Time-optimal universal quantum gates on superconducting circuits

  1. Ze Li,
  2. Ming-Jie Liang,
  3. and Zheng-Yuan Xue
Decoherence is an inevitable problem when targeting to increase the fidelity of quantum gates, and thus is one of the main obstacles for large-scale quantum computation. The longer
a gate operation is, the more decoherence-induced gate infidelity will be. Therefore, how to shorten the gate time becomes an urgent problem to be solved. To this end, time-optimal control based on solving the quantum brachistochron equation is a straightforward solution. Here, based on time-optimal control, we propose a scheme to realize universal quantum gates on superconducting qubits, in a two-dimensional square lattice configuration, and the two-qubit gate fidelity can be higher than 99.7%. Meanwhile, we can further accelerate the z-axis gate considerably by adjusting the time-independent detuning. Finally, in order to reduce the influence of the dephasing error, decoherence free subspace is also incorporated in our physical implementation. Therefore, we present a promising fast scheme for large-scale quantum computation.

Robust and Fast Quantum State Transfer on Superconducting Circuits

  1. Xiao-Qing Liu,
  2. Jia Liu,
  3. and Zheng-Yuan Xue
Quantum computation attaches importance to high-precision quantum manipulation, where the quantum state transfer with high fidelity is necessary. Here, we propose a new scheme to implement
the quantum state transfer of high fidelity and long distance, by adding on-site potential into the qubit chain and enlarging the proportion of the coupling strength between the two ends and the chain. In the numerical simulation, without decoherence, the transfer fidelities of 9 and 11 qubit chain are 0.999 and 0.997, respectively. Moreover, we give a detailed physical realization scheme of the quantum state transfer in superconducting circuits, and discuss the tolerance of our proposal against decoherence. Therefore, our scheme will shed light on quantum computation with long chain and high-fidelity quantum state transfer.

Experimental Implementation of Noncyclic and Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit

  1. Zhuang Ma,
  2. Jianwen Xu,
  3. Tao Chen,
  4. Yu Zhang,
  5. Wen Zheng,
  6. Dong Lan,
  7. Zheng-Yuan Xue,
  8. Xinsheng Tan,
  9. and Yang Yu
Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum
computation 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.

Nonadiabatic geometric quantum computation with shortened path on superconducting circuits

  1. Cheng-Yun Ding,
  2. Yan Liang,
  3. Kai-Zhi Yu,
  4. and Zheng-Yuan Xue
Recently, nonadiabatic geometric quantum computation has been received much attention, due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain
universal geometric quantum control, only limited and special evolution paths have been proposed, which usually requires longer gate-time and more operational steps, and thus leads to lower quality of the implemented quantum gates. Here, we present an effective scheme to find the shortest geometric path under the conventional conditions of geometric quantum computation, where high-fidelity and robust geometric gates can be realized by only single-loop evolution, and the gate performances are better than the corresponding dynamical ones. Furthermore, we can optimize the pulse shapes in our scheme to further shorten the gate-time, determined by how fast the path is travelled. In addition, we also present its physical implementation on superconducting circuits, consisting of capacitively coupled transmon qubits, where the fidelities of geometric single- and two-qubit gates can be higher than 99.95% and 99.80% within the current state-of-the-art experimental technologies, respectively. These results indicate that our scheme is promising for large-scale fault-tolerant quantum computation.

Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

  1. Cheng-Yun Ding,
  2. Li-Na Ji,
  3. Tao Chen,
  4. and Zheng-Yuan Xue
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 universal
geometric 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.

Robust Nonadiabatic Holonomic Quantum Gates on Decoherence-Protected Qubits

  1. Zhi-Cheng He,
  2. and Zheng-Yuan Xue
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.

Realization of Super-Robust Geometric Control in a Superconducting Circuit

  1. Sai Li,
  2. Bao-Jie Liu,
  3. Zhongchu Ni,
  4. Libo Zhang,
  5. Zheng-Yuan Xue,
  6. Jian Li,
  7. Fei Yan,
  8. Yuanzhen Chen,
  9. Song Liu,
  10. Man-Hong Yung,
  11. Yuan Xu,
  12. and Dapeng Yu
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A
significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross coupling to the states outside the computational space. We implement a new set of constraints for gate construction in order to suppress such cross coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasi-static transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the above mentioned cross coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.

Robust and Fast Holonomic Quantum Gates with Encoding on Superconducting Circuits

  1. Tao Chen,
  2. Pu Shen,
  3. and Zheng-Yuan Xue
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to the intrinsic operational robustness, quantum manipulation induced by geometric
phases 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.

Nonadiabatic geometric quantum computation with optimal control on superconducting circuits

  1. Jing Xu,
  2. Sai Li,
  3. Tao Chen,
  4. and Zheng-Yuan Xue
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 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.

Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit

  1. Yuan Xu,
  2. Ziyue Hua,
  3. Tao Chen,
  4. Xiaoxuan Pan,
  5. Xuegang Li,
  6. Jiaxiu Han,
  7. Weizhou Cai,
  8. Yuwei Ma,
  9. Haiyan Wang,
  10. Yipu Song,
  11. Zheng-Yuan Xue,
  12. and Luyan Sun
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 nonadiabatic
geometric 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.