Single-shot readout and relaxation of singlet and triplet states in exchange-coupled 31P electron spins in silicon

The multi-photon induced Fano effect

The ordinary Fano effect occurs in many-electron atoms and requires an autoionizing state. With such a state, photo-ionization may proceed via pathways that interfere, and the characteristic asymmetric resonance structures appear in the continuum. Here we demonstrate that Fano structure may also be induced without need of auto-ionization, by dressing the continuum with an ordinary bound state in any atom by a coupling laser. Using multi-photon processes gives complete, ultra-fast control over the interference. We show that a line-shape index q near unity (maximum asymmetry) may be produced in hydrogenic silicon donors with a relatively weak beam. Since the Fano lineshape has both constructive and destructive interference, the laser control opens the possibility of state-selective detection with enhancement on one side of resonance and invisibility on the other. We discuss a variety of atomic and molecular spectroscopies, and in the case of silicon donors we provide a calculation for a qubit readout application.

Fano resonances occur in many platforms that have auto-ionizing states. Here the authors show that auto-ionizing states are not required for multi-photon Fano resonance in a Si:P system with significant screening by using a pump-probe method.

Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device

Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single-donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of ³¹P donors implanted in silicon. The coupling strength, J = 32.06 ± 0.06 MHz, is measured spectroscopically with high precision. Since the coupling is weaker than the electron-nuclear hyperfine coupling A ≈ 90 MHz which detunes the two electrons, a native two-qubit controlled-rotation gate can be obtained via a simple electron spin resonance pulse. This scheme is insensitive to the precise value of J, which makes it suitable for the scale-up of donor-based quantum computers in silicon that exploit the metal-oxide-semiconductor fabrication protocols commonly used in the classical electronics industry.

Valley interference and spin exchange at the atomic scale in silicon

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Coupled donor wavefunctions in silicon are spatially resolved to evidence valley interference processes. An atomic-scale understanding of the interplay between interference, envelope anisotropy and crystal symmetries unveils a placement strategy compatible with existing technology where the exchange is insensitive to interference.

Semiconductor quantum computation

Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In recent decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The research varied from initialization, control and readout of qubits, to the architecture of fault-tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single- and two-qubit gate control in semiconductors. Up to now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor has even been demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of the readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.

Nanometrology of field gradient using donor spins in silicon

We proposed a novel scheme for nanometrology of magnetic field gradient based on Kane's silicon quantum computer proposal. When the system is placed in an unknown magnetic field gradient, the inhomogeneous precession of the donor nuclear spins records the field gradient information to the phase pattern of donor nuclear spins. By adding AC voltage modulations on each A-gate to induce hyperfine-mediated electron-nuclear collective flip-flop process, we demonstrate that the gradient value can be obtained by tuning the modulation phases of the A-gates. Errors of the measurements of such scheme is discussed and estimated. It is also discussed that in presence of the external field with a known gradient, the same system is possible to be used to obtain the unknown displacement of donor locations.

Coherent coupling between a quantum dot and a donor in silicon

Individual donors in silicon chips are used as quantum bits with extremely low error rates. However, physical realizations have been limited to one donor because their atomic size causes fabrication challenges. Quantum dot qubits, in contrast, are highly adjustable using electrical gate voltages. This adjustability could be leveraged to deterministically couple donors to quantum dots in arrays of qubits. In this work, we demonstrate the coherent interaction of a ³¹P donor electron with the electron of a metal-oxide-semiconductor quantum dot. We form a logical qubit encoded in the spin singlet and triplet states of the two-electron system. We show that the donor nuclear spin drives coherent rotations between the electronic qubit states through the contact hyperfine interaction. This provides every key element for compact two-electron spin qubits requiring only a single dot and no additional magnetic field gradients, as well as a means to interact with the nuclear spin qubit.

In silicon, quantum information can be stored in donors or quantum dots, each with its advantages and limitations—particularly in terms of fabrication. Here the authors coherently couple a phosphorous donor’s electron spin to a quantum dot, encoding information in the hybrid two-electron system’s state.

Quantum information processing with superconducting circuits: a review

During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

Silicon quantum processor with robust long-distance qubit couplings

Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.

High-Fidelity Single-Shot Singlet-Triplet Readout of Precision-Placed Donors in Silicon

In this work we perform direct single-shot readout of the singlet-triplet states in exchange coupled electrons confined to precision-placed donor atoms in silicon. Our method takes advantage of the large energy splitting given by the Pauli-spin blockaded (2,0) triplet states, from which we can achieve a single-shot readout fidelity of 98.4±0.2%. We measure the triplet-minus relaxation time to be of the order 3 s at 2.5 T and observe its predicted decrease as a function of magnetic field, reaching 0.5 s at 1 T.

Observation of current-induced, long-lived persistent spin polarization in a topological insulator: A rechargeable spin battery

Topological insulators (TIs), with their helically spin-momentum-locked topological surface states (TSSs), are considered promising for spintronics applications. Several recent experiments in TIs have demonstrated a current-induced electronic spin polarization that may be used for all-electrical spin generation and injection. We report spin potentiometric measurements in TIs that have revealed a long-lived persistent electron spin polarization even at zero current. Unaffected by a small bias current and persisting for several days at low temperature, the spin polarization can be induced and reversed by a large "writing" current applied for an extended time. Although the exact mechanism responsible for the observed long-lived persistent spin polarization remains to be better understood, we speculate on possible roles played by nuclear spins hyperfine-coupled to TSS electrons and dynamically polarized by the spin-helical writing current. Such an electrically controlled persistent spin polarization with unprecedented long lifetime could enable a rechargeable spin battery and rewritable spin memory for potential applications in spintronics and quantum information.

