12,571 research outputs found
High-order noise filtering in nontrivial quantum logic gates
Treating the effects of a time-dependent classical dephasing environment
during quantum logic operations poses a theoretical challenge, as the
application of non-commuting control operations gives rise to both dephasing
and depolarization errors that must be accounted for in order to understand
total average error rates. We develop a treatment based on effective
Hamiltonian theory that allows us to efficiently model the effect of classical
noise on nontrivial single-bit quantum logic operations composed of arbitrary
control sequences. We present a general method to calculate the
ensemble-averaged entanglement fidelity to arbitrary order in terms of noise
filter functions, and provide explicit expressions to fourth order in the noise
strength. In the weak noise limit we derive explicit filter functions for a
broad class of piecewise-constant control sequences, and use them to study the
performance of dynamically corrected gates, yielding good agreement with
brute-force numerics.Comment: Revised and expanded to include filter function terms beyond first
order in the Magnus expansion. Related manuscripts available from
http://www.physics.usyd.edu.au/~mbiercu
Approximate controllability of the Schr\"{o}dinger Equation with a polarizability term in higher Sobolev norms
This analysis is concerned with the controllability of quantum systems in the
case where the standard dipolar approximation, involving the permanent dipole
moment of the system, is corrected with a polarizability term, involving the
field induced dipole moment. Sufficient conditions for approximate
controllability are given. For transfers between eigenstates of the free
Hamiltonian, the control laws are explicitly given. The results apply also for
unbounded or non-regular potentials
Controllability of the discrete-spectrum Schrodinger equation driven by an external field
We prove approximate controllability of the bilinear Schr\"odinger equation
in the case in which the uncontrolled Hamiltonian has discrete non-resonant
spectrum. The results that are obtained apply both to bounded or unbounded
domains and to the case in which the control potential is bounded or unbounded.
The method relies on finite-dimensional techniques applied to the Galerkin
approximations and permits, in addition, to get some controllability properties
for the density matrix. Two examples are presented: the harmonic oscillator and
the 3D well of potential, both controlled by suitable potentials
Designing High-Fidelity Single-Shot Three-Qubit Gates: A Machine Learning Approach
Three-qubit quantum gates are key ingredients for quantum error correction
and quantum information processing. We generate quantum-control procedures to
design three types of three-qubit gates, namely Toffoli, Controlled-Not-Not and
Fredkin gates. The design procedures are applicable to a system comprising
three nearest-neighbor-coupled superconducting artificial atoms. For each
three-qubit gate, the numerical simulation of the proposed scheme achieves
99.9% fidelity, which is an accepted threshold fidelity for fault-tolerant
quantum computing. We test our procedure in the presence of decoherence-induced
noise as well as show its robustness against random external noise generated by
the control electronics. The three-qubit gates are designed via the machine
learning algorithm called Subspace-Selective Self-Adaptive Differential
Evolution (SuSSADE).Comment: 18 pages, 13 figures. Accepted for publication in Phys. Rev. Applie
Controllability of the bilinear Schr\"odinger equation with several controls and application to a 3D molecule
We show the approximate rotational controllability of a polar linear molecule
by means of three nonresonant linear polarized laser fields. The result is
based on a general approximate controllability result for the bilinear
Schr\"odinger equation, with wavefunction varying in the unit sphere of an
infinite-dimensional Hilbert space and with several control potentials, under
the assumption that the internal Hamiltonian has discrete spectrum
Periodic excitations of bilinear quantum systems
A well-known method of transferring the population of a quantum system from
an eigenspace of the free Hamiltonian to another is to use a periodic control
law with an angular frequency equal to the difference of the eigenvalues. For
finite dimensional quantum systems, the classical theory of averaging provides
a rigorous explanation of this experimentally validated result. This paper
extends this finite dimensional result, known as the Rotating Wave
Approximation, to infinite dimensional systems and provides explicit
convergence estimates.Comment: Available online
http://www.sciencedirect.com/science/article/pii/S000510981200286
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