  The work proposes an extension of the quantum circuit formalism where qubits
(wires) are circular instead of linear. The left-to-right interpretation of a
quantum circuit is replaced by a circular representation which allows to select
the starting point and the direction in which gates are executed. The
representation supports all the circuits obtained after computing cyclic
permutations of an initial quantum gate list. Two circuits, where one has a
gate list which is a cyclic permutation of the other, will implement different
functions. The main question appears in the context of scalable quantum
computing, where multiple subcircuits are used for the construction of a larger
fault-tolerant one: can the same circular representation be used by multiple
subcircuits? The circular circuits are sufficient for constructing
computationally universal, fault-tolerant circuits formed entirely of qubit
initialisation, CNOT gates and qubit measurements. The main result of modelling
circular CNOT circuits is that a derived Boolean representation allows to
define a set of equations for $X$ and $Z$ stabiliser transformations. Through a
well defined set of steps it is possible to reduce the initial equations to a
set of stabiliser transformations given a series of cuts through the circular
circuit.
