Single-shot read-out of an individual electron spin in a quantum dot

Self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom

Usually, the hyperparallel quantum computation can speed up quantum computing, reduce the quantum resource consumed largely, resist to noise, and simplify the storage of quantum information. Here, we present the first scheme for the self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom of photon systems simultaneously. It can prevent bit-flip errors from happening with an imperfect nonlinear interaction in the nearly realistic condition. We give the way to design the universal hyperparallel photonic quantum controlled-NOT (CNOT) gate on a two-photon system, resorting to the nonlinear interaction between the circularly polarized photon and the electron spin in the quantum dot in a double-sided microcavity system, by taking the imperfect interaction in the nearly realistic condition into account. Its self-error-corrected pattern prevents the bit-flip errors from happening in the hyperparallel quantum CNOT gate, guarantees the robust fidelity, and relaxes the requirement for its experiment. Meanwhile, this scheme works in a failure-heralded way. Also, we generalize this approach to achieve the self-error-corrected hyperparallel quantum CNOTN gate working on a multiple-photon system. These good features make this scheme more useful in the photonic quantum computation and quantum communication in the future.

Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond

The diamond nitrogen-vacancy (NV) center is a leading platform for quantum information science due to its optical addressability and room-temperature spin coherence. However, measurements of the NV center’s spin state typically require averaging over many cycles to overcome noise. Here, we review several approaches to improve the readout performance and highlight future avenues of research that could enable single-shot electron-spin readout at room temperature.

Spin Lifetime and Charge Noise in Hot Silicon Quantum Dot Qubits

We investigate the magnetic field and temperature dependence of the single-electron spin lifetime in silicon quantum dots and find a lifetime of 2.8 ms at a temperature of 1.1 K. We develop a model based on spin-valley mixing and find that Johnson noise and two-phonon processes limit relaxation at low and high temperature, respectively. We also investigate the effect of temperature on charge noise and find a linear dependence up to 4 K. These results contribute to the understanding of relaxation in silicon quantum dots and are promising for qubit operation at elevated temperatures.

Fast and Unconditional All-Microwave Reset of a Superconducting Qubit

Active qubit reset is a key operation in many quantum algorithms, and particularly in quantum error correction. Here, we experimentally demonstrate a reset scheme for a three-level transmon artificial atom coupled to a large bandwidth resonator. The reset protocol uses a microwave-induced interaction between the |f,0⟩ and |g,1⟩ states of the coupled transmon-resonator system, with |g⟩ and |f⟩ denoting the ground and second excited states of the transmon, and |0⟩ and |1⟩ the photon Fock states of the resonator. We characterize the reset process and demonstrate reinitialization of the transmon-resonator system to its ground state in less than 500 ns and with 0.2% residual excitation. Our protocol is of practical interest as it has no additional architectural requirements beyond those needed for fast and efficient single-shot readout of transmons, and does not require feedback.

Scheme for media conversion between electronic spin and photonic orbital angular momentum based on photonic nanocavity

Light with nonzero orbital angular momentum (OAM) or twisted light is promising for quantum communication applications such as OAM-entangled photonic qubits. Methods and devices for the conversion of the photonic OAM to photonic spin angular momentum (SAM), as well as for the photonic SAM to electronic SAM transformation are known but the direct conversion between the photonic OAM and electronic SAM is not available within a single device. Here, we propose a scheme which converts photonic OAM to electronic SAM and vice versa within a single nanophotonic device. We employed a photonic crystal nanocavity with an embedded quantum dot (QD) which confines an electron spin as a stationary qubit. The confined spin-polarized electrons could recombine with holes to give circularly polarized emission, which could drive the rotation of the nanocavity modes via the strong optical spin-orbit interaction. The rotating modes then radiate light with nonzero OAM, allowing this device to serve as a transmitter. As this can be a unitary process, the time-reversed case enables the device to function as a receiver. This scheme could be generalized to other systems with a resonator and quantum emitters such as a microdisk and defects in diamond for example. Our scheme shows the potential for realizing an (ultra)compact electronic SAM-photonic OAM interface to accommodate OAM as an additional degree of freedom for quantum information purposes.

