28,791 research outputs found
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
Spatiotemporal Orthogonal Polynomial Approximation for Partial Differential Equations
Starting with some fundamental concepts, in this article we present the
essential aspects of spectral methods and their applications to the numerical
solution of Partial Differential Equations (PDEs). We start by using Lagrange
and Techbychef orthogonal polynomials for spatiotemporal approximation of PDEs
as a weighted sum of polynomials. We use collocation at some clustered grid
points to generate a system of equations to approximate the weights for the
polynomials. We finish the study by demonstrating approximate solutions of some
PDEs in one space dimension.Comment: 9 pages, 9 figure
Limitations of Passive Protection of Quantum Information
The ability to protect quantum information from the effect of noise is one of
the major goals of quantum information processing. In this article, we study
limitations on the asymptotic stability of quantum information stored in
passive N-qubit systems. We consider the effect of small imperfections in the
implementation of the protecting Hamiltonian in the form of perturbations or
weak coupling to a ground state environment. We prove that, regardless of the
protecting Hamiltonian, there exists a perturbed evolution that necessitates a
final error correcting step when the state of the memory is read. Such an error
correction step is shown to require a finite error threshold, the lack thereof
being exemplified by the 3D compass model. We go on to present explicit weak
Hamiltonian perturbations which destroy the logical information stored in the
2D toric code in a time O(log(N)).Comment: 17 pages and appendice
Density Matrix Renormalization Group for Dummies
We describe the Density Matrix Renormalization Group algorithms for time
dependent and time independent Hamiltonians. This paper is a brief but
comprehensive introduction to the subject for anyone willing to enter in the
field or write the program source code from scratch.Comment: 29 pages, 9 figures. Published version. An open source version of the
code can be found at http://qti.sns.it/dmrg/phome.htm
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