Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session B37: Quantum Computing with Donor Spins IFocus Recordings Available

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Sponsoring Units: DQI Chair: Will Koehl, HRL Room: McCormick Place W194B 
Monday, March 14, 2022 11:30AM  11:42AM 
B37.00001: Fabrication and Characterization of Dopantbased 2D Lattices for Analog Quantum Simulation of an Extended Fermi Hubbard Model Xiqiao Wang, Ehsan Khatami, Fan Fei, Jonathan Wyrick, Pradeep Namboodiri, ranjit V Kashid, Albert F Rigosi, Garnett W Bryant, Richard M Silver The Hubbard model is one of the primary models for understanding the essential manybody physics in condensed matter systems such as Mott insulators and cuprate highTc superconductors. Recent advances in atomically precise fabrication in silicon using scanning tunneling microscopy (STM) have made possible atombyatom fabrication of single and fewdopant quantum dots and atomicscale control of tunneling in dopantbased devices, enabling the engineering of dopantbased artificial lattices with atomicscale precision. In this talk, we present our recent experimental implementation of STMfabricated 3x3 arrays of fewdopant quantum dots as a tunable 2D artificial lattice. We discuss tuning of the array parameters, such as the electron ensemble, hopping and longrange interactions, and thermal activations within the arrays, and probing different manybody properties within the array using lowtemperature transport. The results demonstrate the viability of simulating extended FermiHubbard Hamiltonians using dopantbased 2D artificial lattices having finite disorder. 
Monday, March 14, 2022 11:42AM  11:54AM 
B37.00002: Numerical Study of the Extended FermiHubbard Model Simulated in a Lattice of Quantum Dots Ehsan Khatami, Xiqiao Wang, Fan Fei, Jonathan Wyrick, Pradeep Namboodiri, ranjit V Kashid, Albert F Rigosi, Garnett W Bryant, Richard M Silver The extended FermiHubbard model has recently been realized in an artificial lattice of dopantbased quantum dots in silicon [1]. It is shown that parameters such as the nearestneighbor hopping amplitude and local as well as longrange interactions can be effectively tuned using controlled placement of dopant atoms with atomicscale precision. Access to low temperatures, the permanent nature of array systems, and the availability of measurement tools in a condensed matter setting make them an exciting new class of engineered artificial lattices to simulate FermiHubbard models. In this talk, I will discuss the numerical results for charge stability diagrams and lowtemperature transport properties of 3x3 arrays used to verify the experimental observation of the finitesize analogue of a Mott insulating to metallic transition. 
Monday, March 14, 2022 11:54AM  12:06PM 
B37.00003: Magnetic Shifts of Coulomb Peaks in Strongly Coupled Quantum Dot Array in Silicon Fan Fei, Xiqiao Wang, Ehsan Khatami, Jonathan Wyrick, ranjit V Kashid, Pradeep Namboodiri, Garnett W Bryant, Richard M Silver Atomically precise donorbased quantum devices in silicon are fabricated using STM lithography, which has become a promising platform for solid state quantum computation and analog quantum simulation. Recently, we have been made arrayed quantum dot devices with varying array constants to include coupling regimes from weak to strong. As the array constants become smaller, the individual dots no longer act as discrete sites with localized electrons in the FermiHubbard model and instead behave as a single, large coherent quantum construct with complex internal structure and electrons occupying many body eigenstates across the array. I will discuss the behavior of arrayed quantum dots in the strongly coupled regime where the electrons delocalize across the ordered 3x3 dot arrays. We describe quantum transport measurements through the arrays. We apply an external magnetic field to explore the effects on charge/spin configurations inside the arrays. The positions of the Coulomb peaks shift in complex ways revealing the subtle dependence of the array energy spectrum on an external B field. We quantify the magnetic field induced shifts in the electron addition spectrum of our quantum dot arrays and analyze the addition spectrum using a generalized FermiHubbard model from the strong to weak coupling regime. 
