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arXiv:1608.04195 · Physical Review A

Heralded quantum controlled-phase gates with dissipative dynamics in macroscopically distant resonators

Wei Qin, Xin Wang, Adam Miranowicz, Zhi‐Rong Zhong, Franco Nori

Published Jul 11, 2017• 46 citations
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Abstract

Heralded near-deterministic multiqubit controlled-phase gates with integrated error detection have recently been proposed by Borregaard et al. [Phys. Rev. Lett. 114, 110502 (2015)]. This protocol is based on a single four-level atom (a heralding quartit) and $N$ three-level atoms (operational qutrits) coupled to a single-resonator mode acting as a cavity bus. Here we generalize this method for two distant resonators without the cavity bus between the heralding and operational atoms. Specifically, we analyze the two-qubit controlled-$Z$ gate and its multiqubit-controlled generalization (i.e., a Toffoli-like gate) acting on the two-lowest levels of $N$ qutrits inside one resonator, with their successful actions being heralded by an auxiliary microwave-driven quartit inside the other resonator. Moreover, we propose a circuit-quantum-electrodynamics realization of the protocol with flux and phase qudits in linearly coupled transmission-line resonators with dissipation. These methods offer a quadratic fidelity improvement compared to cavity-assisted deterministic gates.

DOI
10.1103/physreva.96.012315

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Heralded near-deterministic multiqubit controlled-phase gates with integrated error detection have recently been proposed by Borregaard et al. [Phys. Rev. Lett. 114, 110502 (2015)]. This protocol is based on a single four-level atom (a heralding quartit) and NNN three-level atoms (operational qutrits) coupled to a single-resonator mode acting as a cavity bus. Here we generalize this method for two distant resonators without the cavity bus between the heralding and operational atoms. Specifically, we analyze the two-qubit controlled-ZZZ gate and its multiqubit-controlled generalization (i.e., a Toffoli-like gate) acting on the two-lowest levels of NNN qutrits inside one resonator, with their successful actions being heralded by an auxiliary microwave-driven quartit inside the other resonator. Moreover, we propose a circuit-quantum-electrodynamics realization of the protocol with flux and phase qudits in linearly coupled transmission-line resonators with dissipation. These methods offer a quadratic fidelity improvement compared to cavity-assisted deterministic gates.
We propose and analyze heralded quantum gates between qubits in optical cavities. They employ an auxiliary qubit to report if a successful gate occurred. In this manner, the errors, which would have corrupted a deterministic gate, are converted into a nonunity probability of success: once successful, the gate has a much higher fidelity than a similar deterministic gate. Specifically, we describe that a heralded, near-deterministic controlled phase gate (CZ gate) with the conditional error arbitrarily close to zero and the success probability that approaches unity as the cooperativity of the system, C, becomes large. Furthermore, we describe an extension to near-deterministic N-qubit Toffoli gate with a favorable error scaling. These gates can be directly employed in quantum repeater networks to facilitate near-ideal entanglement swapping, thus greatly speeding up the entanglement distribution.
Cat-state qubits (qubits encoded with cat states) have recently drawn intensive attention due to their enhanced lifetimes with quantum error correction. We here propose a method to implement a universal controlled-phase gate of two cat-state qubits via two microwave resonators coupled to a superconducting transmon qutrit. During the gate operation, the qutrit remains in the ground state; thus decoherence from the qutrit is greatly suppressed. This proposal requires only two basic operations and neither classical pulse nor measurement is needed; therefore the gate realization is simple. Numerical simulations show that high-fidelity implementation of this gate is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate with two microwave resonators or two optical cavities coupled to a single three-level natural or artificial atom.
Hybrid qubits have recently drawn intense attention in quantum computing. We here propose a method to implement a universal controlled-phase gate of two hybrid qubits via two three-dimensional (3D) microwave cavities coupled to a superconducting flux qutrit. For the gate considered here, the control qubit is a microwave photonic qubit (particle-like qubit), whose two logic states are encoded by the vacuum state and the single-photon state of a cavity, while the target qubit is a cat-state qubit (wave-like qubit), whose two logic states are encoded by the two orthogonal cat states of the other cavity. During the gate operation, the qutrit remains in the ground state; therefore, decoherence from the qutrit is greatly suppressed. The gate realization is quite simple, because only a single basic operation is employed and neither classical pulse nor measurement is used. Our numerical simulations demonstrate that with current circuit quantum electrodynamics technology, this gate can be realized with a high fidelity. The generality of this proposal allows implementing the proposed gate in a wide range of physical systems, such as two 1D or 3D microwave or optical cavities coupled to a natural or artificial three-level atom. Finally, this proposal can be applied to create a novel entangled state between a particle-like photonic qubit and a wave-like cat-state qubit.
Based on a microwave-photon quantum processor with two superconducting resonators coupled to one transmon qutrit, we construct the controlled-phase (c-phase) gate on microwave-photon-resonator qudits, by combination of the photon-number-dependent frequency-shift effect on the transmon qutrit by the first resonator and the resonant operation between the qutrit and the second resonator. This distinct feature provides us a useful way to achieve the c-phase gate on the two resonator qudits with a higher fidelity and a shorter operation time, compared with the previous proposals. The fidelity of our c-phase gate can reach 99.5199.51%99.51 within 93 ns. Moreover, our device can be extended easily to construct the three-qudit gates on three resonator qudits, far different from the existing proposals. Our controlled-controlled-phase gate on three resonator qudits is accomplished with the assistance of a transmon qutrit and its fidelity can reach 92.9292.92%92.92 within 124.64 ns.
We present two protocols for realizing deterministic nonlocal multiqubit quantum gates on qubits coupled to a common cavity mode. The protocols rely only on a classical drive of the cavity mode, while no external drive of the qubits is required. Applied to just two qubits, both protocols provide a universal gate set for quantum computing, together with single-qubit gates. In the first protocol, the state of the cavity follows a closed trajectory in phase space and accumulates a geometric phase depending on the state of the qubits. This geometric phase gate can be used together with global single-qubit gates to generate high-fidelity Greenberger--Horne--Zeilinger (GHZ) states. The second protocol uses an adiabatic evolution of the combined qubit-cavity system to accumulate a dynamical phase. Repeated applications of this protocol allow for the realization of a family of phase gates with arbitrary phases, e.g., phase-rotation gates and multi-controlled-Z gates. For both protocols, we provide analytic solutions for the error rates, which scale as $\ensuremath{\sim}N/\sqrt{C}$ in the presence of relevant losses, with CCC the cooperativity and NNN the qubit number. Our protocols are applicable to a variety of systems and can be generalized by replacing the cavity by a different bosonic mode, such as a phononic mode. We provide estimates of gate fidelities and durations for atomic and molecular qubits as well as superconducting fluxonium qubits coupled to optical or microwave cavities, and we outline implications for quantum error correction.
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.