32 research outputs found
Parameter estimation from measurements along quantum trajectories
The dynamics of many open quantum systems are described by stochastic master
equations. In the discrete-time case, we recall the structure of the derived
quantum filter governing the evolution of the density operator conditioned to
the measurement outcomes. We then describe the structure of the corresponding
particle quantum filters for estimating constant parameter and we prove their
stability. In the continuous-time (diffusive) case, we propose a new
formulation of these particle quantum filters. The interest of this new
formulation is first to prove stability, and also to provide an efficient
algorithm preserving, for any discretization step-size, positivity of the
quantum states and parameter classical probabilities. This algorithm is tested
on experimental data to estimate the detection efficiency for a superconducting
qubit whose fluorescence field is measured using a heterodyne detector.Comment: 8 pages, 3 figures, submitte
Stability and decoherence rates of a GKP qubit protected by dissipation
We analyze an experimentally accessible Lindblad master equation for a
quantum harmonic oscillator. It approximately stabilizes finite-energy periodic
grid states called Gottesman-Kitaev-Preskill (GKP) states, that can be used to
encode and protect a logical qubit. We give explicit upper bounds for the
energy of the solutions of the Lindblad master equation. Using three periodic
observables to define the Bloch sphere coordinates of a logical qubit, we show
that their dynamics is governed by a diffusion partial differential equation on
a 2D-torus with a Witten Laplacian. We show that the evolution of these logical
coordinates is exponentially slow even in presence of small diffusive noise
processes along the two quadratures of the phase space. Numerical simulations
indicate similar results for other physically relevant noise processes.Comment: 16 pages, 1 figure. This work has been accepted to IFAC for
publication under a Creative Commons Licence CC-BY-NC-N
Quantum state tomography with non-instantaneous measurements, imperfections and decoherence
Tomography of a quantum state is usually based on positive operator-valued
measure (POVM) and on their experimental statistics. Among the available
reconstructions, the maximum-likelihood (MaxLike) technique is an efficient
one. We propose an extension of this technique when the measurement process
cannot be simply described by an instantaneous POVM. Instead, the tomography
relies on a set of quantum trajectories and their measurement records. This
model includes the fact that, in practice, each measurement could be corrupted
by imperfections and decoherence, and could also be associated with the record
of continuous-time signals over a finite amount of time. The goal is then to
retrieve the quantum state that was present at the start of this measurement
process. The proposed extension relies on an explicit expression of the
likelihood function via the effective matrices appearing in quantum smoothing
and solutions of the adjoint quantum filter. It allows to retrieve the initial
quantum state as in standard MaxLike tomography, but where the traditional POVM
operators are replaced by more general ones that depend on the measurement
record of each trajectory. It also provides, aside the MaxLike estimate of the
quantum state, confidence intervals for any observable. Such confidence
intervals are derived, as the MaxLike estimate, from an asymptotic expansion of
multi-dimensional Laplace integrals appearing in Bayesian Mean estimation. A
validation is performed on two sets of experimental data: photon(s) trapped in
a microwave cavity subject to quantum non-demolition measurements relying on
Rydberg atoms; heterodyne fluorescence measurements of a superconducting qubit.Comment: 11 pages, 4 figures, submitte
Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator
Based on the stabilizer formalism underlying Quantum Error Correction (QEC),
the design of an original Lindblad master equation for the density operator of
a quantum harmonic oscillator is proposed. This Lindblad dynamics stabilizes
exactly the finite-energy grid states introduced in 2001 by Gottesman, Kitaev
and Preskill for quantum computation. Stabilization results from an exponential
Lyapunov function with an explicit lower-bound on the convergence rate.