Monday, March 14, 2022 12:06PM  12:18PM 
B37.00004: TightBinding Configuration Interaction Formalism for PDoped Silicon Nanodevices Maicol A Ochoa, Keyi Liu, Michal Gawelczyk, Michal Zielinski, Garnett W Bryant Atomscale Silicon quantum devices incorporating dopants with atomic precision are promising platforms for future quantum computing technologies. This dopant placement precision allows for finetuning device properties, such as tunnel couplings and charging energies, making dopant array structures ideal for exploring manybody physics. Additional control is achieved with atomically aligned contacts. Accurate electronic structure calculations are needed to understand how the dopant placement determines state properties. We introduce an efficient formalism for calculating the electronic and transport properties on realistic devices. Our approach combines tightbinding calculations for the silicon matrix and configuration interaction level theory for the multielectron charged states of dopant structures, incorporating electronelectron interactions and corrections due to exchange and correlation. We present detailed calculations of devices with two, three, and four P atoms in different configurations and their corresponding stability diagrams. By comparing with the FermiHubbard model and HartreeFock level theory predictions, we show when exchange and correlation effects and coupling to higher energy orbitals are relevant in predicting the stability diagrams of these devices. 
Monday, March 14, 2022 12:18PM  12:30PM 
B37.00005: Single Dopant Placement for Quantum Applications:Reacting Phosphine withAtomic PrecisionDangling Bond Structures Jonathan Wyrick, Xiqiao Wang, Pradeep Namboodiri, Fan Fei, Joseph B Fox, Richard M Silver The use of STMbased hydrogen depassivation lithography (HDL) to position P atoms in silicon is now a proven platform for quantum devices (e.g. qubit and analog quantum simulation architectures). The electronic and nuclear properties at key sites of these devices such as spin, on site Coulomb repulsion, local chemical potential, etc., depend critically on the precise number of P atoms at a site. Despite the high degree of positional control demonstrated by HDL of +/1 nm, it has proven difficult to ensure true single P atom placement as opposed to small clusters of P atoms. To address this, we experimentally explore two lithographic structures capable of hosting the P precursor molecule, phosphine, and develop strategies for using them to incorporate single P atoms. By perfecting these strategies we hope to achieve precision control over both P atom position and number in silicon enabling a higher complexity of quantum devices than what is currently possible. 
Monday, March 14, 2022 12:30PM  12:42PM 
B37.00006: Dopant arrays in Si as quantum simulators of magnetic field effects Garnett W Bryant, Yan Li, Emily Townsend, Michal Gawelczyk, Michal Zielinski Atomically precise fabrication of dopant arrays in Si provides exciting opportunities to perform quantum simulations and study the dynamics of engineered quantum systems. We describe theoretical simulations done for twodimensional arrays of dopants in Si in a magnetic field. An extended range FermiHubbard model with a magnetic field is studied. Theoretical simulations are done for a range of magnetic fields, as a function of the electronelectron interaction to test the limits of weak and strong interaction. 2x2 arrays are considered to show the effects of magnetic field on interacting electrons when there is a single plaquette. Recent quantumdot experiments have shown that Nagaoka ferromagnetism can be realized in these structures. 3x3 dopant arrays are also studied theoretically as an example of magnetic field effects when there are four connected plaquettes. Experiments on 3x3 dopant structures have been recently started at NIST. Timedependent studies of these arrays have been developed to model the evolution of the local charge distribution in the array during transport. Results will be presented with and without a magnetic field to show how the magnetic field changes the local transport of charge through an array with interacting electrons. 
Monday, March 14, 2022 12:42PM  1:18PM 
B37.00007: Precision tomography of a threequbit electronnuclear quantum processor in silicon Invited Speaker: Mateusz T Madzik Nuclear spins were among the first physical platforms to be considered for quantum information processing, because of their exceptional quantum coherence and atomicscale footprint. However, their full potential for quantum computing has not yet been realized, due to the lack of methods to link nuclear qubits within a scalable device combined with multiqubit operations with sufficient fidelity to sustain faulttolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ionimplanted 31P nuclei in a silicon nanoelectronic device. A nuclear twoqubit controlledZ gate is obtained by imparting a geometric phase to a shared electron spin, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterised using gate set tomography (GST) yielding onequbit average gate fidelities up to 99.95(2)%, twoqubit average gate fidelity of 99.37(11)% and twoqubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in faulttolerant quantum processors. We then demonstrate entanglement between the two nuclei and the shared electron by producing a GreenbergerHorneZeilinger threequbit state with 92.5(1.0)% fidelity. Since electron spin qubits in semiconductors can be further coupled to other electrons or physically shuttled across different locations these results establish a viable route for scalable quantum information processing using nuclear spins. 
