11 research outputs found
Effects of dynamical phases in Shor's factoring algorithm with operational delays
Ideal quantum algorithms usually assume that quantum computing is performed
continuously by a sequence of unitary transformations. However, there always
exist idle finite time intervals between consecutive operations in a realistic
quantum computing process. During these delays, coherent "errors" will
accumulate from the dynamical phases of the superposed wave functions. Here we
explore the sensitivity of Shor's quantum factoring algorithm to such errors.
Our results clearly show a severe sensitivity of Shor's factorization algorithm
to the presence of delay times between successive unitary transformations.
Specifically, in the presence of these {\it coherent "errors"}, the probability
of obtaining the correct answer decreases exponentially with the number of
qubits of the work register. A particularly simple phase-matching approach is
proposed in this paper to {\it avoid} or suppress these {\it coherent errors}
when using Shor's algorithm to factorize integers. The robustness of this
phase-matching condition is evaluated analytically or numerically for the
factorization of several integers: , and 33.Comment: 8 pages with 5 figure
Error Avoiding Quantum Codes and Dynamical Stabilization of Grover's Algorithm
An error avoiding quantum code is presented which is capable of stabilizing
Grover's quantum search algorithm against a particular class of coherent
errors. This error avoiding code consists of states only which are factorizable
in the computational basis. Furthermore, its redundancy is smaller than the one
which is achievable with a general error correcting quantum code saturating the
quantum Hamming bound. The fact that this code consists of factorizable states
only may offer advantages for the implementation of quantum gates in the error
free subspace
Stabilizing distinguishable qubits against spontaneous decay by detected-jump correcting quantum codes
A new class of error-correcting quantum codes is introduced capable of
stabilizing qubits against spontaneous decay arising from couplings to
statistically independent reservoirs. These quantum codes are based on the idea
of using an embedded quantum code and exploiting the classical information
available about which qubit has been affected by the environment. They are
immediately relevant for quantum computation and information processing using
arrays of trapped ions or nuclear spins. Interesting relations between these
quantum codes and basic notions of design theory are established
Detected-jump-error correcting quantum codes, quantum error designs and quantum computation
The recently introduced detected-jump-correcting quantum codes are capable of stabilizing qubit systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit classical information about which qubit has emitted spontaneously and correspond to an active error-correcting code embedded in a passive error-correcting code. The construction of a family of one-detected-jump-error-correcting quantum codes is shown and the optimal redundancy, encoding, and recovery as well as general properties of detected-jump-error-correcting quantum codes are discussed. By the use of design theory, multiple-jump-error-correcting quantum codes can be constructed. The performance of one-jump-error-correcting quantum codes under nonideal conditions is studied numerically by simulating a quantum memory and Grover’s algorithm.10 page(s