Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantumcomputation typically require a long pulse time of gates. As a result, their experimental control inevitably suffers from the cumulative disturbances of systematic errors due to excessive time consumption. Here, we experimentally implement a set of noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit, which greatly shortens the gate time. And also, we experimentally verify that our universal single-qubit geometric gates are more robust to both the Rabi frequency error and qubit frequency shift-induced error, compared to the conventional dynamical gates, by using the randomized benchmarking method. Moreover, this scheme can be utilized to construct two-qubit geometric operations, while the generation of the maximally entangled Bell states is demonstrated. Therefore, our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates in superconducting quantum circuits.
Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, to obtain universalgeometric quantum gates, the required evolution paths are usually limited to some special ones, and the evolution times of which are still longer than dynamical quantum gates, resulting in weakening of robustness and more infidelity of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Through our numerical simulations, we obtain the fidelities for single-qubit geometric Phase, π/8 and Hadamard gates as 99.93%, 99.95% and 99.95%, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as 99.87%. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to the intrinsic operational robustness, quantum manipulation induced by geometricphases is one of the promising candidates. However, the longer gate time for geometric operations and more physical-implementation difficulties hinder its practical and wide applications. Here, we propose a simplified implementation of universal holonomic quantum gates on superconducting circuits with experimentally demonstrated techniques, which can remove the two main challenges by introducing the time-optimal control into the construction of quantum gates. Remarkably, our scheme is also based on a decoherence-free subspace encoding, with minimal physical qubit resource, which can further immune to error caused by qubit-frequency drift, which is regarded as the main error source for large scale superconducting circuits. Meanwhile, we deliberately design the quantum evolution to eliminate gate error caused by unwanted leakage sources. Therefore, our scheme is more robust than the conventional ones, and thus provides a promising alternative strategy for scalable fault-tolerant quantum computation.
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 quantummanipulation. 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 the 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.
Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabaticgeometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977 and 0.977, respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamic gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.
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 manipulationand the intrinsic leakage of the encoded quantum information to 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 decoherence-free subspace encoding on a two-dimensional square superconducting transmon-qubit lattice, where only the two-body interaction of neighbouring qubits, from the simplest capacitive coupling, is needed. Meanwhile, we introduce qubit-frequency driving to achieve tunable resonant coupling for the neighbouring transmon qubits, and thus avoiding 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 phase factor plays a vital role in modern quantum physics. Especially, geometric phases induced in quantum evolutions have the built-in noise-resilient character, and thus foundcomprehensive applications in many robust quantum manipulation tasks. Here, we propose a fast scheme to construct universal quantum gates on superconducting circuits with non-Abelian geometric phases using resonant interaction of three-level quantum systems. As the evolution state always fulfill the Schrödinger equation of the govern Hamiltonian, during the cyclic quantum evolution, there will be no nonadiabatic transitions from the evolution state to other states, i.e., the orthogonal states of the evolution state. Meanwhile, arbitrary single-qubit quantum gates can be implemented in a single-loop scenario by shaping both the amplitudes and phases of two microwave fields, resonantly coupled to a transmon qubit. 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, our proposal can be compatible to various optimal control techniques, which further enhances the robustness of the quantum operations. Therefore, our proposal represents a promising way towards fault-tolerant quantum computation on solid-state quantum circuits.
The implementation of nonadiabatic geometric quantum computation is promising since its robustness against certain types of noises. Meanwhile, it is also challenging due to the needof complex control on the quantum multiple and/or multi-level systems. Here, we propose to implement nonadiabatic geometric quantum computation on a two-dimensional square superconducting qubit lattice. In our construction of the geometric quantum gates, we merely adopt simple and experimentally accessible control over the quantum systems, which only involve their qubit states. Specifically, our scheme is achieved by parametrically tunable all-resonant interactions, which leads to high-fidelity quantum gates. Moreover, this simple implementation can be conveniently generalized to a composite scenario, which can further suppress the systematic error during the gate operations. In addition, universal nonadiabatic geometric quantum gates in decoherence-free subspaces can also be implemented based on the tunable coupling between only two transmon qubits, without consulting to multiple qubits and only using two physical qubits to construct the logical qubit. Therefore, our scheme possesses promising prospects for experimental implementation of geometric quantum computation.
The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions on multilevel quantum systems. Here we propose to implementthe nonadiabatic holonomic quantum computation with the conventional capacitive coupled superconducting transmon qubits, where a universal set of quantum gates is constructed with the help of the interaction to an auxiliary qubit rather than consulting to 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 only use the two lowest 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. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.
Faithfully transferring quantum state is essential for quantum information processing. Here, we demonstrate a fast (in 84~ns) and high-fidelity (99.2%) quantum state transfer in achain of four superconducting qubits with nearest-neighbor coupling. This transfer relies on full control of the effective couplings between neighboring qubits, which is realized only by parametrically modulating the qubits without increasing circuit complexity. Once the couplings between qubits fulfill specific ratio, a perfect quantum state transfer can be achieved in a single step, therefore robust to noise and accumulation of experimental errors. This quantum state transfer can be extended to a larger qubit chain and thus adds a desirable tool for future quantum information processing. The demonstrated flexibility of the coupling tunability is suitable for quantum simulation of many-body physics which requires different configurations of qubit couplings.