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Annalen der Physik

Quantum Interface between a Superconducting Qubit and Spin Ensembles

Feng‐Yang Zhang, Wenlin Li, Wei‐Bin Yan, Chui‐Ping Yang

Published May 20, 2019• 4 citations
Publisher

Abstract

Abstract An experimentally feasible strong coupling system between a spin ensemble and a superconducting qubit is studied. The coupling strength can be exponentially enhanced by applying the squeezing transformations to the system. By means of the two spin ensembles commonly coupled to a superconducting qubit, a set of universal nonadiabatic holonomic single‐qubit quantum gates can be realized in a decoherence‐free subspace. Furthermore, this proposal is robust with respect to decay of the system parameters, and it is experimentally feasible with currently available technology.

DOI
10.1002/andp.201900036

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Abstract An experimentally feasible strong coupling system between a spin ensemble and a superconducting qubit is studied. The coupling strength can be exponentially enhanced by applying the squeezing transformations to the system. By means of the two spin ensembles commonly coupled to a superconducting qubit, a set of universal nonadiabatic holonomic single‐qubit quantum gates can be realized in a decoherence‐free subspace. Furthermore, this proposal is robust with respect to decay of the system parameters, and it is experimentally feasible with currently available technology.
To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfill for superconducting qubits and appears to be a main reason why only single-qubit gates were implemented in a recent experiment [A. A. Abdumalikov, Jr. et al., Nature (London) 496, 482 (2013)]. Here we propose to realize nonadiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where one can use only the two levels in transmon qubits, a usual interaction, and a minimal resource for the decoherence-free subspace encoding. In particular, our scheme not only overcomes the difficulties encountered in previous studies but also can still achieve considerably large effective coupling strength, such that high-fidelity quantum gates can be achieved. Therefore, the present scheme makes realizing robust holonomic quantum computation with superconducting circuits very promising.
Abstract Geometric phases induced in quantum evolutions have built‐in noise‐resilient characters, and thus can find applications in many robust quantum manipulation tasks. Here, a feasible and fast scheme for universal quantum computation on superconducting circuits with nonadiabatic non‐Abelian geometric phases is proposed, using resonant interaction of three‐level quantum system. In this scheme, arbitrary single‐qubit quantum gates can be implemented in a single‐loop scenario by shaping both the amplitudes and phases of the two driving microwave fields resonantly coupled to a transmon device. Moreover, nontrivial two‐qubit gates can also be realized with an auxiliary transmon simultaneously coupled to the two target transmons in an effective resonant way. In particular, this proposal can be compatible to various optimal control techniques, which further enhances the robustness of the quantum operations. Therefore, this proposal represents a promising way toward fault‐tolerant quantum computation on solid‐state quantum circuits.
The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in a tunable and all-resonant way through a hybrid transmon--transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.
ABSTRACT Nonadiabatic holonomic quantum computation (NHQC) leverages non‐Abelian geometric phases within a nonadiabatic framework to achieve fast and robust quantum gate operations. However, the practical implementation of NHQC is challenged by the imperfect control inherent in experimental environments. Ensuring deep suppression of control error is critical. In this work, we propose a dynamically optimized NHQC scheme to construct universal super‐robust holonomic quantum gates. The proposed scheme is implemented by strategically designing a set of dynamically correcting pulses to achieve cyclic evolution, while ensuring that unwanted and disruptive dynamical phase elements, including previously neglected cross‐coupling terms, are not accumulated. This constructed super‐robust NHQC scheme efficiently safeguards the cyclic evolution process and makes the holonomic gate immune to control error by effectively correcting the error up to the fourth order. Furthermore, when integrated with decoherence‐free subspace (DFS) encoding in superconducting quantum circuits, our scheme can achieve high‐fidelity holonomic gates, and demonstrate robust resilience against both control errors and collective dephasing errors. Consequently, our work offers a promising pathway toward the realization of scalable and fault‐tolerant holonomic quantum computation.
Abstract A protocol is proposed to realize one‐step implementation of the N‐qubit nonadiabatic holonomic quantum gates with superconducting qubits. The inverse Hamiltonian engineering is applied in designing microwave pulses to drive superconducting qubits. By combining curve fitting, the wave shapes of the designed pulses can be described by simple functions, which are not hard to realize in experiments. To demonstrate the effectiveness of the protocol, a three‐qubit holonomic controlled π‐phase gate is taken as an example in numerical simulations. The results show that the protocol holds robustness against noise and decoherence. Therefore, the protocol may provide an alternative approach for implementing N‐qubit nonadiabatic holonomic quantum gates.
We propose a method to achieve strong coupling between a spin ensemble and a large Josephson junctions (LJJ). Then, the strong coupling between two spin ensembles can be induced by a LJJ. A non-adiabatic holonomic single-qubit quantum gates is realized. Moreover, with the dispersive interaction between the spin ensembles and the LJJ, the high-fidelity two-qubit phase gate can be implemented with two spin ensembles within an operation time 0.41 ns and πππ phase-swap gate can be realized within an operation time 103.11 ns with a high fidelity greater than 99%.