  We study n-qubit operation rules on (n+1)-sphere with the target to help
developing a (photon or other technique) based programmable quantum computer.
In the meanwhile, we derive the scaling limits (called reflecting Gaussian
random fields on a (n+1)-sphere) for n-qubit quantum computer based queueing
systems under two different heavy traffic regimes. The queueing systems are
with multiple classes of users and batch quantum random walks over the
$(n+1)$-sphere as arrival inputs. In the first regime, the qubit number $n$ is
fixed and the scaling is in terms of both time and space. Under this regime,
performance modeling during deriving the scaling limit in terms of balancing
the arrival and service rates under first-in first-out and work conserving
service policy is conducted. In the second regime, besides the time and space
scaling parameters, the qubit number $n$ itself is also considered as a varying
scaling parameter with the additional aim to find a suitable number of qubits
for the design of a quantum computer. This regime is in contrast to the
well-known Halfin-Whitt regime.