Numerical simulations indicate the potential interest of such autonomous QEC in
presence of non-negligible photon-losses.Comment: Submitted, 15 pages, 1 figure
Persistent control of a superconducting qubit by stroboscopic measurement feedback
Making a system state follow a prescribed trajectory despite fluctuations and
errors commonly consists in monitoring an observable (temperature,
blood-glucose level...) and reacting on its controllers (heater power, insulin
amount ...). In the quantum domain, there is a change of paradigm in feedback
since measurements modify the state of the system, most dramatically when the
trajectory goes through superpositions of measurement eigenstates. Here, we
demonstrate the stabilization of an arbitrary trajectory of a superconducting
qubit by measurement based feedback. The protocol benefits from the long
coherence time (s) of the 3D transmon qubit, the high efficiency
(82%) of the phase preserving Josephson amplifier, and fast electronics
ensuring less than 500 ns delay. At discrete time intervals, the state of the
qubit is measured and corrected in case an error is detected. For Rabi
oscillations, where the discrete measurements occur when the qubit is supposed
to be in the measurement pointer states, we demonstrate an average fidelity of
85% to the targeted trajectory. For Ramsey oscillations, which does not go
through pointer states, the average fidelity reaches 75%. Incidentally, we
demonstrate a fast reset protocol allowing to cool a 3D transmon qubit down to
0.6% in the excited state.Comment: 7 pages, 3 figures and 1 table. Supplementary information available
as an ancilla fil
Quantum control of a cat-qubit with bit-flip times exceeding ten seconds
Binary classical information is routinely encoded in the two metastable
states of a dynamical system. Since these states may exhibit macroscopic
lifetimes, the encoded information inherits a strong protection against
bit-flips. A recent qubit - the cat-qubit - is encoded in the manifold of
metastable states of a quantum dynamical system, thereby acquiring bit-flip
protection. An outstanding challenge is to gain quantum control over such a
system without breaking its protection. If this challenge is met, significant
shortcuts in hardware overhead are forecast for quantum computing. In this
experiment, we implement a cat-qubit with bit-flip times exceeding ten seconds.
This is a four order of magnitude improvement over previous cat-qubit
implementations, and six orders of magnitude enhancement over the single photon
lifetime that compose this dynamical qubit. This was achieved by introducing a
quantum tomography protocol that does not break bit-flip protection. We prepare
and image quantum superposition states, and measure phase-flip times above 490
nanoseconds. Most importantly, we control the phase of these superpositions
while maintaining the bit-flip time above ten seconds. This work demonstrates
quantum operations that preserve macroscopic bit-flip times, a necessary step
to scale these dynamical qubits into fully protected hardware-efficient
architectures
Backaction et retour quantiques dans les circuits supraconducteurs
This thesis presents a series of experiments highlighting measurement back action and decoherence in a basic open quantum system, the superconducting qubit. These observations are enabled by recent advances in amplification close to the quantum limit using Josephson circuits. The information extracted from the system can then be used as input in quantum feedback. A stroboscopic projective readout is performed and a feedback loop is used to correct for detected errors, thus stabilizing an arbitrary predetermined state of the qubit. When monitoring continuously the environment of the qubit by heterodyne detection of its fluorescence, we reconstruct individual quantum trajectories during relaxation. Conditioning this detection to the outcome of a following projective measurement, we access the weak values of the fluorescence signal. Included in a continuous feedback loop, this detection is also used to stabilize an arbitrary state of the qubit. Finally, a last experiment witnesses quantum Zeno dynamics of a resonant microwave mode, entailed by its coupling to the qubit.Cette thĂšse dĂ©crit une sĂ©rie dâexpĂ©riences mettant en lumiĂšre lâaction en retour de la mesure et la dĂ©cohĂ©rence pour un systĂšme quantique ouvert Ă©lĂ©mentaire, le qubit supraconducteur. Ces observations sont rendues possibles grĂące au dĂ©veloppement rĂ©cent dâamplificateurs Josephson proches de la limite quantique. Lâinformation extraite