Electrical Silicon Spin Qubits: A Probable Route to Scalability

Physical Review A, 2019

A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control-fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking the realistic system parameters and the experimental constraints on the control pulses into account, we construct experimentally realizable high-fidelity CNOT gates robust against electrical noise with the experimentally measured 1/f 1.01 noise spectrum and also against the uncertainty in the interdot tunnel coupling amplitude. Our fine-tuned optimal CNOT gate has about two orders of magnitude improvement in gate infidelity over the ideal C-phase gate constructed without considering any noise effect. Furthermore, within the same control framework, high-fidelity and robust single-qubit gates can also be constructed, paving the way for large-scale FTQC.

Journal of Physics: Condensed Matter, 2006

Given the effectiveness of semiconductor devices for classical computation one is naturally led to consider semiconductor systems for solid state quantum information processing. Semiconductors are particularly suitable where local control of electric fields and charge transport are required. Conventional semiconductor electronics is built upon these capabilities and has demonstrated scaling to large complicated arrays of interconnected devices. However, the requirements for a quantum computer are very different from those for classical computation, and it is not immediately obvious how best to build one in a semiconductor. One possible approach is to use spins as qubits: of nuclei, of electrons, or both in combination. Long qubit coherence times are a prerequisite for quantum computing, and in this paper we will discuss measurements of spin coherence in silicon. The results are encouraging -both electrons bound to donors and the donor nuclei exhibit low decoherence under the right circumstances. Doped silicon thus appears to pass the first test on the road to a quantum computer.

2010

Research on Si quantum dot spin qubits is motivated by the long spin coherence times measured in Si, yet the orbital spectrum of Si dots is increased as a result of the valley degree of freedom. The valley degeneracy may be lifted by the interface potential, which gives rise to a valley-orbit coupling, but the latter depends on the detailed structure of the interface and is generally unknown a priori. These facts motivate us to provide an extensive study of spin qubits in Si double quantum dots, accounting fully for the valley degree of freedom and assuming no prior knowledge of the valleyorbit coupling. For single-spin qubits we analyze the spectrum of a multivalley double quantum dot, discuss the initialization of one qubit, identify the conditions for the lowest energy two-electron states to be a singlet and a triplet well separated from other states, and determine analytical expressions for the exchange splitting. For singlet-triplet qubits we analyze the single-dot spectrum and initialization process, the double-dot spectrum, singlet-triplet mixing in an inhomogeneous magnetic field and the peculiarities of spin blockade in multivalley qubits. We review briefly the hyperfine interaction in Si and discuss its role in spin blockade in natural Si, including intravalley and intervalley effects. We study the evolution of the double-dot spectrum as a function of magnetic field. We address briefly the situation in which the valley-orbit coupling is different in each dot due to interface roughness. We propose a new experiment for measuring the valley splitting in a single quantum dot. We discuss the possibility of devising other types of qubits in Si QDs, and the size of the intervaley coupling due to the Coulomb interaction.

arXiv (Cornell University), 2017

We propose a method to electrically control electron spins in donor-based qubits in silicon. By taking advantage of the hyperfine coupling difference between a single-donor and a two-donor quantum dot, spin rotation can be driven by inducing an electric dipole between them and applying an alternating electric field generated by in-plane gates. These qubits can be coupled with exchange interaction controlled by top detuning gates. The qubit device can be fabricated deep in the silicon lattice with atomic precision by scanning tunneling probe technique. We have combined a large-scale full band atomistic tight-binding modeling approach with a time-dependent effective Hamiltonian description, providing a design with quantitative guidelines.

2018 48th European Solid-State Device Research Conference (ESSDERC), 2018

We present recent advances made towards the realization of hole and electron spin quantum bits (qubits) localized within Si Quantum Dots (QDs). These devices, operated at cryogenic temperatures, can be defined by slightly modifying an SOI NanoWire FET fabrication flow, and are thus particularly relevant in the perspective of large-scale cointegration of qubits and their cryogenic control electronics. I.

APL Photonics, 2021

Paper published as part of the special topic on Integrated Quantum Photonics ARTICLES YOU MAY BE INTERESTED IN Why I am optimistic about the silicon-photonic route to quantum computing APL Photonics 2, 030901 (2017);

Single-Atom Nanoelectronics, 2013

Spins of donor electrons and nuclei in silicon are promising quantum bit (qubit) candidates which combine long coherence times with the fabrication finesse of the silicon nanotechnology industry. We outline a potentially scalable spin qubit architecture where donor nuclear and electron spins are coupled to spins of electrons in quantum dots and discuss requirements for donor placement aligned to quantum dots by single ion implantation.

