157 research outputs found
Lyapunov Control on Quantum Open System in Decoherence-free Subspaces
A scheme to drive and manipulate a finite-dimensional quantum system in the
decoherence-free subspaces(DFS) by Lyapunov control is proposed. Control fields
are established by Lyapunov function. This proposal can drive the open quantum
system into the DFS and manipulate it to any desired eigenstate of the free
Hamiltonian. An example which consists of a four-level system with three
long-lived states driven by two lasers is presented to exemplify the scheme. We
have performed numerical simulations for the dynamics of the four-level system,
which show that the scheme works good.Comment: 5 pages, 6 figure
Observing quantum state diffusion by heterodyne detection of fluorescence
A qubit can relax by fluorescence, which prompts the release of a photon into
its electromagnetic environment. By counting the emitted photons, discrete
quantum jumps of the qubit state can be observed. The succession of states
occupied by the qubit in a single experiment, its quantum trajectory, depends
in fact on the kind of detector. How are the quantum trajectories modified if
one measures continuously the amplitude of the fluorescence field instead?
Using a superconducting parametric amplifier, we have performed heterodyne
detection of the fluorescence of a superconducting qubit. For each realization
of the measurement record, we can reconstruct a different quantum trajectory
for the qubit. The observed evolution obeys quantum state diffusion, which is
characteristic of quantum measurements subject to zero point fluctuations.
Independent projective measurements of the qubit at various times provide a
quantitative validation of the reconstructed trajectories. By exploring the
statistics of quantum trajectories, we demonstrate that the qubit states span a
deterministic surface in the Bloch sphere at each time in the evolution.
Additionally, we show that when monitoring fluorescence, coherent
superpositions are generated during the decay from excited to ground state.
Counterintuitively, measuring light emitted during relaxation can give rise to
trajectories with increased excitation probability.Comment: Supplementary material can be found in the ancillary sectio
Quantum feedback by discrete quantum non-demolition measurements: towards on-demand generation of photon-number states
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
non-demolition 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, Fock states are efficiently produced and
protected against decoherence.Comment: 8 pages, 5 figure
Single-photon Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-number States
Quantum states can be stabilized in the presence of intrinsic and
environmental losses by either applying active feedback conditioned on an
ancillary system or through reservoir engineering. Reservoir engineering
maintains a desired quantum state through a combination of drives and designed
entropy evacuation. We propose and implement a quantum reservoir engineering
protocol that stabilizes Fock states in a microwave cavity. This protocol is
realized with a circuit quantum electrodynamics platform where a Josephson
junction provides direct, nonlinear coupling between two superconducting
waveguide cavities. The nonlinear coupling results in a single photon resolved
cross-Kerr effect between the two cavities enabling a photon number dependent
coupling to a lossy environment. The quantum state of the microwave cavity is
discussed in terms of a net polarization and is analyzed by a measurement of
its steady state Wigner function.Comment: 8 pages, 6 figure
Explicit approximate controllability of the Schr\"odinger equation with a polarizability term
We consider a controlled Schr\"odinger equation with a dipolar and a
polarizability term, used when the dipolar approximation is not valid. The
control is the amplitude of the external electric field, it acts non linearly
on the state. We extend in this infinite dimensional framework previous
techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in
finite dimension. We consider a highly oscillating control and prove the
semi-global weak stabilization of the averaged system using a Lyapunov
function introduced by Nersesyan. Then it is proved that the solutions of the
Schr\"odinger equation and of the averaged equation stay close on every finite
time horizon provided that the control is oscillating enough. Combining these
two results, we get approximate controllability to the ground state for the
polarizability system
Stabilizing a Bell state of two superconducting qubits by dissipation engineering
We propose a dissipation engineering scheme that prepares and protects a
maximally entangled state of a pair of superconducting qubits. This is done by
off-resonantly coupling the two qubits to a low-Q cavity mode playing the role
of a dissipative reservoir. We engineer this coupling by applying six
continuous-wave microwave drives with appropriate frequencies. The two qubits
need not be identical. We show that our approach does not require any
fine-tuning of the parameters and requires only that certain ratios between
them be large. With currently achievable coherence times, simulations indicate
that a Bell state can be maintained over arbitrary long times with fidelities
above 94%. Such performance leads to a significant violation of Bell's
inequality (CHSH correlation larger than 2.6) for arbitrary long times.Comment: 5 pages, 4 figure
Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information
The remarkable discovery of Quantum Error Correction (QEC), which can
overcome the errors experienced by a bit of quantum information (qubit), was a
critical advance that gives hope for eventually realizing practical quantum
computers. In principle, a system that implements QEC can actually pass a
"break-even" point and preserve quantum information for longer than the
lifetime of its constituent parts. Reaching the break-even point, however, has
thus far remained an outstanding and challenging goal. Several previous works
have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers,
photons, and superconducting transmons. However, these works primarily
illustrate the signatures or scaling properties of QEC codes rather than test
the capacity of the system to extend the lifetime of quantum information over
time. Here we demonstrate a QEC system that reaches the break-even point by
suppressing the natural errors due to energy loss for a qubit logically encoded
in superpositions of coherent states, or cat states of a superconducting
resonator. Moreover, the experiment implements a full QEC protocol by using
real-time feedback to encode, monitor naturally occurring errors, decode, and
correct. As measured by full process tomography, the enhanced lifetime of the
encoded information is 320 microseconds without any post-selection. This is 20
times greater than that of the system's transmon, over twice as long as an
uncorrected logical encoding, and 10% longer than the highest quality element
of the system (the resonator's 0, 1 Fock states). Our results illustrate the
power of novel, hardware efficient qubit encodings over traditional QEC
schemes. Furthermore, they advance the field of experimental error correction
from confirming the basic concepts to exploring the metrics that drive system
performance and the challenges in implementing a fault-tolerant system
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