Single-Shot Ternary Readout of Two-Electron Spin States in a Quantum Dot Using Spin Filtering by Quantum Hall Edge States

We report on the single-shot readout of three two-electron spin states-a singlet and two triplet substates-whose z components of spin angular momentum are 0 and +1, in a gate-defined GaAs single quantum dot. The three spin states are distinguished by detecting spin-dependent tunnel rates that arise from two mechanisms: spin filtering by spin-resolved edge states and spin-orbital correlation with orbital-dependent tunneling. The three states form one ground state and two excited states, and we observe the spin relaxation dynamics among the three spin states.

Single donor electronics and quantum functionalities with advanced CMOS technology

Recent progresses in quantum dots technology allow fundamental studies of single donors in various semiconductor nanostructures. For the prospect of applications figures of merits such as scalability, tunability, and operation at relatively large temperature are of prime importance. Beyond the case of actual dopant atoms in a host crystal, similar arguments hold for small enough quantum dots which behave as artificial atoms, for instance for single spin control and manipulation. In this context, this experimental review focuses on the silicon-on-insulator devices produced within microelectronics facilities with only very minor modifications to the current industrial CMOS process and tools. This is required for scalability and enabled by shallow trench or mesa isolation. It also paves the way for real integration with conventional circuits, as illustrated by a nanoscale device coupled to a CMOS circuit producing a radio-frequency drive on-chip. At the device level we emphasize the central role of electrostatics in etched silicon nanowire transistors, which allows to understand the characteristics in the full range from zero to room temperature.

Interface effects on acceptor qubits in silicon and germanium

Dopant-based quantum computing implementations often require the dopants to be situated close to an interface to facilitate qubit manipulation with local gates. Interfaces not only modify the energies of the bound states but also affect their symmetry. Making use of the successful effective mass theory we study the energy spectra of acceptors in Si or Ge taking into account the quantum confinement, the dielectric mismatch and the central cell effects. The presence of an interface puts constraints to the allowed symmetries and leads to the splitting of the ground state in two Kramers doublets (Mol et al 2015 Appl. Phys. Lett. 106 203110). Inversion symmetry breaking also implies parity mixing which affects the allowed optical transitions. Consequences for acceptor qubits are discussed.

Electrical current through individual pairs of phosphorus donor atoms and silicon dangling bonds

Nuclear spins of phosphorus [P] donor atoms in crystalline silicon are among the most coherent qubits found in nature. For their utilization in scalable quantum computers, distinct donor electron wavefunctions must be controlled and probed through electrical coupling by application of either highly localized electric fields or spin-selective currents. Due to the strong modulation of the P-donor wavefunction by the silicon lattice, such electrical coupling requires atomic spatial accuracy. Here, the spatially controlled application of electrical current through individual pairs of phosphorus donor electron states in crystalline silicon and silicon dangling bond states at the crystalline silicon (100) surface is demonstrated using a high‐resolution scanning probe microscope operated under ultra‐high vacuum and at a temperature of 4.3K. The observed pairs of electron states display qualitatively reproducible current-voltage characteristics with a monotonous increase and intermediate current plateaus.

Single atom devices by ion implantation

To expand the capabilities of semiconductor devices for new functions exploiting the quantum states of single donors or other impurity atoms requires a deterministic fabrication method. Ion implantation is a standard tool of the semiconductor industry and we have developed pathways to deterministic ion implantation to address this challenge. Although ion straggling limits the precision with which atoms can be positioned, for single atom devices it is possible to use post-implantation techniques to locate favourably placed atoms in devices for control and readout. However, large-scale devices will require improved precision. We examine here how the method of ion beam induced charge, already demonstrated for the deterministic ion implantation of 14 keV P donor atoms in silicon, can be used to implant a non-Poisson distribution of ions in silicon. Further, we demonstrate the method can be developed to higher precision by the incorporation of new deterministic ion implantation strategies that employ on-chip detectors with internal charge gain. In a silicon device we show a pulse height spectrum for 14 keV P ion impact that shows an internal gain of 3 that has the potential of allowing deterministic implantation of sub-14 keV P ions with reduced straggling.

Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking

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.

Theory of one and two donors in silicon

We provide here a roadmap for modeling silicon nano-devices with one or two group V donors (D). We discuss systems containing one or two electrons, that is, D(0), D(-), D(+)(2) and D(0)(2) centers. The impact of different levels of approximation is discussed. The most accurate instances--for which we provide quantitative results--are within multivalley effective mass including the central cell correction and a configuration interaction account of the electron-electron correlations. We also derive insightful, yet less accurate, analytical approximations and discuss their validity and limitations--in particular, for a donor pair, we discuss the single orbital LCAO method, the Hückel approximation and the Hubbard model. Finally, we connect these results with recent experiments on devices with few dopants.

An exchange-coupled donor molecule in silicon

We present a combined experimental-theoretical demonstration of the energy spectrum and exchange coupling of an isolated donor pair in a silicon nanotransistor. The molecular hybridization of the atomic orbitals leads to an enhancement of the one- and two-electron binding energies and charging energy with respect to the single donor case, a desirable feature for quantum electronic devices. Our hydrogen molecule-like model based on a multivalley central-cell corrected effective mass theory incorporating a full configuration interaction treatment of the 2-electron spectrum matches the measured data for an arsenic diatomic molecule with interatomic distance R = 2.3 ± 0.5 nm.