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Physical Review A

Simplified realization of two-qubit quantum phase gate with four-level systems in cavity QED

Chui‐Ping Yang, Shih‐I Chu, Siyuan Han

Published Oct 14, 2004• 44 citations
Publisher

Abstract

We propose a method for realizing two-qubit quantum phase gate with 4-level systems in cavity QED. In this proposal, the two logical states of a qubit are represented by the two lowest levels of each system, and two intermediate levels of each system are utilized to facilitate coherent control and manipulation of quantum states of the qubits. The present method does not involve cavity-photon population during the operation. In addition, we show that the gate can be achieved using only two-step operations.

DOI
10.1103/physreva.70.044303

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We propose a method for realizing two-qubit quantum phase gate with 4-level systems in cavity QED. In this proposal, the two logical states of a qubit are represented by the two lowest levels of each system, and two intermediate levels of each system are utilized to facilitate coherent control and manipulation of quantum states of the qubits. The present method does not involve cavity-photon population during the operation. In addition, we show that the gate can be achieved using only two-step operations.
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.
We propose a simple method for achieving a multiqubit phase gate of one qubit simultaneously controlling n target qubits, by using three-level quantum systems (i.e., qutrits) coupled to a cavity or resonator. The gate can be realized via one operational step, without need of classical pulses, and by a virtual photon process. Thus, the gate operation is greatly simplified and decoherence from the cavity decay is much reduced, when compared with previous proposals. In addition, the operation time is independent of the number of qubits and no adjustment of the qutrit level spacings or the cavity frequency is needed during the operation.
We propose a scheme for realization of three-qubit controlled-phase gate via passing two three-level atoms through a high-Q optical cavity in a cavity QED system. In the presented protocol, the two stable ground states of the atoms act as the two controlling qubits and the zero- and one-photon Fock states of the cavity-field form the target qubit, and no auxiliary state or any measurement is required. The numerical simulation shows that the gate fidelities remain at a high level under the influence of the atomic spontaneous emission, the decay of the cavity mode and deviation of the coupling strength. The experimental feasibility of our proposal is also discussed.
We show that with the assistance of a third level of qubits an nnn-qubit phase gate can be constructed from $2n\ensuremath{-}4$ two-qutrit conditional swap gates, a single qutrit-qubit controlled phase gate, and two single-qutrit operations. Unlike previous schemes, our scheme uses the auxiliary level to ``expose'' some state to the qutrit-qubit controlled phase gate, instead of using it to ``hide'' states from the conditional dynamics. Neither the number of the additional levels nor that of single-qutrit operations needs to increase with nnn. We propose a physical implementation of the required elementary gates in cavity QED and show that the total gate time may be greatly reduced compared with that required in previous methods.
We propose a scheme for realizing quantum three-qubit phase gate operation, in a three-mode cavity where the large detuned cavity-mode fields interact with the four-level artificial atom of an rf-SQUID in tripod-type configuration. In this scheme, the two lowest levels of the artificial atom represent the two logical states of the target qubit and two cavity-mode states are the control qubits, while the third cavity-mode field serves the gate manipulation. Since only the metastable lower levels are involved in the gate operations, the gate is insensitive to the decay rates of the artificial atom, which makes this scheme advantageous and it is important in view of decoherence.
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.