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Physical Review A

Simplified construction and physical realization of n -qubit controlled phase gates

Shi‐Biao Zheng

Published Jul 23, 2012• 16 citations
Publisher

Abstract

We show that with the assistance of a third level of qubits an $n$-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 $n$. 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.

DOI
10.1103/physreva.86.012326

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We show that with the assistance of a third level of qubits an nnn-qubit phase gate can be constructed from 2n\ensuremath−42n\ensuremath{-}42n\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 show that with the assistance of a third level of the qubits an n-qubit phase gate can be constructed from 2n−42n-42n−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 as compared with that required in the previous methods.
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 present a way to realize a multiplex-controlled phase gate of $n\ensuremath{-}1$ control qubits simultaneously controlling one target qubit, with nnn qubits distributed in nnn different cavities. This multiqubit gate is implemented by using nnn qutrits ( three-level natural or artificial atoms) placed in nnn different cavities, which are coupled to an auxiliary qutrit. Here, the two logic states of a qubit are represented by the two lowest levels of a qutrit placed in a cavity. We show that this nnn-qubit controlled phase gate can be realized using only 2n+22n+22n+2 basic operations, i.e., the number of required basic operations only increases linearly with the number nnn of qubits. Since each basic operation employs the qutrit-cavity or qutrit-pulse resonant interaction, the gate can be fast implemented when the number of qubits is not large. Numerical simulations show that a three-qubit controlled phase gate, which is executed on three qubits distributed in three different cavities, can be high-fidelity implemented by using a circuit QED system. This proposal is quite general and can be applied to a wide range of physical systems, with atoms, NV centers, quantum dots, or various superconducting qutrits distributed in different cavities. Finally, this method can be applied to implement a multiqubit controlled phase gate with atoms using a cavity. A detailed discussion on implementing a three-qubit controlled phase gate with atoms and one cavity is presented.
We propose a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit ( cqubit ) simultaneously controlling n –1 target cqubits . The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.
We show how a nonlocal N-qubit controlled unitary gate can be implemented locally and effectively by using non-symmetric quantum channels. We construct respectively two quantum networks for realizing conclusively this nonlocal quantum gate. The first one hires (N–2) symmetric qubit-qubit Bell states and a non-symmetric qubit-qudit Bell state as quantum channels. The basic idea of this scheme is to use (N–2) additional levels of this qudit to “hide” certain computational states of (N–1) nonlocal control states from the conditional dynamics, which results in an effective nonlocal N-qubit controlled unitary gate design. In this scheme, however, either the number of the additional levels or that of 1-qudit gates needs to increase with N. The other one can improve significantly the local implementation of this nonlocal gate if we harness (N–1) non-symmetric qubit-qutrit Bell states as quantum channels. This scheme uses respectively (N–1) qutrits’s additional levels to expose one and only one initial computational state of (N–1) nonlocal control states to the conditional dynamics. In comparison with the first one, the procedure is greatly simplified, and the total gate time is reduced. The fact that the quantum network that does the proposed implementation is built entirely of local single-body and two-body gates, and has only (3N–4) two-body gates is notable.
We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling n - 1 target microwave photonic qubits. This gate is implemented with n microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires only a single-step operation and thus the gate implementation is quite simple. The gate operation time is independent of the number of the qubits. In addition, this proposal does not need applying classical pulse or any measurement. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one microwave photonic qubit simultaneously controlling two target microwave photonic qubits is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a natural or artificial Λ-type three-level atom.