Monday, March 14, 2022 1:18PM  1:30PM 
B37.00008: Current Paths in an Atomic Precision Advanced Manufactured Device Imaged by Nitrogen Vacancy Diamond Magnetic Microscopy Luca Basso, Pauli Kehayias, Jacob D Henshaw, Heejun Byeon, Maziar Saleh Ziabari, Deanna M Campbell, Ezra Bussmann, Shashank Misra, Michael P Lilly, Andrew M Mounce Atomicprecision (AP) Si:P Ddoped materials are a channel to new microelectronics technologies based on quantumconfined 2D electron transport in Si. Critical questions include where current flow is actually occurring in or near AP structures. To identify flow and leakage paths, we performed ensemble NitrogenVacancy (NV) widefield magnetic imaging of current densities, J, in AP material, over a mmfield of view with µmresolution. AP material was patterned into Halleffect devices shaped like mmsized ribbons. We integrated the AP device with the diamond sensor, a bulk diamond having a 12C enriched, 4 μmthick, NV ensemble on the surface. Then, we used an NV widefield magnetometer to map the magnetic (B) field from J flowing through these devices. From the Bfield map we reconstructed the J density vector field, which allowed us to detect device failures, such as choke points where flow is impeded, as well as current leakage paths. We found that transport is predominantly 2D, highly confined to the AP doping with small vicinal leakage while choke points result from materials defects. Our results bode well for leveraging extreme lithographic precision of AP devices in technologies at T≥300K. 
Monday, March 14, 2022 1:30PM  1:42PM 
B37.00009: Readout and coherent control of precision atom qubits in isotopically pure silicon Pascal Macha, Jonathan Reiner, Yousun Chung, Saiful H Misha, Samuel K Gorman, Ludwik Kranz, Ian Thorvaldson, Serjaum Monir, Sam Sutherland, Brandur Thorgrimsson, Rajib Rahman, Joris G Keizer, Michelle Y Simmons The ability to address and individually control nuclear spins in solid state systems [1,2] has established them amongst the most promising platforms for quantum information science. Nuclear spin qubits in silicon in particular have demonstrated the longest coherence times by isotopically purifying the silicon host material, thereby eliminating the most dominant decoherence mechanism [3]. Here we demonstrate singleshot spin readout and control of multiple nuclear spins in precision engineered multidonor quantum dot qubits [4,5] realised in 210 ppm isotopically pure Si28. This work demonstrates the advantages of multiple donor nuclei in the operation of donorbased qubits. 
Monday, March 14, 2022 1:42PM  1:54PM 
B37.00010: Coherent electrical control of an electronnuclear flipflop qubit in silicon Tim Botzem, Rostyslav Savytskyy, Irene Fernandez De Fuentes, Kohei M Itoh, David N Jamieson, Fay E Hudson, Andrew S Dzurak, Andrea Morello Donors in silicon provide a wellestablished platform for highly coherent spin qubits. Operated as individual electron or nuclear spin qubits, coherent control requires oscillating magnetic fields which are challenging to generate locally and result in slow qubit drive. Encoding quantum information in the combined antiparallel electronnuclear flipflop states instead, allows for electrical control as the hyperfine interaction becomes susceptible to electric fields when displacing the electron away from the donor nucleus. Contrary to magnetic fields, local electric fields can be generated straightforwardly by leveraging existing gate electrodes. Here, we present coherent electric control of an implanted Phosphorus flipflop qubit via hyperfinemodulated electric dipole spin resonance (EDSR). The electric drive leads to a Rabi frequency of up to 117.7 kHz, 5 times faster than traditional nuclear magnetic resonance techniques. We discuss coherence times and benchmark the control fidelities of the flipflop qubit. The electric drive mechanism is applicable to both, topdown and bottomup donor devices, and in combination with nuclear electric resonance offers a pathway to allelectrical control in donorbased quantum processors. 
