We have shown via a careful error analysis that it is possible to do this deflation via a structure preserving real orthogonal or unitary transformation as well as with a Schur complement approach.
In the real case, the unitary transformations can be chosen to be real orthogonal, but to simplify, in the following when speaking of unitary transformations, we implicitly mean real orthogonal transformations in the case of real matrices.
The second unitary transformation is an inversion about average operation.
Calculations are carried out on vectors by quantum gates that apply unitary transformations to these vectors to produce other vectors.
When anyons move around each other along braided paths, the motion changes the pattern of the anyons' interactions with each other--a change physicists call a unitary transformation.
Different fluids have different unitary transformations and so carry out different calculations.
Although most of the unitary transformations
can only be implemented by approximation very inefficiently, that is the number of fault-tolerant gates is exponential in the number of qubits of the operator, it may be possible that some universal bases are more efficient than others to approximate some specific set of unitary operators.
Focusing mainly on the unitary transformations
, which the Fourier transform shares with other transforms that have been derived from it, they seek to help graduate students and engineers use new forms and methods of signals and images in the frequency domain, as well as in the so-called frequency-and-time domain.
Background appendices are included on mathematical concepts, quantum measurement, the harmonic oscillator, and unitary transformations
For the transformation from the Cartesian OXYZ into the O'X'Y'Z' the following unitary transformations
have been used:
Furthermore, all the computations are carried out using unitary transformations and, therefore, the algorithms are both fast and numerically robust.
n] into tridiagonal form by unitary transformations.