 
Summary: On the generation of sequential unitary gates from continuous time
Schršodinger equations driven by external fields
Claudio Altafini
SISSAISAS
International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy
In most of the proposals for quantum computers, a common feature is that the quantum circuits
are expected to be made of cascades of unitary transformations acting on the quantum states.
Such unitary gates are normally assumed to belong to a given discrete set of transformations.
However, arbitrary superposition of quantum states may be achieved by utilizing a fixed number of
transformations, each depending on a parameter. A framework is proposed to dynamically express
these parameters directly in terms of the control inputs entering into the continuous time forced
Schršodinger equation.
PACS numbers: 03.67.Lx, 03.65.Fd, 02.30.Mv, 02.30.Xy
I. INTRODUCTION
In quantum information, the "computing" with quantum states is accomplished by applying sequences of
discrete unitary gates, i.e. predetermined elements of the transformation group that acts on the state of the
quantum system and determines its dynamical properties. One could say that what in a different context
would be simply a parameterization of a group manifold, like a set of Euler angles, in the context of quantum
computing becomes the "hardware" basis for the construction of quantum circuits. This "mimicking" the
