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arXiv:1212.3059 · Progress of Theoretical and Experimental Physics

Realizing an n-target-qubit controlled-phase gate in cavity QED: An approach without classical pulses

Qi-Ping Su, Man Liu, Chui-Ping Yang

Published Feb 1, 2013• 0 citations
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Abstract

We propose a way to realize a multiqubit controlled-phase gate with one qubit simultaneously controlling n target qubits using atoms in cavity QED. In this proposal, there is no need to use classical pulses during the entire gate operation. The gate operation time scales as |$\sqrt {n}$| only and thus the gate can be performed faster when compared with sending atoms through the cavity one at a time. In addition, only three operational steps are required to realize this n-target-qubit controlled-phase gate. This proposal is quite general and can be applied to other physical systems, such as various superconducting qubits coupled to a resonator, NV centers coupled to a microsphere cavity, or quantum dots in cavity QED.

DOI
10.1093/ptep/pts092

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We propose a way to realize a multiqubit controlled-phase gate with one qubit simultaneously controlling n target qubits using atoms in cavity QED. In this proposal, there is no need to use classical pulses during the entire gate operation. The gate operation time scales as |n\sqrt {n}n​| only and thus the gate can be performed faster when compared with sending atoms through the cavity one at a time. In addition, only three operational steps are required to realize this n-target-qubit controlled-phase gate. This proposal is quite general and can be applied to other physical systems, such as various superconducting qubits coupled to a resonator, NV centers coupled to a microsphere cavity, or quantum dots in cavity QED.
We propose a way to realize a multiqubit tunable phase gate of one qubit simultaneously controlling nnn target qubits with atoms in cavity QED. In this proposal, classical pulses interact with atoms outside a cavity only, thus the experimental challenge of applying a pulse to an intracavity single atom without affecting other atoms in the same cavity is avoided. Because of employing a first-order large detuning, the gate can be performed fast when compared with the use of a second-order large detuning. Furthermore, the gate operation time is independent of the number of qubits. This proposal is quite general and can be applied to various superconducting qubits coupled to a resonator, nitrogen-vacancy centers coupled to a microsphere cavity, or quantum dots in cavity QED.
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 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 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.
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 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.