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arXiv:2303.12111 · Physical Review A

Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array

Yunzhao Wang, Kyrylo Snizhko, Alessandro Romito, Yuval Gefen, Kater W. Murch

Published Jul 28, 2023• 26 citations
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Abstract

We present and analyze a protocol for driven-dissipatively preparing and stabilizing a manifold of quantum many-body entangled states with symmetry-protected topological order. Specifically, we consider the experimental platform consisting of superconducting transmon circuits and linear microwave resonators. We perform theoretical modeling of this platform via pulse-level simulations based on physical features of real devices. In our protocol, transmon qutrits are mapped onto spin-1 systems. The qutrits' sharing of nearest-neighbor dispersive coupling to a dissipative microwave resonator enables elimination of state population in the ${S}^{\mathrm{total}}=2$ subspace for each adjacent pair, and thus, the stabilization of the many-body system into the Affleck, Kennedy, Lieb, and Tasaki state up to the edge mode configuration. We also analyze the performance of our protocol as the system size scales up to four qutrits, in terms of its fidelity as well as the stabilization time. Our work shows the capacity of driven-dissipative superconducting cQED systems to host robust and self-corrected quantum many-body states that are topologically nontrivial.

DOI
10.1103/physreva.108.013712

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Quantum reservoir engineering is a powerful framework for autonomous quantum state preparation and error correction. However, traditional approaches to reservoir engineering are hindered by unavoidable coherent leakage out of the target state, which imposes an inherent trade off between achievable steady-state state fidelity and stabilization rate. In this work we demonstrate a protocol that achieves trade off-free Bell state stabilization in a qutrit-qubit system realized on a circuit-QED platform. We accomplish this by creating a purely dissipative channel for population transfer into the target state, mediated by strong parametric interactions coupling the second-excited state of a superconducting transmon and the engineered bath resonator. Our scheme achieves a state preparation fidelity of 84% with a stabilization time constant of 339 ns, leading to a 54 ns error-time product in a solid-state quantum information platform.
We propose and analyze a method for efficient dissipative preparation of matrix product states that exploits their symmetry properties. Specifically, we construct an explicit protocol that makes use of driven-dissipative dynamics to prepare a many-body quantum state that features symmetry-protected topological order and nontrivial edge excitations. The preparation protocol is protected from errors that respect the symmetry, allowing for robust experimental implementation without fine-tuned control. Numerical simulations show that the preparation time scales polynomially in system size nnn. Furthermore, we demonstrate that this scaling can be improved to O(log2n)O({log}^{2}n)O(log2n) by using parallel preparation of individual segments and fusing them via quantum feedback. A concrete scheme using excitation of trapped neutral atoms into the Rydberg state via electromagnetically induced transparency is proposed and generalizations to a broader class of matrix product states are discussed.
We present a dissipative scheme to generate an entangled steady-state between two superconducting transmon qutrits separately embedded in two coupled transmission line resonators in a circuit quantum electrodynamics (QED) setup. In our scheme, the resonant qutrit-resonator interaction and photon hopping between resonators jointly induce asymmetric energy gaps in the dressed state subspaces. The coherent driving fields induce the specific dressed state transition and the dissipative processes lead to the gradual accumulation in the population of target state, combination of both drives the system into a steady-state entanglement. Numerical simulation shows that the maximally entangled state can be produced with high fidelity and strong robustness against the cavity decay and qutrit decay, and no requirements for accurate time control. The scheme is achievable with the current experimental technologies.
An attractive approach for stabilizing entangled many-body spin states is to employ engineered dissipation. Most existing proposals either target relatively simple collective spin states or require numerous independent and complex dissipative processes. Here, we show a surprisingly versatile scheme for many-body reservoir engineering that relies solely on fully collective single-excitation decay, augmented with local Hamiltonian terms. Crucially, all these ingredients are readily available in cavity QED setups. Our method is based on splitting the spin system into groups of subensembles and provides an easily tunable setup for stabilizing a broad family of pure, highly entangled states with closed-form analytic descriptions. Our results have immediate application to multiensemble quantum metrology, enabling Heisenberg-limited sensing of field gradients and curvatures. Notably, our approach solves an important challenge in differential quantum sensing by providing an example of Heisenberg-limited differential sensing immune to common-mode noise and accessible with only simple one-body measurements. The same setup also allows the stabilization of an entire family of entangled states in a one-dimensional chain of spin ensembles with symmetry-protected topological order and has a direct connection to the outputs of sequential unitary circuits. A special case of our protocol efficiently stabilizes the celebrated Affleck-Kennedy-Lieb-Tasaki state.
We propose an efficient approach for the generation of a stable entangled state of microwave fields in circuit quantum electrodynamics. The system under consideration consists of two linearly coupled superconducting resonators, each of which is coupled to a superconducting flux qubit. By individually driving the qubits to engineer the desired interactions with the resonators, we show that the energy relaxation of qubits can be exploited to steer the two resonators into the two-mode entangled state via a dissipative dynamical process. Since our protocol is based on quantum reservoir engineering, neither specific initialization nor unitary dynamics is required. Moreover, the distinct advantage of our scheme is that the quantum state preparation is robust in relation to inhomogeneous parameters, i.e., there is no need for identical qubit-field couplings, as well as the same resonance frequencies of the resonators. These features make the present scheme pretty feasible for experimental implementation.
We present a scheme for the dissipative preparation of an entangled steady state of two superconducting qubits in a circuit quantum electrodynamics (QED) setup. Combining resonator photon loss---a dissipative process already present in the setup---with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of the two qubits. This state is then maintained as the steady state of the driven, dissipative evolution. The performance of the dissipative state preparation protocol is studied analytically and verified numerically. In view of the experimental implementation of the presented scheme we investigate the effects of potential experimental imperfections and show that our scheme is robust to small deviations in the parameters. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmons. The promising results of our study thus open a route for the demonstration of a highly entangled steady state in circuit QED.