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.
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 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.
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 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.
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 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.
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.