Multiqubit tunable phase gate of one qubit simultaneously controlling
$n$ qubits in a cavity

Chui-Ping Yang, Shi-Biao Zheng, Franco Nori

Published:

We propose how to realize a multiqubit tunable phase gate of one qubit
simultaneously controlling $n$ qubits with four-level quantum systems in a
cavity or coupled to a resonator. Each of the $n$ two-qubit controlled-phase
(CP) gates involved in this multiqubit phase gate has a shared control qubit
but a {\it different} target qubit. In this propose, the two lowest levels of
each system represent the two logical states of a qubit while the two
higher-energy intermediate levels are used for the gate implementation. The
method presented here operates essentially by creating a single photon through
the control qubit, which then induces a phase shift to the state of each target
qubit. The phase shifts on each target qubit can be adjusted by changing the
Rabi frequencies of the pulses applied to the target qubit systems. The
operation time for the gate implementation is independent of the number of
qubits, and neither adjustment of the qubit level spacings nor adjustment of
the cavity mode frequency during the gate operation is required by this
proposal. It is also noted that this approach can be applied to implement
certain types of significant multiqubit phase gates, e.g., the multiqubit phase
gate consisting of $n$ two-qubit CP gates which are key elements in quantum
Fourier transforms. A possible physical implementation of our approach is
presented. Our proposal is quite general, and can be applied to physical
systems such as various types of superconducting devices coupled to a resonator
and trapped atoms in a cavity.