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Optically addressable universal holonomic quantum gates on diamond spins


The ability to individually control the numerous spins in a solid-state crystal is a promising technology for the development of large-scale quantum processors and memories. A localized laser field offers spatial selectivity for electron spin manipulation through spin–obit coupling, but it has been difficult to simultaneously achieve precise and universal manipulation. Here, we demonstrate microwave-driven holonomic quantum gates on an optically selected electron spin in a nitrogen-vacancy centre in diamond. The electron spin is precisely manipulated with global microwaves tuned to the frequency shift induced by the local optical Stark effect. We show the universality of the operations, including state initialization, preparation, readout and echo. We also generate optically addressable entanglement between the electron and adjacent nitrogen nuclear spin. High-fidelity operations are achieved by applying amplitude-alternating pulses, which are tolerant to fluctuations in microwave intensity and detuning. These techniques enable site-selective quantum teleportation transfer from a photon to a nuclear spin memory, paving the way for the realization of distributed quantum computers and the quantum Internet with large-scale quantum storage.

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Fig. 1: Principle of optically addressable universal holonomic gates.
Fig. 2: Experimental demonstration of the gate contrast depending on the laser power or the NV position.
Fig. 3: Experimental demonstration of optically addressable universal single-qubit operations.
Fig. 4: Optically addressable entanglement generation.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.

Code availability

All codes used to produce the findings of this study are available from the corresponding author upon request.


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We thank H. Kato, T. Makino, T. Teraji, Y. Matsuzaki, K. Nemoto, N. Mizuochi, F. Jelezko and J. Wrachtrup for their discussions and experimental help. This work was supported by Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (grant numbers 20H05661 and 20K2044120); by the Japan Science and Technology Agency (JST) CREST (grant number JPMJCR1773); and by JST Moonshot R&D (grant number JPMJMS2062). We also acknowledge the assistance of the Ministry of Internal Affairs and Communications (MIC) under the initiative Research and Development for Construction of a Global Quantum Cryptography Network (grant number JPMI00316).

Author information

Authors and Affiliations



Y.S., K.M. and Y.K. carried out the experiment. Y.S. analysed the data. Y.S. and H.K. wrote the manuscript. H.K. supervised the project. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Hideo Kosaka.

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Nature Photonics thanks Philip Hemmer and Tim Hugo Taminiau for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Ramsey interference induced by an optical Stark shift.

a, Ramsey interference at the laser power of 640 nW and the detuning of 1.6 GHz. After initializing the spin to |0〉S, the addressing laser is irradiated during the free evolution time between π/2 pulses of the Ramsey interference (Top). b, Ramsey interference at the laser power of 1440 nW and the detuning of 1.6 GHz. c, Stark shift ΔS as functions of the laser power and detuning. d, Coherence time in the bright space T2Stark as functions of the laser power and detuning. e, Their product ΔST2Stark as functions of the laser power and detuning. Error bars show standard deviations.

Extended Data Fig. 2 Simulations of an amplitude-alternating pulse.

a, b, Fidelity of the X and identity (I) gates implemented by (a) a square envelope pulse and (b) an amplitude-alternating pulse as a function of ΔtMW. The top graphs show the time dependence of the microwave Rabi frequency ΩMW. c, Process fidelity as a function of Rabi frequency error α, which denotes the magnification from ideal Rabi frequency Ω0 as ΩMW = αΩ0. The gate fidelity is defined as |Tr(UsUi)|/2, where Ui and Us denote an ideal gate and a simulated gate.

Extended Data Fig. 3 Numerical simulations of the gate fidelity.

a, b, c, Infidelities of Pauli-X (a), Y (b), and Z (c) gates as a function of the hyperfine splitting. Fidelity is defined as Tr(χsimχi), where χsim, χi denote simulated and ideal gates. Red lines show the active cases and blue lines show the inactive cases.

Extended Data Fig. 4 Experimental sequence of an optically addressable initialization.

First, the optically addressable manipulation transfers |+1〉S into |0〉S by the addressing laser for the optical stark shift of ΔS = 2 MHz (given by ΩL = 80√2 MHz and ΔL = 1.6 GHz) and the amplitude-alternating microwave pulse with Rabi frequency of ΩMW = 2 MHz. Next, a spin pumping by a resonant excitation to |Ey〉 equally distributes the |0〉S population into |±1〉S. This process is repeated 10 times.

Extended Data Fig. 5 Optically addressable nuclear spin manipulations.

a, Experimental sequence of quantum state tomography and quantum process tomography shown in b, c. First, optically addressable electron spin manipulation is performed to an initial state of |0, 0〉S, N. When the electron spin is in |0〉S (|±1〉S) the nuclear spin manipulation is active (inactive). After the manipulations, the electron spin is initialized to |0〉S to readout the nuclear spin state by the repetitive readout of electron spin with CNOT-like gates. b, State probabilities of the six prepared states {|+〉N = (|+1〉N+|−1〉N)/√2, |−〉N = (|+1〉N−|−1〉N)/√2, |+i〉N = (|+1〉N+i|−1〉N)/√2, |−i〉N = (|+1〉Ni|−1〉N)/√2, |+1〉N, |−1〉N}. Without the addressing laser, the nuclear spin state stays in |0〉S. c, Absolute values of χ matrix elements reconstructed by the quantum process tomography for the optically addressable Pauli-X, Y, Z gate. Red (blue) bars are elements with unity (zero) values in the ideal state. Error bars show standard deviations.

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Sekiguchi, Y., Matsushita, K., Kawasaki, Y. et al. Optically addressable universal holonomic quantum gates on diamond spins. Nat. Photon. (2022).

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