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arXiv:1705.02064 · Physical Review A

Universal quantum control in zero-field nuclear magnetic resonance

Ji Bian, Min Jiang, Jiangyu Cui, Xiaomei Liu, Botao Chen, Yunlan Ji, Bo Zhang, John W. Blanchard, Xinhua Peng, Jiangfeng Du

Published May 23, 2017• 23 citations
arXivHTMLPDF

Abstract

This paper describes a general method for the manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-$\frac{1}{2}$ nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary single-qubit gates and a two-qubit controlled-not gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing, and fundamental physics.

DOI
10.1103/physreva.95.052342

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This paper describes a general method for the manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-12\frac{1}{2}21​ nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary single-qubit gates and a two-qubit controlled-not gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing, and fundamental physics.
Zero-field nuclear magnetic resonance (NMR) provides complementary analysis modalities to those of high-field NMR and allows for ultra-high-resolution spectroscopy and measurement of untruncated spin-spin interactions. Unlike for the high-field case, however, universal quantum control -- the ability to perform arbitrary unitary operations -- has not been experimentally demonstrated in zero-field NMR. This is because the Larmor frequency for all spins is identically zero at zero field, making it challenging to individually address different spin species. We realize a composite-pulse technique for arbitrary independent rotations of 1^11H and 13^{13}13C spins in a two-spin system. Quantum-information-inspired randomized benchmarking and state tomography are used to evaluate the quality of the control. We experimentally demonstrate single-spin control for 13^{13}13C with an average gate fidelity of 0.9960(2)0.9960(2)0.9960(2) and two-spin control via a controlled-not (CNOT) gate with an estimated fidelity of 0.990.990.99. The combination of arbitrary single-spin gates and a CNOT gate is sufficient for universal quantum control of the nuclear spin system. The realization of complete spin control in zero-field NMR is an essential step towards applications to quantum simulation, entangled-state-assisted quantum metrology, and zero-field NMR spectroscopy.
Nuclear magnetic resonance as a matured technique has extensive applications. However, since controlling the magnetic field in micro regions is technically difficult, it is still quite challenging to precisely manipulate single quantum state through nuclear magnetic resonance. Here we explicitly show how to realize nuclear electric resonance where a nucleus is directly driven by electric field. Elementary universal quantum gates are constructed with well-designed external electric field. These universal gates are practicable for arbitrary S>1 spin nuclei. Our proposal improves the number of single-qubit operations by three orders of magnitude in its coherence time period, compared with indirectly electrical nuclear manipulation.
Zero-field nuclear magnetic resonance (NMR) has been recently developed as a complementary tool for nondestructive structural investigations of matter. However, precise and efficient control in such systems is still at the beginning. Based on the controllability of spin systems, we theoretically study the issue of quantum control in zero-field NMR by using a numerical optimization method based on the gradient ascent pulse engineering (GRAPE) algorithm. A set of quantum gates, including single-qubit and two-qubit gates, are achieved as examples. In particular, we show that homonuclear spins can be individually manipulated in zero-field NMR by the GRAPE method, which extends the ability to manipulate spin systems at zero magnetic field. Quantum control realized by the numerical GRAPE method features the properties of high fidelity, robustness, and hardware-friendly characteristics. High-fidelity quantum control in zero-field NMR systems might provide promising applications in material science, chemical analysis, quantum information processing, and fundamental physics.
The presence of an external magnetic field leads to the loss of anisotropic physical information and is responsible for the broadening of spectra in sensing experiments with solid-state quantum sensors. However, the range of applicable sensing protocols at zero field was limited due to the incomplete manipulations. Here we propose and demonstrate a precise geometric control protocol in a spin-1 quantum sensor for zero-field multiquantum gates. By employing specific phased geometric controls, state leakage is prevented at zero field even under low control power, which allows much more complicated multipulse control especially under living biological conditions. Our method offers an approach to implement an arbitrary multiquantum gate on the spin-1 quantum sensor, rendering it a valuable tool for zero-field multipulse quantum technologies, such as nanoscale zero-field multidimensional nuclear magnetic resonance.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.