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arXiv:quant-ph/0504188 · Physical Review A

n -qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator

Chui‐Ping Yang, Siyuan Han

Published Sep 9, 2005• 92 citations
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Abstract

We present a way to realize an $n$-qubit controlled phase gate with superconducting quantum-interference devices (SQUIDs) by coupling them to a superconducting resonator. In this proposal, the two logical states of a qubit are represented by the two lowest levels of a SQUID. An intermediate level of each SQUID is utilized to facilitate coherent control and manipulation of quantum states of the qubits. It is interesting to note that an $n$-qubit controlled phase gate can be achieved with $n$ SQUIDs by successively applying a $\ensuremath{\pi}∕2$ Jaynes-Cummings pulse to each of the $n\ensuremath{-}1$ control SQUIDs before and after a $\ensuremath{\pi}$ Jaynes-Cummings pulse on the target SQUID.

DOI
10.1103/physreva.72.032311

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We propose an approach to realize an nnn-qubit controlled-UUU gate with superconducting quantum interference devices (SQUIDs) in cavity QED. In this approach, the two lowest levels of a SQUID represent the two logical states of a qubit while a higher-energy intermediate level serves the gate manipulation. Our method operates essentially by creating a single photon through one of the control SQUIDs and then performing an arbitrary unitary transformation on the target SQUID with the assistance of the cavity photon. In addition, we show that the method can be applied to implement an nnn-qubit controlled-UUU gate with atomic qubits in cavity QED.
An alternative approach is proposed to realize an n -qubit Toffoli gate with superconducting quantum-interference devices (SQUIDs) in cavity quantum electrodynamics (QED). In the proposal, we represent two logical gates of a qubit with the two lowest levels of a SQUID while a higher-energy intermediate level of each SQUID is utilized for the gate manipulation. During the operating process, because the cavity field is always in vacuum state, the requirement on the cavity is greatly loosened and there is no transfer of quantum information between the cavity and SQUIDs.
We propose how to realize a multiqubit tunable phase gate of one qubit simultaneously controlling nnn qubits with four-level quantum systems in a cavity or coupled to a resonator. Each of the nnn two-qubit controlled-phase (cp) gates involved in this multiqubit phase gate has a shared control qubit but a different target qubit. In this proposal, 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 nnn 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.