Addressable electron spin resonance using donors and donor molecules in silicon

Phosphorus donor impurities in silicon are a promising candidate for solid-state quantum computing due to their exceptionally long coherence times and high fidelities. However, individual addressability of exchange coupled donors with separations ~15 nm is challenging. We show that by using atomic precision lithography, we can place a single P donor next to a 2P molecule 16 ± 1 nm apart and use their distinctive hyperfine coupling strengths to address qubits at vastly different resonance frequencies. In particular, the single donor yields two hyperfine peaks separated by 97 ± 2.5 MHz, in contrast to the donor molecule that exhibits three peaks separated by 262 ± 10 MHz. Atomistic tight-binding simulations confirm the large hyperfine interaction strength in the 2P molecule with an interdonor separation of ~0.7 nm, consistent with lithographic scanning tunneling microscopy images of the 2P site during device fabrication. We discuss the viability of using donor molecules for built-in addressability of electron spin qubits in silicon.

Two-qubit logical operations in three quantum dots system

We consider a model of two interacting always-on, exchange-only qubits for which controlled phase (CPHASE), controlled NOT (CNOT), quantum Fourier transform (QFT) and SWAP operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the CPHASE gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: CNOT, QFT and SWAP. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations.

Quantum transport through MoS2 constrictions defined by photodoping

We present a device scheme to explore mesoscopic transport through molybdenum disulfide (MoS₂) constrictions using photodoping. The devices are based on van-der-Waals heterostructures where few-layer MoS₂ flakes are partially encapsulated by hexagonal boron nitride (hBN) and covered by a few-layer graphene flake to fabricate electrical contacts. Since the as-fabricated devices are insulating at low temperatures, we use photo-induced remote doping in the hBN substrate to create free charge carriers in the MoS₂ layer. On top of the device, we place additional metal structures, which define the shape of the constriction and act as shadow masks during photodoping of the underlying MoS₂/hBN heterostructure. Low temperature two- and four-terminal transport measurements show evidence of quantum confinement effects.

Amplified Sensitivity of Nitrogen-Vacancy Spins in Nanodiamonds Using All-Optical Charge Readout

Nanodiamonds containing nitrogen-vacancy (NV) centers offer a versatile platform for sensing applications spanning from nanomagnetism to in vivo monitoring of cellular processes. In many cases, however, weak optical signals and poor contrast demand long acquisition times that prevent the measurement of environmental dynamics. Here, we demonstrate the ability to perform fast, high-contrast optical measurements of charge distributions in ensembles of NV centers in nanodiamonds and use the technique to improve the spin-readout signal-to-noise ratio through spin-to-charge conversion. A study of 38 nanodiamonds with sizes ranging between 20 and 70 nm, each hosting a small ensemble of NV centers, uncovers complex, multiple time scale dynamics due to radiative and nonradiative ionization and recombination processes. Nonetheless, the NV-containing nanodiamonds universally exhibit charge-dependent photoluminescence contrasts and the potential for enhanced spin readout using spin-to-charge conversion. We use the technique to speed up a T₁ relaxometry measurement by a factor of 5.

Large tunable valley splitting in edge-free graphene quantum dots on boron nitride

Coherent manipulation of the binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid-state systems, whereas exploitation of the valley has only recently been started, albeit without control at the single-electron level. Here, we show that van der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunnelling microscope and demonstrate valley splitting that is tunable from -5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits.

Microwave Detection of Electron-Phonon Interactions in a Cavity-Coupled Double Quantum Dot

Quantum confinement leads to the formation of discrete electronic states in quantum dots. Here we probe electron-phonon interactions in a suspended InAs nanowire double quantum dot (DQD) that is electric-dipole coupled to a microwave cavity. We apply a finite bias across the wire to drive a steady state population in the DQD excited state, enabling a direct measurement of the electron-phonon coupling strength at the DQD transition energy. The amplitude and phase response of the cavity field exhibit oscillations that are periodic in the DQD energy level detuning due to the phonon modes of the nanowire. The observed cavity phase shift is consistent with theory that predicts a renormalization of the cavity center frequency by coupling to phonons.

