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arXiv:1905.11263 · Advanced Quantum Technologies

Fast Holonomic Quantum Computation on Superconducting Circuits With Optimal Control

Sai Li, Tao Chen, Zheng‐Yuan Xue

Published Jan 23, 2020• 50 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/qute.202000001

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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.
Geometric phases are well known to be noise resilient in quantum evolutions and operations. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced by non-Abelian geometric phases. Here we propose and elaborate how to efficiently implement universal nonadiabatic holonomic quantum gates on simpler superconducting circuits, with a single transmon serving as a qubit. In our proposal, an arbitrary single-qubit holonomic gate can be realized in a single-loop scenario by varying the amplitudes and phase difference of two microwave fields resonantly coupled to a transmon, while nontrivial two-qubit holonomic gates may be generated with a transmission-line resonator being simultaneously coupled to the two target transmons in an effective resonant way. Moreover, our scenario may readily be scaled up to a two-dimensional lattice configuration, which is able to support large scalable quantum computation, paving the way for practically implementing universal nonadiabatic holonomic quantum computation with superconducting circuits.
Quantum gates, which are the essential building blocks of quantum computers, are very fragile. Thus, to realize robust quantum gates with high fidelity is the ultimate goal of quantum manipulation. Here, we propose a nonadiabatic geometric quantum computation scheme on superconducting circuits to engineer arbitrary quantum gates, which share both the robust merit of geometric phases and the capacity to combine with optimal control technique to further enhance the gate robustness. Specifically, in our proposal, arbitrary geometric single-qubit gates can be realized on a transmon qubit, by a resonant microwave field driving, with both the amplitude and phase of the driving being time-dependent. Meanwhile, nontrivial two-qubit geometric gates can be implemented by two capacitively coupled transmon qubits, with one of the transmon qubits’ frequency being modulated to obtain effective resonant coupling between them. Therefore, our scheme provides a promising step towards fault-tolerant solid-state quantum computation.
In quantum computing, robustness against noise is a primary concern. Meanwhile, geometric (topological) phases in physical systems are determined by global properties that are insensitive to the details of evolution, and thus offer some built-in noise resilience. Marrying these ideas for superconducting qubits is not easy, but this study details a scalable scheme for fast holonomic quantum computation based on superconducting circuits with all-resonant microwave control. The main difficulties for physical implementation in this context are overcome, with both single-qubit and nontrivial two-qubit gates being described.
Geometric phases are noise resilient, and thus provide a robust way towards high-fidelity quantum manipulation. Here we experimentally demonstrate arbitrary nonadiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmarking and the ones on the cavity show an averaged fidelity of 0.978 based on a full quantum process tomography. In principle, a nontrivial two-qubit holonomic gate between the qubit and the cavity can also be realized based on our presented experimental scheme. Our experiment thus paves the way towards practical nonadiabatic holonomic quantum manipulation with both qubits and cavities in a superconducting circuit.
High-fidelity quantum gates are essential for large-scale quantum computation. However, any quantum manipulation will inevitably affected by noises, systematic errors and decoherence effects, which lead to infidelity of a target quantum task. Therefore, implementing high-fidelity, robust and fast quantum gates is highly desired. Here, we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity. In our proposal, the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally, leading to high-fidelity quantum gates in a simple setup. Besides, our scheme is readily realizable in physical system currently pursued for implementation of quantum computation. Therefore, our proposal represents a promising way towards fault-tolerant geometric 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.