Monday, March 14, 2022 1:54PM  2:06PM 
B37.00011: Isotopic enrichment of silicon by high fluence^{28}Si^{}ion implantation Danielle Holmes, Brett C Johnson, Cassandra Chua, Benoit Voisin, Sacha Kocsis, Simon G Robson, Jeffrey C McCallum, Dane R McCamey, Sven Rogge, David N Jamieson Spins in the “semiconductor vacuum” of silicon28 (^{28}Si) are suitable qubit candidates due to their long coherence times. An isotopically purified substrate of ^{28}Si is required to limit the decoherence pathway caused by magnetic perturbations from surrounding ^{29}Si nuclear spins (I = 1/2), present in natural Si (^{nat}Si) at an abundance of 4.67%. We isotopically enrich surface layers of ^{nat}Si by sputtering using high fluence ^{28}Si^{−} implantation. Phosphorus (P) donors implanted into one such ^{28}Si layer with ∼3000 ppm ^{29}Si, produced by implanting 30 keV ^{28}Si^{−} ions at a fluence of 4 × 10^{18} cm^{−2}, were measured with pulsed electron spin resonance, confirming successful donor activation upon annealing. The monoexponential decay of the Hahn echo signal indicates a depletion of ^{29}Si. A coherence time of T_{2} = 285 ± 14 μs is extracted, which is longer than that obtained in ^{nat}Si for similar doping concentrations and can be increased by reducing the P concentration in the future. Guided by simulations, the isotopic enrichment was improved by employing oneforone ion sputtering using 45 keV ^{28}Si^{−} implanted with a fluence of 2.63 × 10^{18} cm^{−2} into ^{nat}Si. This resulted in an isotopically enriched surface layer ∼100 nm thick, suitable for providing a sufficient volume of ^{28}Si for donor qubits implanted into the nearsurface region. We observe a depletion of ^{29}Si to 250 ppm as measured by secondary ion mass spectrometry. The impurity content and the crystallization kinetics via solid phase epitaxy are discussed. The ^{28}Si layer is confirmed to be a single crystal using transmission electron microscopy. This method of Si isotopic enrichment shows promise for incorporation into the fabrication process flow of Si spinqubit devices. 
Monday, March 14, 2022 2:06PM  2:18PM 
B37.00012: Impact of nuclear spin dynamics on twoqubit SWAP oscillations in donors Ludwik Kranz, Samuel K Gorman, Brandur Thorgrimsson, Serajim Monir, Yu He, Daniel Keith, Joris G Keizer, Rajib Rahman, Michelle Y Simmons Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While the control of the individual electron spin and nuclear spin has been demonstrated, the interplay between electron and nuclear spins in multiqubit architectures remains unexplored experimentally. Here, we investigate the role that the phosphorus nuclear spins play during the exchangebased operations between donorbound electron spins. We perform coherent exchange oscillations between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. We observe beating in exchange oscillations which arises from the dynamics of nuclear spins that effectively modulate the energy difference between the antiparallel electron spin states ↓↑〉and ↑↓〉. Based on the observed beating, we determine the individual hyperfine couplings between electron spin and each of the qubithosting nuclear spins. From this result we infer the corresponding crystallographic arrangements of phosphorus atoms for each qubit, which constitutes a unique metrology technique in which probing the Hamiltonian of a multispin donorbased system provides an insight into the atomic composition of qubits. Furthermore, we demonstrate strategies for achieving high fidelity twoqubit √SWAP gate fidelities. The framework presented here can be used for designing donor qubits to optimise interqubit operations. 
Monday, March 14, 2022 2:18PM  2:30PM 
B37.00013: Tomography of universal twoqubit logic operations in exchangecoupled donor electron spin qubits Holly G Stemp, Serwan Asaad, Mark A Johnson, Mateusz T Mądzik, Amber J Heskes, Hannes R Firgau, Arne Laucht, Kenneth M Rudinger, Robin J BlumeKohout, Fay E Hudson, Andrew S Dzurak, Kohei M Itoh, Alexander M Jakob, Brett C Johnson, David N Jamieson, Andrea Morello Scalable quantum processors require highfidelity universal quantum logic operations, in a manufacturable physical platform. The spin of an electron bound to a single donor atom in silicon has shown coherence times of almost a second, with single qubit quantum operation fidelities of over 99.9%. Here we present the experimental demonstration and tomography of universal 1 and 2qubit gates in a system of two weakly exchangecoupled electrons, with each electron bound to a single donor phosphorus nucleus. By deterministically preparing the two nuclear spins in opposite directions, each electron spin resonance pulse constitutes a native conditional twoqubit gate. We carefully benchmark the fidelity of these native operations using the technique of gate set tomography (GST), achieving qubit gate fidelities above 99% for both electrons separately. We show that, as a result of working in the weak exchange regime, this coupling mechanism has negligible effect on qubit coherence. The GST method provides precious insights into the nature of the residual errors, and informs strategies for further improvement. 
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