ...irreversibly corrupting the encoded information. We demonstrate a fault-tolerant error-detection scheme that suppresses spreading of ancilla errors by a factor of 5, while maintaining the assignment fidelity. The same method is used to prevent propagation of ancilla excitations, increasing the logical qubit dephasing time by an order of magnitude. Our approach is hardware-efficient, as it uses a single multilevel transmon ancilla and a cavity-encoded logical qubit, whose interaction is engineered in situ by using an off-resonant sideband drive. The results demonstrate that hardware-efficient approaches that exploit system-specific error models can yield advances toward fault-tolerant quantum computation.
Current implementations of quantum bits (qubits) continue to undergo too many errors to be scaled into useful quantum machines. An emerging strategy is to encode quantum information in the two ...meta-stable pointer states of an oscillator exchanging pairs of photons with its environment, a mechanism shown to provide stability without inducing decoherence. Adding photons in these states increases their separation, and macroscopic bit-flip times are expected even for a handful of photons, a range suitable to implement a qubit. However, previous experimental realizations have saturated in the millisecond range. In this work, we aim for the maximum bit-flip time we could achieve in a two-photon dissipative oscillator. To this end, we design a Josephson circuit in a regime that circumvents all suspected dynamical instabilities, and employ a minimally invasive fluorescence detection tool, at the cost of a two-photon exchange rate dominated by single-photon loss. We attain bit-flip times of the order of 100 seconds for states pinned by two-photon dissipation and containing about 40 photons. This experiment lays a solid foundation from which the two-photon exchange rate can be gradually increased, thus gaining access to the preparation and measurement of quantum superposition states, and pursuing the route towards a logical qubit with built-in bit-flip protection.
On stability of continuous-time quantum filters Amini, H.; Mirrahimi, M.; Rouchon, P.
2011 50th IEEE Conference on Decision and Control and European Control Conference,
2011-Dec.
Conference Proceeding
Odprti dostop
We prove that the fidelity between the quantum state governed by a continuous time stochastic master equation driven by a Wiener process and its associated quantum-filter state is a sub-martingale. ...This result is a generalization to non-pure quantum states where fidelity does not coincide in general with a simple Frobenius inner product. This result implies the stability of such filtering process but does not necessarily ensure the asymptotic convergence of such quantum-filters.
A Lyapunov-based approach for the trajectory generation of a Schrodinger equation is proposed. For the case of a quantum particle in a 3-dimensional finite potential well with an arbitrary shape the ...convergence is precisely analyzed. Similar assumptions to those formerly used for the finite dimensional configurations ensure the quasi-global approximate stabilization of the partial differential equation around an isolated eigenstate of the free system. Dispersive estimates of Strichartz type are widely used for the proof of the convergence result
We consider discrete-time quantum systems subject to Quantum Non-Demolition (QND) measurements and controlled by an adjustable unitary evolution between two successive QND measures. In open-loop, ...such QND measurements provide a non-deterministic preparation tool exploiting the back-action of the measurement on the quantum state. We propose here a systematic method based on elementary graph theory and inversion of Laplacian matrices to construct strict control-Lyapunov functions. This yields an appropriate feedback law that stabilizes globally the system towards a chosen target state among the open-loop stable ones, and that makes in closed-loop this preparation deterministic. We illustrate such feedback laws through simulations corresponding to an experimental setup with QND photon counting.
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depends on the quantity which is measured. In a partial measurement performed by an ideal ...apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrate this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures is observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.
Quantum bits are more robust to noise when they are encoded non-locally. In such an encoding, errors affecting the underlying physical system can then be detected and corrected before they corrupt ...the encoded information. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a qubit, which is delocalised in the phase-space of a single oscillator. However, implementing measurements that reveal error syndromes of the oscillator while preserving the encoded information has proved experimentally challenging: the only realisation so far relied on post-selection, which is incompatible with quantum error correction (QEC). The novelty of our experiment is precisely that it implements these non-destructive error-syndrome measurements for a superconducting microwave cavity. We design and implement an original feedback protocol that incorporates such measurements to prepare square and hexagonal GKP code states. We then demonstrate QEC of an encoded qubit with unprecedented suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous variable systems and, in contrast with previous implementations of QEC, can mitigate all logical errors generated by a wide variety of noise processes, and open a way towards fault-tolerant quantum computation.
Nonlinear processes in the quantum regime are essential for many applications, such as quantum-limited amplification, measurement and control of quantum systems. In particular, the field of quantum ...error correction relies heavily on high-order nonlinear interactions between various modes of a quantum system. However, the required order of nonlinearity is often not directly available or weak compared to dissipation present in the system. Here, we experimentally demonstrate a route to obtain higher-order nonlinearity by combining more easily available lower-order nonlinear processes, using a generalization of the Raman transition. In particular, we show a transformation of four photons of a high-Q superconducting resonator into two excitations of a superconducting transmon mode and vice versa. The resulting six-quanta process is obtained by cascading two fourth-order nonlinear processes through a virtual state. We expect this type of process to become a key component of hardware efficient quantum error correction using continuous-variable error correction codes.
We consider a non relativistic charged particle in a 1D infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It ...is represented by a complex probability amplitude, solution of a Schrödinger equation on a 1D bounded domain, with Dirichlet boundary conditions. We prove the almost global approximate stabilization of the eigenstates by explicit feedback laws.
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