du systĂšme peut ĂȘtre utilisĂ©e dans des boucles de rĂ©troaction quantique. Pour stabiliser un Ă©tat arbitraire prĂ©dĂ©terminĂ© du qubit, une mesure projective est rĂ©alisĂ©e pĂ©riodiquement et une boucle de rĂ©troaction permet de corriger les erreurs dĂ©tectĂ©es. En se substituant Ă l'environnement et en rĂ©alisant une mesure hĂ©tĂ©rodyne continue de la fluorescence du qubit, nous reconstituons des trajectoires quantiques individuelles lors de sa relaxation. En conditionnant cette dĂ©tection au rĂ©sultat d'une mesure projective postĂ©rieure, nous dĂ©terminons les weak values du signal de fluorescence. En formant une boucle de rĂ©troaction continue Ă partir de ce signal, nous stabilisons Ă©galement un Ă©tat arbitraire du qubit. Enfin, nous observons dans une derniĂšre expĂ©rience la dynamique quantique ZĂ©non d'un mode micro-onde, induite par son couplage au qubit
Action en retour de la mesure et rétroaction sur un circuit supraconducteur
This thesis presents a series of experiments highlighting measurement back action and decoherence in a basic open quantum system, the superconducting qubit. These observations are enabled by recent advances in amplification close to the quantum limit using Josephson circuits. The information extracted from the system can then be used as input in quantum feedback. A stroboscopic projective readout is performed and a feedback loop is used to correct for detected errors, thus stabilizing an arbitrary predetermined state of the qubit. When monitoring continuously the environment of the qubit by heterodyne detection of its fluorescence, we reconstruct individual quantum trajectories during relaxation. Conditioning this detection to the outcome of a following projective measurement, we access the weak values of the fluorescence signal. Included in a continuous feedback loop, this detection is also used to stabilize an arbitrary state of the qubit. Finally, a last experiment witnesses quantum Zeno dynamics of a resonant microwave mode, entailed by its coupling to the qubit.Cette thĂšse dĂ©crit une sĂ©rie dâexpĂ©riences mettant en lumiĂšre lâaction en retour de la mesure et la dĂ©cohĂ©rence pour un systĂšme quantique ouvert Ă©lĂ©mentaire, le qubit supraconducteur. Ces observations sont rendues possibles grĂące au dĂ©veloppement rĂ©cent dâamplificateurs Josephson proches de la limite quantique. Lâinformation extraite du systĂšme peut ĂȘtre utilisĂ©e dans des boucles de rĂ©troaction quantique.Pour stabiliser un Ă©tat arbitraire prĂ©dĂ©terminĂ© du qubit, une mesure projective est rĂ©alisĂ©e pĂ©riodiquement et une boucle de rĂ©troaction permet de corriger les erreurs dĂ©tectĂ©es. En se substituant Ă l'environnement et en rĂ©alisant une mesure hĂ©tĂ©rodyne continue de la fluorescence du qubit, nous reconstituons des trajectoires quantiques individuelles lors de sa relaxation. En conditionnant cette dĂ©tection au rĂ©sultat d'une mesure projective postĂ©rieure, nous dĂ©terminons les weak values du signal de fluorescence. En formant une boucle de rĂ©troaction continue Ă partir de ce signal, nous stabilisons Ă©galement un Ă©tat arbitraire du qubit. Enfin, nous observons dans une derniĂšre expĂ©rience la dynamique quantique ZĂ©non d'un mode micro-onde, induite par son couplage au qubit
Robust suppression of noise propagation in GKP error-correction
International audienceStraightforward logical operations contrasting with complex state preparation are the hallmarks of the bosonic encoding proposed by Gottesman, Kitaev and Preskill (GKP). The recently reported generation and error-correction of GKP qubits in trapped ions and superconducting circuits thus holds great promise for the future of quantum computing architectures based on such encoded qubits. However, these experiments rely on the measurement of error-syndromes via an ancillary two-level system (TLS), whose noise may propagate and corrupt the encoded qubit. We propose a simple module composed of two oscillators and a TLS, operated with two experimentally accessible quantum gates and elementary feedback controls to implement an error-corrected GKP qubit protected from such propagating errors. In the idealized setting of periodic GKP states, we develop efficient numerical methods to optimize our protocol parameters and show that errors of the encoded qubit stemming from flips of the TLS and diffusion of the oscillators state in phase-space may be exponentially suppressed as the noise strength over individual operations is decreased. Our approach circumvents the main roadblock towards fault-tolerant quantum computation with GKP qubits