1,498 research outputs found
Quantum Circuits for General Multiqubit Gates
We consider a generic elementary gate sequence which is needed to implement a
general quantum gate acting on n qubits -- a unitary transformation with 4^n
degrees of freedom. For synthesizing the gate sequence, a method based on the
so-called cosine-sine matrix decomposition is presented. The result is optimal
in the number of elementary one-qubit gates, 4^n, and scales more favorably
than the previously reported decompositions requiring 4^n-2^n+1 controlled NOT
gates.Comment: 4 pages, 3 figure
A Birkhoff connection between quantum circuits and linear classical reversible circuits
Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers
Nearest-Neighbor Interaction Systems in the Tensor-Train Format
Low-rank tensor approximation approaches have become an important tool in the
scientific computing community. The aim is to enable the simulation and
analysis of high-dimensional problems which cannot be solved using conventional
methods anymore due to the so-called curse of dimensionality. This requires
techniques to handle linear operators defined on extremely large state spaces
and to solve the resulting systems of linear equations or eigenvalue problems.
In this paper, we present a systematic tensor-train decomposition for
nearest-neighbor interaction systems which is applicable to a host of different
problems. With the aid of this decomposition, it is possible to reduce the
memory consumption as well as the computational costs significantly.
Furthermore, it can be shown that in some cases the rank of the tensor
decomposition does not depend on the network size. The format is thus feasible
even for high-dimensional systems. We will illustrate the results with several
guiding examples such as the Ising model, a system of coupled oscillators, and
a CO oxidation model
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