A programmable two-qubit quantum processor in silicon

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch-Josza algorithm and the Grover search algorithm-canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85-89 per cent and concurrences of 73-82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

A coherent spin-photon interface in silicon

Electron spins in silicon quantum dots are attractive systems for quantum computing owing to their long coherence times and the promise of rapid scaling of the number of dots in a system using semiconductor fabrication techniques. Although nearest-neighbour exchange coupling of two spins has been demonstrated, the interaction of spins via microwave-frequency photons could enable long-distance spin-spin coupling and connections between arbitrary pairs of qubits ('all-to-all' connectivity) in a spin-based quantum processor. Realizing coherent spin-photon coupling is challenging because of the small magnetic-dipole moment of a single spin, which limits magnetic-dipole coupling rates to less than 1 kilohertz. Here we demonstrate strong coupling between a single spin in silicon and a single microwave-frequency photon, with spin-photon coupling rates of more than 10 megahertz. The mechanism that enables the coherent spin-photon interactions is based on spin-charge hybridization in the presence of a magnetic-field gradient. In addition to spin-photon coupling, we demonstrate coherent control and dispersive readout of a single spin. These results open up a direct path to entangling single spins using microwave-frequency photons.

Room temperature magneto-optic effect in silicon light-emitting diodes

In weakly spin-orbit coupled materials, the spin-selective nature of recombination can give rise to large magnetic-field effects, e.g. on the electro-luminescence of molecular semiconductors. Although silicon has weak spin-orbit coupling, observing spin-dependent recombination through magneto-electroluminescence is challenging: silicon's indirect band-gap causes an inefficient emission and it is difficult to separate spin-dependent phenomena from classical magneto-resistance effects. Here we overcome these challenges and measure magneto-electroluminescence in silicon light-emitting diodes fabricated via gas immersion laser doping. These devices allow us to achieve efficient emission while retaining a well-defined geometry, thus suppressing classical magnetoresistance effects to a few percent. We find that electroluminescence can be enhanced by up to 300% near room temperature in a seven Tesla magnetic field, showing that the control of the spin degree of freedom can have a strong impact on the efficiency of silicon LEDs.

Probing the internal energy structure of a serially coupled double quantum dot system with Rashba spin-orbit coupling through finite-frequency shot noise

The finite-frequency shot noise of electron transport through a serially coupled double quantum dot system with Rashba spin-orbit coupling is studied based on an effective particle-number-resolved quantum master equation. We demonstrate that the finite-frequency shot noise displays an obvious dip, and the dip position, which is independent of the spin polarizations of the source and drain electrodes, is determined by the energy difference between the coherent singly-occupied eigenstates of the quantum dot system. These results suggest that the dip position of the finite-frequency shot noise can be used to quantitatively extract the information about the energy difference between the coherent singly-occupied eigenstates and the magnitude of Rashba spin-orbit coupling. The predicted properties of the finite-frequency shot noise are of particular interest for understanding of the internal dynamics of the coupled quantum dot systems.

Silicon CMOS architecture for a spin-based quantum computer

Recent advances in quantum error correction codes for fault-tolerant quantum computing and physical realizations of high-fidelity qubits in multiple platforms give promise for the construction of a quantum computer based on millions of interacting qubits. However, the classical-quantum interface remains a nascent field of exploration. Here, we propose an architecture for a silicon-based quantum computer processor based on complementary metal-oxide-semiconductor (CMOS) technology. We show how a transistor-based control circuit together with charge-storage electrodes can be used to operate a dense and scalable two-dimensional qubit system. The qubits are defined by the spin state of a single electron confined in quantum dots, coupled via exchange interactions, controlled using a microwave cavity, and measured via gate-based dispersive readout. We implement a spin qubit surface code, showing the prospects for universal quantum computation. We discuss the challenges and focus areas that need to be addressed, providing a path for large-scale quantum computing.

Realisation of large-scale quantum computation requires both error correction capability and a large number of qubits. Here, the authors propose to use a CMOS-compatible architecture featuring a spin qubit surface code and individual qubit control via floating memory gate electrodes.

