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arXiv:2004.12008 · Physica Scripta

Dynamics and multiqubit entanglement in distant resonators

Muhammad Waseem, Muhammad Nehal Khan, Shahid Qamar

Published Apr 15, 2020• 2 citations
arXivHTMLPDF

Abstract

Abstract We consider the dynamics of the photon states in distant resonators coupled to a common bus resonator at different positions. The frequencies of distant resonators from a common bus resonator are equally detuned. These frequency detunings are kept larger than the coupling strengths of each resonator to the common bus resonator to satisfy the dispersive interaction regime. In the dispersive regime, we show that the time dynamics of the system evolve to an arbitrary W-type state in a single step at various interaction times. Our results show that a one-step generation of arbitrary W-type states can be achieved with high fidelity in a system of superconducting resonators.

DOI
10.1088/1402-4896/ab894f

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Abstract We consider the dynamics of the photon states in distant resonators coupled to a common bus resonator at different positions. The frequencies of distant resonators from a common bus resonator are equally detuned. These frequency detunings are kept larger than the coupling strengths of each resonator to the common bus resonator to satisfy the dispersive interaction regime. In the dispersive regime, we show that the time dynamics of the system evolve to an arbitrary W-type state in a single step at various interaction times. Our results show that a one-step generation of arbitrary W-type states can be achieved with high fidelity in a system of superconducting resonators.
We present a scalable quantum-bus-based device for generating the entanglement on microwave photons (MPs) in distant superconducting resonators (SRs). Different from the processors in previous works with some resonators coupled to a superconducting qubit (SQ), our device is composed of some 1D SRs rjr_jrj​ which are coupled to the quantum bus (another common resonator RRR) in its different positions simply, assisted by superconducting quantum interferometer devices. By using the technique for catching and releasing a MP state in a 1D SR, it can work as an entanglement generator or a node in quantum communication. To demonstrate the performance of this device, we propose a one-step scheme to generate high-fidelity Bell states on MPs in two distant SRs. It works in the dispersive regime of rjr_jrj​ and RRR, which enables us to extend it to generate high-fidelity multi-Bell states on different resonator pairs simultaneously.
Superconducting circuits consisting of a few low-anharmonic transmons coupled to readout and bus resonators can perform basic quantum computations. Since the number of qubits in such circuits is limited to not more than a few tens, the qubits can be designed to operate within the dispersive regime where frequency detunings are much stronger than coupling strengths. However, scaling up the number of qubits will bring the circuit out of the regime, and this invalidates current theories. We develop a formalism that allows to consistently diagonalize the superconducting circuit Hamiltonian beyond the dispersive regime. This will allow to study qubit-qubit interaction unperturbatively, therefore, our formalism remains valid and accurate at small or even negligible frequency detuning; thus, our formalism serves as a theoretical ground for designing qubit characteristics for scaling up the number of qubits in superconducting circuits. We study the most important circuits with single- and two-qubit gates, i.e., a single transmon coupled to a resonator and two transmons sharing a bus resonator. Surprisingly, our formalism allows to determine the circuit characteristics, such as dressed frequencies and Kerr couplings, in closed-form formulas that not only reproduce perturbative results, but also extrapolate beyond the dispersive regime and can ultimately reproduce (and even modify) the Jaynes-Cumming results at resonant frequencies.
We propose a one-step scheme for implementing multi-qubit phase gates on microwave photons in multiple resonators mediated by a superconducting bus in circuit quantum electrodynamics (QED) system. In the scheme, multiple single-mode resonators carry quantum information with their vacuum and single-photon Fock states, and a multi-level artificial atom acts as a quantum bus which induces the indirect interaction among resonators. The method of pulse engineering is used to shape the coupling strength between resonators and the bus so as to improve the fidelity and robustness of the scheme. We also discuss the influence of finite coherence time for the bus and resonators on gate fidelity respectively. Finally, we consider the suppression of unwanted transitions and propose the method of optimized detuning compensation for offsetting unwanted transitions, showing the feasibility of the scheme within the current experiment technology.
We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic XYXYXY interaction. This impacts on the entanglement characteristics of the qubits.
We describe a simple, practical scheme for generating multi-qubit W states in resonator-based architectures, in which N Josephson phase qubits are capacitively coupled to a common resonator bus. The entire control sequence consists of three pulses: a local Rabi pulse that excites a single qubit in the circuit; a coupling pulse that transfers the qubit excitation to the resonator bus; and the main, entangling operation that simultaneously couples the bus to all N qubits. If the qubit-resonator coupling strength g is much smaller than the qubit energy splitting, the system initially excited into the near-degenerate single-excitation subspace stays within that subspace, while smoothly evolving toward the fully uniform W state superposition. The duration of the final entangling operation is found to decrease with the total number of the qubits according to t = pi/[2gN^(1/2)], in agreement with some of the previously proposed cavity QED W state generation schemes.
A critical element towards the realization of scalable quantum processors is nonlocal coupling between nodes. Scaling connectivity beyond nearest-neighbor interactions requires the implementation of a mediating interaction often termed a quantum bus. Cavity photons have long been used as a bus by the superconducting qubit community, but it has only recently been demonstrated that spin-based qubits in double quantum dot architectures can reach the strong coupling regime and exhibit spin-spin interactions via the exchange of real or virtual photons. Two-qubit gate operations are predicted in the dispersive regime where cavity loss plays a less prominent role. In this work we combine a cross-resonance entangling drive with simultaneous local rotations to propose a framework for a resonant direct-cnot operation, between two nonlocal single-spin qubits dispersively coupled to a common mode of a superconducting resonator. We expect gate times near 100 ns and fidelities above 90% with existing technology.