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arXiv:2404.03397 · APL Quantum

Controllable non-Hermitian qubit–qubit coupling in superconducting quantum circuit

Hui Wang, Yan-Jun Zhao, Xun‐Wei Xu

Published Dec 1, 2024• 4 citations
arXivHTMLPDF

Abstract

We propose a theoretical scheme to realize the controllable non-Hermitian qubit–qubit coupling by adding a high-loss resonator in a tunable coupling superconducting quantum circuit. By changing the effective qubit–qubit coupling, the phase and amplitude of resonator–qubit interaction, and the qubits’ quantum states, we can continually tune the energy level attraction, the position of EP (exceptional point), and the non-reciprocity in the non-Hermitian superconducting circuit. The EPs and non-reciprocity can affect the quantum states’ evolutions and exchange efficiencies for two qubits in the non-Hermitian superconducting circuit. The controllable non-Hermitian and non-reciprocal interactions between two qubits provide new insights and methods for exploring the unconventional quantum effects in superconducting quantum circuits.

DOI
10.1063/5.0217493

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We propose a theoretical scheme to realize the controllable non-Hermitian qubit–qubit coupling by adding a high-loss resonator in a tunable coupling superconducting quantum circuit. By changing the effective qubit–qubit coupling, the phase and amplitude of resonator–qubit interaction, and the qubits’ quantum states, we can continually tune the energy level attraction, the position of EP (exceptional point), and the non-reciprocity in the non-Hermitian superconducting circuit. The EPs and non-reciprocity can affect the quantum states’ evolutions and exchange efficiencies for two qubits in the non-Hermitian superconducting circuit. The controllable non-Hermitian and non-reciprocal interactions between two qubits provide new insights and methods for exploring the unconventional quantum effects in superconducting quantum circuits.
As quantum systems are understood better from a fundamental physics perspective, we are gaining more insight and ideas for their many applications. Among them are quantum computation, sensing, and materials. Some difficulties that have been encountered are short lifetimes and coupling to unwanted modes while attempting to control these systems, resulting in error propagation. Previously, physicists have pursued Hermitian descriptions of systems to preserve unitary evolution and real-valued measurements. However, non-Hermitian systems not only provide a realistic description of physical systems within larger environments, but also a rich topological landscape from their complex energy spectrum. In this thesis, we will explore how to control a non-Hermitian qubit to utilize its complex spectrum and the role of its Hamiltonian in energetics and time dynamics. Because superconducting qubits offer flexibility in parameter tuning, we can tune the values of the non-Hermitian Hamiltonian to explore this complex spectrum across regions of both $\PT$-symmetry and $\PT$-symmetry breaking. This complex energy spectrum forms a Riemann surface that has a branch cut and branch points (exceptional points). Encircling these exceptional points adiabatically allows for state transport that can non-trivially convert between eigenstates. Previous experimental studies of this process revealed a chirality: eigenstate conversion occurs when following the state with higher gain, but breaks down when following the state with higher loss. We explore how the interplay between gain and loss in modes of the system results in the breakdown of this adiabaticity and how we can use a method based on shortcuts to adiabaticity to circumvent this. Finally, we leverage this tunability to further investigate how the components of the non-Hermitian Hamiltonian relate to classical thermodynamic notions of internal energy and work in time-dependent protocols via the Jarzynski equality.
Non-Hermitian physical systems have attracted considerable attention in recent years for their unique properties around exceptional points (EPs), where the eigenvalues and eigenstates of the system coalesce. Phase transitions near exceptional points can lead to various interesting phenomena, such as unidirectional wave transmission. However, most of those studies are in the classical regime and whether these properties can be maintained in the quantum regime is still a subject of ongoing studies. Using a non-Hermitian on-chip superconducting quantum circuit, here we observe a phase transition and the corresponding exceptional point between the two phases. Furthermore, we demonstrate that unidirectional microwave transmission can be achieved even in the few-photon regime within the broken symmetry phase. This result holds some potential applications, such as on-chip few-photon microwave isolators. Our study reveals the possibility of exploring the fundamental physics and practical quantum devices with non-Hermitian systems based on superconducting quantum circuits. The authors observe an exceptional point and the corresponding phase transition in a superconducting non-Hermitian circuit. They find non-reciprocal microwave transmission can be achieved within the broken symmetry phase in the few-photon regime.
We study the dynamics of a driven non-Hermitian superconducting qubit which is perturbed by quantum jumps between energy levels, a purely quantum effect with no classical correspondence. The quantum jumps mix the qubit states leading to decoherence. We observe that this decoherence rate is enhanced near the exceptional point, owing to the cube-root topology of the non-Hermitian eigenenergies. Together with the effect of non-Hermitian gain or loss, quantum jumps can also lead to a breakdown of adiabatic evolution under the slow-driving limit. Our study shows the critical role of quantum jumps in generalizing the applications of classical non-Hermitian systems to open quantum systems for sensing and control.
Abstract Open quantum systems are susceptible to losses in information, energy, and particles due to their surrounding environment. One novel strategy to mitigate these losses is to transform them into advantages for quantum technologies through tailored non-Hermitian quantum systems. In this work, we theoretically propose a fast generation of multipartite entanglement in non-Hermitian qubits. Our findings reveal that weakly coupled non-Hermitian qubits can accelerate multiparty entanglement generation by thousands of times compared to Hermitian qubits, in particular when approaching the 2 n -th order exceptional points of n qubits in the P T − symmetric regime. Furthermore, we show that Hermitian qubits can generate GHZ states with a high fidelity more than 0.9995 in a timescale comparable to that of non-Hermitian qubits, but at the expense of intense driving and large coupling constant. Our approach is scalable to a large number of qubits, presenting a promising pathway for advancing quantum technologies through the non-Hermiticity and higher-order exceptional points in many-body quantum systems.
The exploration of the effect of non-Hermitian (NH) in quantum systems is gaining renewed momentum as a result of the recent progress in experiments. It has been indicated that the ability to engineer the orders of exceptional points (EPs) can be fundamental to its applications in quantum control, such as accelerating entanglement generation; however, an initial survey of the interactions between different orders of EPs is still missing. In this work, we try to partially address this issue by employing a non-reciprocally coupled cavity system which can be experimentally realizable with a two-dimensional reconfigurable NH gauged laser array. With deliberate design, our systems display both second and third orders of EPs. The sign of a novel, purely quantum continuous entanglement phase transition is observed, which reveals how multi-EP interactions alter entanglement dynamics across different regimes while maintaining accelerated generation. Our findings reveil the genuinely quantum NH physics of higher-order EPs, which has opened up a new avenue for future investigations of the higher-order degeneracy application and the dynamic phase transitions of quantum systems.
We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable qubit-resonator coupling strength g. This coupling can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0, the qubit is in a decoherence-free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore, we show that in this decoherence-free subspace, the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.