Obtaining high-fidelity and robust quantum gates is the key for scalable quantum computation, and one of the promising ways is to implement quantum gates using geometric phases, where the influence of local noises can be greatly reduced. To obtain robust quantum gates, we here propose a scheme for quantum manipulation by combining the geometric phase approach with the dynamical correction technique, where the imperfection control induced X-error can be greatly suppressed. Moreover, to be robust against the decoherence effect and the randomized qubit-frequency shift Z-error, our scheme is also proposed based on the polariton qubit, the eigenstates of the light–matter interaction, which is immune to both errors up to the second order, due to its near symmetric energy spectrum. Finally, our scheme is implemented on the superconducting circuits, which also simplifies previous implementations. Since the main errors can be greatly reduced in our proposal, it provides a promising strategy for scalable solid-state fault-tolerant quantum computation.
Obtaining high-fidelity and robust quantum gates is the key for scalable quantum computation, and one of the promising ways is to implement quantum gates using geometric phases, where the influence of local noises can be greatly reduced. To obtain robust quantum gates, we here propose a scheme for quantum manipulation by combining the geometric phase approach with the dynamical correction technique, where the imperfection control induced X-error can be greatly suppressed. Moreover, to be robust against the decoherence effect and the randomized qubit-frequency shift Z-error, our scheme is also proposed based on the polariton qubit, the eigenstates of the light–matter interaction, which is immune to both errors up to the second order, due to its near symmetric energy spectrum. Finally, our scheme is implemented on the superconducting circuits, which also simplifies previous implementations. Since the main errors can be greatly reduced in our proposal, it provides a promising strategy for scalable solid-state fault-tolerant quantum computation.
The key for realizing fault-tolerant quantum computation lies in maintaining the coherence of all qubits so that high-fidelity and robust quantum manipulations on them can be achieved. One of the promising approaches is to use geometric phases in the construction of universal quantum gates, due to their intrinsic robustness against certain types of local noise. However, due to limitations in previous implementations, the noise-resilience feature of nonadiabatic holonomic quantum computation (NHQC) still needs to be improved. Here, in combination with the dynamical-correction technique, we propose a general protocol of universal NHQC with simplified control, which can greatly suppress the effect of the accompanied X errors, retaining the main merit of geometric quantum operations. Numerical simulation shows that the performance of our gate can be much better than that of previous protocols. Remarkably, when incorporating a decoherence-free subspace encoding for the collective dephasing noise, our scheme can also be robust against the involved Z errors. In addition, we also outline the physical implementation of the protocol, which is insensitive to both X and Z errors. Therefore, our protocol provides a promising strategy for scalable fault-tolerant 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.
Besides the intrinsic noise resilience property, nonadiabatic geometric phases are of the fast evolution nature, and thus can naturally be used in constructing quantum gates with excellent performance, i.e., the so-called nonadiabatic geometric quantum computation (NGQC). However, previous single-loop NGQC schemes are sensitive to the operational control error, i.e., the X error, due to the limitations of the implementation. Here, we propose a robust scheme for NGQC combining with the dynamical correction technique, which still uses only simplified pulses, and thus being experimental friendly. We numerically show that our scheme can greatly improve the gate robustness in previous protocols, retaining the intrinsic merit of geometric phases. Furthermore, to fight against the dephasing noise, due to the Z error, we can incorporate the decoherence-free subspace encoding strategy. In this way, our scheme can be robust against both types of errors. Finally, we also propose how to implement the scheme with encoding on superconducting quantum circuits with experimentally demonstrated technology. Therefore, due to the intrinsic robustness, our scheme provides a promising alternation for the future scalable fault-tolerant quantum computation.
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus faster gate operations are highly desired. Here, we propose a nonadiabatic holonomic quantum-computation (NHQC) scheme with detuned interactions on a $\mathrm{\ensuremath{\Delta}}$-type three-level system, which combines the time-optimal control technique with the time-independent detuning adjustment to further accelerate universal gate operations, so that the gate time can be greatly shortened within the hardware limitation, and thus high-fidelity gates can be obtained. Meanwhile, our numerical simulations show that the gate robustness is also stronger than previous schemes. Finally, we present an implementation of our proposal on superconducting quantum circuits, with a decoherence-free subspace encoding, based on the experimentally demonstrated parametrically tunable coupling technique, which simplifies previous investigations. Therefore, our protocol provides a more promising alternative for future fault-tolerant quantum computation.
Recently, nonadiabatic geometric quantum computation has been received great attentions, due to its fast operation and intrinsic error resilience. However, compared with the corresponding dynamical gates, the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop geometric scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls, and the inherent geometric fault-tolerance characteristic is not fully explored. Here, we present an effective geometric scheme combined with a general dynamical-corrected technique, with which the super-robust nonadiabatic geometric quantum gates can be constructed over the conventional single-loop geometric and two-loop composite-pulse geometric strategies, in terms of resisting the systematic error, i.e., σx error. In addition, combined with the decoherence-free subspace (DFS) coding, the resulting geometric gates can also effectively suppress the σz error caused by the collective dephasing. Notably, our protocol is a general one with simple experimental setups, which can be potentially implemented in different quantum systems, such as Rydberg atoms, trapped ions and superconducting qubits. These results indicate that our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions among multiple levels or qubits and a longer gate time than the corresponding dynamical ones. Here, we propose a general framework of geometric quantum computation with the integration of the time-optimal control technique, where the shortest smooth geometric path is found to realize accelerated geometric quantum gates and thus greatly decreases the gate errors induced by both the decoherence effect and operational imperfections. Meanwhile, we faithfully implement our idea on a scalable platform of a two-dimensional superconducting transmon-qubit lattice, with simple and experimentally accessible interactions. In addition, numerical simulations show that our implemented geometric gates possess higher fidelities and stronger robustness, which outperform the best performance of the corresponding dynamical ones. Therefore, our scheme provides a promising alternative route toward scalable fault-tolerant solid-state quantum computation.