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arXiv:1609.06835 · Physical Review Letters

Experimental Time-Optimal Universal Control of Spin Qubits in Solids

Jianpei Geng, Yang Wu, Xiaoting Wang, Kebiao Xu, Fazhan Shi, Yijin Xie, Xing Rong, Jiangfeng Du

Published Oct 19, 2016• 68 citations
arXivHTMLPDF

Abstract

Quantum control of systems plays an important role in modern science and technology. The ultimate goal of quantum control is to achieve high-fidelity universal control in a time-optimal way. Although high-fidelity universal control has been reported in various quantum systems, experimental implementation of time-optimal universal control remains elusive. Here, we report the experimental realization of time-optimal universal control of spin qubits in diamond. By generalizing a recent method for solving quantum brachistochrone equations [X. Wang et al., Phys. Rev. Lett. 114, 170501 (2015)], we obtained accurate minimum-time protocols for multiple qubits with fixed qubit interactions and a constrained control field. Single- and two-qubit time-optimal gates are experimentally implemented with fidelities of 99% obtained via quantum process tomography. Our work provides a time-optimal route to achieve accurate quantum control and unlocks new capabilities for the emerging field of time-optimal control in general quantum systems.

DOI
10.1103/physrevlett.117.170501

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Quantum control of systems plays an important role in modern science and technology. The ultimate goal of quantum control is to achieve high-fidelity universal control in a time-optimal way. Although high-fidelity universal control has been reported in various quantum systems, experimental implementation of time-optimal universal control remains elusive. Here, we report the experimental realization of time-optimal universal control of spin qubits in diamond. By generalizing a recent method for solving quantum brachistochrone equations [X. Wang et al., Phys. Rev. Lett. 114, 170501 (2015)], we obtained accurate minimum-time protocols for multiple qubits with fixed qubit interactions and a constrained control field. Single- and two-qubit time-optimal gates are experimentally implemented with fidelities of 99% obtained via quantum process tomography. Our work provides a time-optimal route to achieve accurate quantum control and unlocks new capabilities for the emerging field of time-optimal control in general quantum systems.
Decoherence is inevitable when manipulating quantum systems. It decreases the quality of quantum manipulations and thus is one of the main obstacles for large-scale quantum computation, where high-fidelity quantum gates are needed. Generally, 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 brachistochrone 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 approaches 99.999.9%99.9. Meanwhile, we can further accelerate the ZZZ-axis gate considerably by adjusting the detuning of the external driving. Finally, in order to reduce the influence of the dephasing error, decoherence-free subspace encoding is also incorporated in our physical implementation. Therefore, we present a fast quantum scheme which is promising for large-scale quantum computation.
Abstract Time-optimal control holds promise across the full spectrum of quantum technologies, where the rapid generation of unitary gates and state transformations is crucial to mitigate decoherence effects. In practical scenarios, quantum systems are always immersed in an external time-dependent field or potential, either owing to the inevitable influence of the environment or as a sought-after effect for enhanced coherence. The challenge then lies in finding the time-optimal approach to navigate quantum systems amidst dynamical ambient Hamiltonians, a pursuit that has proven elusive thus far. We showcase the implementation of arbitrary quantum state transformations and a universal set of single-qubit gates under a background Landau-Zener Hamiltonian. Leveraging the favorable coherence properties of timedomain Rabi oscillations, we achieve velocities surpassing the Mandelstam-Tamm quantum speed limit and significantly lower energy costs than those incurred by conventional quantum control techniques. These findings highlight a promising pathway to expedite and economize high-fidelity quantum operations.
We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over 99.299.2%99.2 on the spin state of the nitrogen-vacancy center are realized with average durations shortened by 21.521.5%21.5 compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds 96.596.5%96.5 on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.
Experimental realization of a universal set of quantum logic gates with high fidelity is critical to quantum-information processing, which is always challenging due to the inevitable interaction between the quantum system and environment. Geometric quantum computation is noise immune, and thus, offers a robust way to enhance control fidelity. Here, we experimentally implement the recently proposed extensible nonadiabatic holonomic quantum computation with solid spins in diamond at room temperature, which maintains both flexibility and resilience against decoherence and system-control errors. Compared with the previous geometric method, the fidelities of a universal set of holonomic single-qubit and two-qubit quantum logic gates are improved in experiments. Therefore, this work makes a step towards high-fidelity quantum-information processing based on extensible nonadiabatic holonomic quantum computation in realistic systems.
We report on a theoretical and experimental study of time-optimal construction of arbitrary single-qubit rotations under a single strong driving field of finite amplitude. Using radiation-dressed states of nitrogen vacancy centers in diamond we realize a strongly driven two-level system, with driving frequencies four times larger than its precession frequency. We implement time-optimal universal rotations on this system, characterize their performance using quantum process tomography, and demonstrate a dual-axis multiple-pulse control sequence where the qubit is rotated on time scales faster than its precession period. Our results pave the way for applying fast qubit control and high-density pulse schemes in the fields of quantum information processing and quantum metrology.
Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.