Optimal quantum manipulation over many-body spin
system in diamond with a shaped microwave
Kouyou Kuramitani, Yuhei Sekiguchi, and Hideo Kosaka*
Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501, Japan*Corresponding author: kosaka-hideo-yp@ynu.ac.jp

Abstract: We achieved high fidelity control for single qubit and multi qubit by using
optimized microwave pulse in a many-body spin system consisting of an NV center andnuclear spins.
1.

Introduction

Improving scalability is a long-standing problem in implementing quantum information processing in asolid-state system. The interaction between spins, which are resources of quantum entanglement, gives
complex dynamics to the system. Therefore, it is no exaggeration that there is an inverse correlation between
the ease of single qubit operation and that of multi qubit operation.
For realizing quantum information technology, we have succeeded in storing photon polarization into a
nuclear spin in an NV center in diamond [1]. The storage scheme is based on generation of entanglement
between an electron and a 14N nuclear spin and detection of entanglement between a photon and an electron[2], which consists of a geometrical spin under a zero field [3]. However, it is hard to increase the number ofmemory qubits due to complex time evolution of mutually interacting many-body system.
Here, we tried to solve this problem by gradient ascent pulse engineering (GRAPE) algorithm [4]. This
computerized approach allows us to treat many-body complex dynamics straight without bold approximation.
2.

Experimental setup

The GRAPE algorithm is the simplest optimization method using the gradient of the evaluation function.
This method is comparatively easy to calculate, and partially adaptable even when the external field isdependent on time.
We experimentally demonstrate faithful manipulation of an electron spin interacting with two nuclear spins
on 14N and 13C (Fig.1) with optimized microwave pulses based on the GRAPE algorithm. The hyperfine
interaction was 6.275 MHz between the electron spin and the 13C nuclear spin and 2.165 MHz between theelectron spin and the 14N nuclear spin.
3.

Experimental demonstration

First, we optimized the microwave that gives control to the electron spin and attempted to achieve highfidelity single qubit operation. As a result, we succeeded in transitioning the electron spin to the desired statewith 98% fidelity under the disadvantageous condition that microwave power was limited and insufficient.
We also demonstrated coherence swap operation between electron spin and nuclear spin as an example of
optimized multi qubit operation. Its polarizability was 85% for nitrogen 14N nuclear spin (Fig.2) and 78% for
13
C nuclear spin.
4. Conclusion
The demonstrated results indicate the usefulness of control pulse optimization for single and multi-qubit
operation to NV center spin many-body system. They also indicate that “exclusive” entanglement generation
between an electron and a selected nuclear spin keeping the others unchanged could be realized to build an
integrated quantum memory. It is expected that this method will be effective even in the case of controllingelectron spin of NV center by optical process [5].
5. Acknowledgement
We thank Yuichiro Matsuzaki, Burkhard Scharfenberger, Kae Nemoto, William Munro, Norikazu
Mizuochi, Nobuhiko Yokoshi, Fedor Jelezko, and Joerg Wrachtrup for their discussions and experimental
help. This work was supported by National Institute of Information and Communications Technology(NICT) Quantum Repeater Project, and by Japan Society for the Promotion of Science (JSPS) Grant-in-Aidfor Scientific Research (24244044, 16H06326, 16H01052) and Ministry of Education, Culture, Sports,

Science and Technology (MEXT) as “Exploratory Challenge on Post-K computer” (Frontiers of Basic
Science: Challenging the Limits).
6. References[1] S. Yang et al., "High-fidelity transfer and storage of photon states in a single nuclear spin," Nat. Photon. 10, 507-511 (2016).
[2] H. Kosaka and N. Niikura, “Entangled Absorption of a Single Photon with a Single Spin in Diamond,” Phys. Rev. Lett. 114,053603 (2015).
[3] Y. Sekiguchi, Y. Komura, S. Mishima, T. Tanaka, N. Niikura, and H. Kosaka, “Geometric spin echo under zero field,” Nat.
Commun. 7 11668 (2016).
[4] N. Khaneja et al., “Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms,” J.
Magn. Reson. 172, 296-305 (2005).
[5] Y. Sekiguchi, N. Niikura, R. Kuroiwa, H. Kano, and H. Kosaka, “Optical holonomic single quantum gates with a geometric spin
under a zero field” Nat. Photon. in press (2017).

14N nuclear spin

Electron spin

13C nuclear spin

Fig.1. Image of an NV center multi spin system used in the experiment.

Polarization ratio: 85%

Fig.2 ODMR spectrum showing the polarization ratio of a 14N nuclear spin.