Confinement sensitivity in quantum dot singlet-triplet relaxation

Spin-orbit mediated phonon relaxation in a two-dimensional quantum dot is investigated using different confining potentials. Elliptical harmonic oscillator and cylindrical well results are compared to each other in the case of a two-electron GaAs quantum dot subjected to a tilted magnetic field. The lowest energy set of two-body singlet and triplet states are calculated including spin-orbit and magnetic effects. These are used to calculate the phonon induced transition rate from the excited triplet to the ground state singlet for magnetic fields up to where the states cross. The roll of the cubic Dresselhaus effect, which is found to be much more important than previously assumed, and the positioning of 'spin hot-spots' are discussed and relaxation rates for a few different systems are exhibited.

Implementation of controlled quantum teleportation with an arbitrator for secure quantum channels via quantum dots inside optical cavities

We propose a controlled quantum teleportation scheme to teleport an unknown state based on the interactions between flying photons and quantum dots (QDs) confined within single- and double-sided cavities. In our scheme, users (Alice and Bob) can teleport the unknown state through a secure entanglement channel under the control and distribution of an arbitrator (Trent). For construction of the entanglement channel, Trent utilizes the interactions between two photons and the QD-cavity system, which consists of a charged QD (negatively charged exciton) inside a single-sided cavity. Subsequently, Alice can teleport the unknown state of the electron spin in a QD inside a double-sided cavity to Bob's electron spin in a QD inside a single-sided cavity assisted by the channel information from Trent. Furthermore, our scheme using QD-cavity systems is feasible with high fidelity, and can be experimentally realized with current technologies.

High-Resolution Valley Spectroscopy of Si Quantum Dots

We study an accumulation mode Si/SiGe double quantum dot (DQD) containing a single electron that is dipole coupled to microwave photons in a superconducting cavity. Measurements of the cavity transmission reveal dispersive features due to the DQD valley states in Si. The occupation of the valley states can be increased by raising the temperature or applying a finite source-drain bias across the DQD, resulting in an increased signal. Using the cavity input-output theory and a four-level model of the DQD, it is possible to efficiently extract valley splittings and the inter- and intravalley tunnel couplings.

Ubiquitous Nonlocal Entanglement with Majorana Zero Modes

Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We find that any allowed state in the degenerate Majorana space is nonlocally entangled. We show how to measure (with available techniques) the CHSH-violating correlations using either intermediate strength or weak measurement protocols.