Solid State Communications, 2005

Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in this review a particularly important spin decoherence channel, and bandstructure effects on the exchange gate control. Specifically, we review our work on donor electron spin spectral diffusion due to background nuclear spin flip-flops, and how isotopic purification of silicon can significantly enhance the electron spin dephasing time. We then review our calculation of donor electron exchange coupling in the presence of degenerate silicon conduction band valleys. We show that valley interference leads to orders of magnitude variations in electron exchange coupling when donor configurations are changed on an atomic scale. These studies illustrate the substantial potential that donor electron/nuclear spins in silicon have as candidates for qubits and simultaneously the considerable challenges they pose. In particular, our work on spin decoherence through spectral diffusion points to the possible importance of isotopic purification in the fabrication of scalable solid state quantum computer architectures. We also provide a critical comparison between the two main proposed spin-based solid state quantum computer architectures, namely, shallow donor bound states in Si and localized quantum dot states in GaAs.

Physical Review Letters, 2012

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers S 2 = 3/4 (S = 1 2 ) and Sz = − 1 2 , with the two different states being singlet and triplet in the doubly occupied dot. The architecture is relatively simple to fabricate, a universal set of fast operations can be implemented electrically, and the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.

Scientific Reports, 2016

Quantum dots patterned by atomically precise placement of phosphorus donors in single crystal silicon have long spin lifetimes, advantages in addressability, large exchange tunability, and are readily available few-electron systems. To be utilized as quantum bits, it is important to non-invasively characterise these donor quantum dots post fabrication and extract the number of bound electron and nuclear spins as well as their locations. Here, we propose a metrology technique based on electron spin resonance (ESR) measurements with the on-chip circuitry already needed for qubit manipulation to obtain atomic scale information about donor quantum dots and their spin configurations. Using atomistic tight-binding technique and Hartree self-consistent field approximation, we show that the ESR transition frequencies are directly related to the number of donors, electrons, and their locations through the electron-nuclear hyperfine interaction. Silicon is an excellent host for spin qubits as it is a spin-free environment with the added advantage of weak spin-orbit coupling. The coherence time of single electron spins bound to phosphorus donors in enriched silicon-28 was measured to be 0.6 s with Hahn echo in bulk 1. Recent advances in scanning tunneling microscope (STM) based lithography 2 have enabled the realization of donor-based QDs buried deep inside silicon far from hetero-interfaces by atomically precise placement of phosphorus donors 3. Electrons bound to these Si:P QDs are confined not by a surface gate potential that depletes the surrounding two dimensional (2D) electron gas, but by the 3D Coulombic potential of a few donors located within ~nanometers of each other, and form readily available few-electron systems. These donors can be addressed by in-plane gates also fabricated by STM lithography 4. Already, transport spectroscopy has been performed on single, double, and triple QDs of Si:P 5-7 , and single-electron spin readout and two-electron spin blockade have been demonstrated 4,6. Theoretically, it has been shown that Si:P quantum dots can have exceptionally long spin relaxation times 8 , and advantages in addressability 4 as well as large exchange tunability in multi-qubit devices 9. A surface code based potentially scalable architecture has also been proposed recently with STM patterned Si:P dots 10. Spin coherence measurements based on donor ensembles also provide some evidence that buried donors may have better coherence times than donors close to interfaces 11 , which is likely due to deleterious noise sources present near the interface 12. The popular Kane qubit proposal of single phosphorus based quantum computer 13 utilizes an ac-magnetic field for single qubit operations and an inter-donor exchange coupling for two-qubit operations. Experimentally, ac-magnetic fields have been used to perform electron spin resonance (ESR) and nuclear magnetic resonance (NMR) on single phosphorus electron 14 and nuclear spins 15 respectively. Recently, a two-qubit logic gate in gate-defined silicon QDs has also been demonstrated with ESR based single qubit control 16. To utilize Si:P QDs as spin qubits, it is important to know the precise number of electron and nuclear spins bound to these dots, which can also help to identify appropriate spin transitions of the qubit and to deplete the dots down to the ideal regime of one electron occupation. Understanding the extent of the electron wavefunctions of the donor dots is important for optimizing the inter-dot exchange and tunnel coupling useful for two-qubit gates. In this work, we present a metrological method based on a non-invasive atomic-scale characterization technique to extract information about the donor numbers, electron numbers, and donor locations based on ESR measurements using the on-chip circuitry already needed for qubit manipulation. The method relies on probing the spin splittings of the donor dots through the electron-nucleus hyperfine coupling which is sensitive to atomic-scale details of the donor dot.