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arXiv:1909.05768 · Physical Review A

Scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice

Li‐Na Ji, Tao Chen, Zheng‐Yuan Xue

Published Dec 10, 2019• 13 citations
arXivHTMLPDF

Abstract

Geometric phase is an indispensable element for achieving robust and high-fidelity quantum gates due to its built-in noise-resilience feature. However, due to the complexity of manipulation and the intrinsic leakage of the encoded quantum information to a non-logical-qubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very difficult. Here we propose to implement scalable nonadiabatic holonomic quantum computation with a decoherence-free subspace encoding on a two-dimensional square superconducting transmon-qubit lattice, where only the two-body interaction of neighboring qubits, from the simplest capacitive coupling, is needed. Meanwhile, we introduce qubit-frequency driving to achieve tunable resonant coupling for the neighboring transmon qubits, and thus avoid the leakage problem. In addition, our presented numerical simulation shows that high-fidelity quantum gates can be obtained, verifying the advantages of the robustness and scalability of our scheme. Therefore, our scheme provides a promising way towards the physical implementation of robust and scalable quantum computation.

DOI
10.1103/physreva.100.062312

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Geometric phase is an indispensable element for achieving robust and high-fidelity quantum gates due to its built-in noise-resilience feature. However, due to the complexity of manipulation and the intrinsic leakage of the encoded quantum information to a non-logical-qubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very difficult. Here we propose to implement scalable nonadiabatic holonomic quantum computation with a decoherence-free subspace encoding on a two-dimensional square superconducting transmon-qubit lattice, where only the two-body interaction of neighboring qubits, from the simplest capacitive coupling, is needed. Meanwhile, we introduce qubit-frequency driving to achieve tunable resonant coupling for the neighboring transmon qubits, and thus avoid the leakage problem. In addition, our presented numerical simulation shows that high-fidelity quantum gates can be obtained, verifying the advantages of the robustness and scalability of our scheme. Therefore, our scheme provides a promising way towards the physical implementation of robust and scalable quantum computation.
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.
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.
The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions in multilevel quantum systems. Here we propose to implement nonadiabatic holonomic quantum computation with conventional capacitive coupled superconducting transmon qubits. A universal set of holonomic gates is constructed with the help of the interaction with an auxiliary qubit rather than relying on delicate control over an auxiliary level of multilevel quantum systems. Explicitly, these quantum gates are realized by tunable interactions in an all-resonant way, which leads to high-fidelity gate operations. In this way, the distinct merit of our scheme is that we use only the lowest two levels of a transmon to form the qubit states. In addition, the auxiliary qubits are in their ground states before and after every gate operation, so that the holonomic gates can be constructed successively. Therefore, our scheme provides a promising method towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.
The schmeme of nonadiabatic holonomic quantum computation (NHQC) offers an error-resistant method for implementing quantum gates, capable of mitigating certain errors. However, the conventional NHQC schemes often entail longer operations concerning standard gate operations, making them more vulnerable to the effects of quantum decoherence. In this research, we propose an implementation of the Super-Robust NHQC scheme within the Decoherence-Free Subspace (DFS). SR-NHQC has demonstrated robustness against Global Control Errors (GCEs). By utilizing capacitance-coupled transmon qubits within a DFS, our approach enables universal gate operations on a scalable two-dimensional square lattice of superconducting qubits. Numerical simulations demonstrate the practicality of SR-NHQC in DFS, showcasing its superiority in mitigating GCEs and decoherence effects compared to conventional NHQC schemes. Our work presents a promising strategy for advancing the reliability of quantum computation in real-world applications.
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to its intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising strategies. However, the longer gate time for geometric operations and more physical difficulties with regard to implementation hinder its practical and wide application. Here, we propose a simplified implementation of universal holonomic quantum gates on superconducting circuits with experimentally demonstrated techniques, which can remove these two main challenges by introducing time-optimal control into the construction of quantum gates. Notably, our scheme is also based on a decoherence-free subspace encoding and requires minimal physical-qubit resources, which can be partially immune to error caused by qubit-frequency drift, one of the main sources of error for large-scale superconducting circuits. Meanwhile, gate error caused by unwanted leakage can also be eliminated by our deliberate design of quantum evolution paths. Finally, our scheme is numerically shown to be more robust than the conventional ones and thus provides a promising strategy for scalable solid-state fault-tolerant quantum computation.
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.