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Dehollain JP, Mukhopadhyay U, Michal VP, Wang Y, Wunsch B, Reichl C, Wegscheider W, Rudner MS, Demler E, Vandersypen LMK. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature 2020; 579:528-533. [PMID: 32123352 DOI: 10.1038/s41586-020-2051-0] [Citation(s) in RCA: 46] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2019] [Accepted: 01/08/2020] [Indexed: 11/09/2022]
Abstract
Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers1. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots4 to demonstrate Nagaoka ferromagnetism5. This form of itinerant magnetism has been rigorously studied theoretically6-9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems.
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Affiliation(s)
- J P Dehollain
- QuTech, TU Delft, Delft, The Netherlands.,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands.,School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, New South Wales, Australia
| | - U Mukhopadhyay
- QuTech, TU Delft, Delft, The Netherlands.,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands
| | - V P Michal
- QuTech, TU Delft, Delft, The Netherlands.,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands
| | - Y Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - B Wunsch
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - C Reichl
- Solid State Physics Laboratory, ETH Zürich, Zürich, Switzerland
| | - W Wegscheider
- Solid State Physics Laboratory, ETH Zürich, Zürich, Switzerland
| | - M S Rudner
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.,Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - E Demler
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - L M K Vandersypen
- QuTech, TU Delft, Delft, The Netherlands. .,Kavli Institute of Nanoscience, TU Delft, Delft, The Netherlands.
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Muhonen JT, Laucht A, Simmons S, Dehollain JP, Kalra R, Hudson FE, Freer S, Itoh KM, Jamieson DN, McCallum JC, Dzurak AS, Morello A. Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking. J Phys Condens Matter 2015; 27:154205. [PMID: 25783435 DOI: 10.1088/0953-8984/27/15/154205] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual (31)P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized (31)P nucleus of a single P donor in isotopically purified (28)Si. We find average gate fidelities of 99.95% for the electron and 99.99% for the nuclear spin. These values are above certain error correction thresholds and demonstrate the potential of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware and not the intrinsic behaviour of the qubit.
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Affiliation(s)
- J T Muhonen
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, NSW 2052, Australia
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Veldhorst M, Hwang JCC, Yang CH, Leenstra AW, de Ronde B, Dehollain JP, Muhonen JT, Hudson FE, Itoh KM, Morello A, Dzurak AS. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat Nanotechnol 2014; 9:981-985. [PMID: 25305743 DOI: 10.1038/nnano.2014.216] [Citation(s) in RCA: 191] [Impact Index Per Article: 19.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2014] [Accepted: 08/28/2014] [Indexed: 06/04/2023]
Abstract
Exciting progress towards spin-based quantum computing has recently been made with qubits realized using nitrogen-vacancy centres in diamond and phosphorus atoms in silicon. For example, long coherence times were made possible by the presence of spin-free isotopes of carbon and silicon. However, despite promising single-atom nanotechnologies, there remain substantial challenges in coupling such qubits and addressing them individually. Conversely, lithographically defined quantum dots have an exchange coupling that can be precisely engineered, but strong coupling to noise has severely limited their dephasing times and control fidelities. Here, we combine the best aspects of both spin qubit schemes and demonstrate a gate-addressable quantum dot qubit in isotopically engineered silicon with a control fidelity of 99.6%, obtained via Clifford-based randomized benchmarking and consistent with that required for fault-tolerant quantum computing. This qubit has dephasing time T2* = 120 μs and coherence time T2 = 28 ms, both orders of magnitude larger than in other types of semiconductor qubit. By gate-voltage-tuning the electron g*-factor we can Stark shift the electron spin resonance frequency by more than 3,000 times the 2.4 kHz electron spin resonance linewidth, providing a direct route to large-scale arrays of addressable high-fidelity qubits that are compatible with existing manufacturing technologies.
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Affiliation(s)
- M Veldhorst
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - J C C Hwang
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - C H Yang
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - A W Leenstra
- University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
| | - B de Ronde
- University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
| | - J P Dehollain
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - J T Muhonen
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - F E Hudson
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - K M Itoh
- School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - A Morello
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - A S Dzurak
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia
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Abstract
The intense interest in spin-based quantum information processing has caused an increasing overlap between the two traditionally distinct disciplines of magnetic resonance and nanotechnology. In this work we discuss rigorous design guidelines to integrate microwave circuits with charge-sensitive nanostructures, and describe how to simulate such structures accurately and efficiently. We present a new design for an on-chip, broadband, nanoscale microwave line that optimizes the magnetic field used to drive a spin-based quantum bit (or qubit) while minimizing the disturbance to a nearby charge sensor. This new structure was successfully employed in a single-spin qubit experiment, and shows that the simulations accurately predict the magnetic field values even at frequencies as high as 30 GHz.
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Affiliation(s)
- J P Dehollain
- Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney NSW 2052, Australia.
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