Three-electron spin qubits

The goal of this article is to review the progress of three-electron spin qubits from their inception to the state of the art. We direct the main focus towards the exchange-only qubit (Bacon et al 2000 Phys. Rev. Lett. 85 1758-61, DiVincenzo et al 2000 Nature 408 339) and its derived versions, e.g. the resonant exchange (RX) qubit, but we also discuss other qubit implementations using three electron spins. For each three-spin qubit we describe the qubit model, the envisioned physical realization, the implementations of single-qubit operations, as well as the read-out and initialization schemes. Two-qubit gates and decoherence properties are discussed for the RX qubit and the exchange-only qubit, thereby completing the list of requirements for quantum computation for a viable candidate qubit implementation. We start by describing the full system of three electrons in a triple quantum dot, then discuss the charge-stability diagram, restricting ourselves to the relevant subsystem, introduce the qubit states, and discuss important transitions to other charge states (Russ et al 2016 Phys. Rev. B 94 165411). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000 Nature 408 339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502), the spin-charge qubit (Kyriakidis and Burkard 2007 Phys. Rev. B 75 115324), and the hybrid qubit (Shi et al 2012 Phys. Rev. Lett. 108 140503, Koh et al 2012 Phys. Rev. Lett. 109 250503, Cao et al 2016 Phys. Rev. Lett. 116 086801, Thorgrimsson et al 2016 arXiv:1611.04945). The main focus will be on the exchange-only qubit and its modification, the RX qubit, whose single-qubit operations are realized by driving the qubit at its resonant frequency in the microwave range similar to electron spin resonance. Two different types of two-qubit operations are presented for the exchange-only qubits which can be divided into short-ranged and long-ranged interactions. Both of these interaction types are expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses (DiVincenzo et al 2000 Nature 408 339, Fong and Wandzura 2011 Quantum Inf. Comput. 11 1003, Setiawan et al 2014 Phys. Rev. B 89 085314, Zeuch et al 2014 Phys. Rev. B 90 045306, Doherty and Wardrop 2013 Phys. Rev. Lett. 111 050503, Shim and Tahan 2016 Phys. Rev. B 93 121410), while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances (Russ and Burkard 2015 Phys. Rev. B 92 205412, Srinivasa et al 2016 Phys. Rev. B 94 205421). The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection against several sources of noise (DiVincenzo et al 2000 Nature 408 339, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Kempe et al 2001 Phys. Rev. A 63 042307, Russ and Burkard 2015 Phys. Rev. B 91 235411). The price to pay for this advantage is an increase in gate complexity. We also take into account the decoherence of the qubit through the influence of magnetic noise (Ladd 2012 Phys. Rev. B 86 125408, Mehl and DiVincenzo 2013 Phys. Rev. B 87 195309, Hung et al 2014 Phys. Rev. B 90 045308), in particular dephasing due to the presence of nuclear spins, as well as dephasing due to charge noise (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434), fluctuations of the energy levels on each dot due to noisy gate voltages or the environment. Several techniques are discussed which partly decouple the qubit from magnetic noise (Setiawan et al 2014 Phys. Rev. B 89 085314, West and Fong 2012 New J. Phys. 14 083002, Rohling and Burkard 2016 Phys. Rev. B 93 205434) while for charge noise it is shown that it is favorable to operate the qubit on the so-called '(double) sweet spots' (Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434, Malinowski et al 2017 arXiv: 1704.01298), which are least susceptible to noise, thus providing a longer lifetime of the qubit.

Higher-order spin and charge dynamics in a quantum dot-lead hybrid system

Understanding the dynamics of open quantum systems is important and challenging in basic physics and applications for quantum devices and quantum computing. Semiconductor quantum dots offer a good platform to explore the physics of open quantum systems because we can tune parameters including the coupling to the environment or leads. Here, we apply the fast single-shot measurement techniques from spin qubit experiments to explore the spin and charge dynamics due to tunnel coupling to a lead in a quantum dot-lead hybrid system. We experimentally observe both spin and charge time evolution via first- and second-order tunneling processes, and reveal the dynamics of the spin-flip through the intermediate state. These results enable and stimulate the exploration of spin dynamics in dot-lead hybrid systems, and may offer useful resources for spin manipulation and simulation of open quantum systems.

Fast Hole Tunneling Times in Germanium Hut Wires Probed by Single-Shot Reflectometry

Heavy holes confined in quantum dots are predicted to be promising candidates for the realization of spin qubits with long coherence times. Here we focus on such heavy-hole states confined in germanium hut wires. By tuning the growth density of the latter we can realize a T-like structure between two neighboring wires. Such a structure allows the realization of a charge sensor, which is electrostatically and tunnel coupled to a quantum dot, with charge-transfer signals as high as 0.3 e. By integrating the T-like structure into a radiofrequency reflectometry setup, single-shot measurements allowing the extraction of hole tunneling times are performed. The extracted tunneling times of less than 10 μs are attributed to the small effective mass of Ge heavy-hole states and pave the way toward projective spin readout measurements.

Observation of partial relaxation mechanisms via anisotropic strain relief on epitaxial islands using semiconductor nanomembranes

In this work we attempt to directly observe anisotropic partial relaxation of epitaxial InAs islands using transmission electron microscopy (TEM) and synchrotron x-ray diffraction on a 15 nm thick InAs:GaAs nanomembrane. We show that under such conditions TEM provides improved real-space statistics, allowing the observation of partial relaxation processes that were not previously detected by other techniques or by usual TEM cross section images. Besides the fully coherent and fully relaxed islands that are known to exist above previously established critical thickness, we prove the existence of partially relaxed islands, where incomplete 60° half-loop misfit dislocations lead to a lattice relaxation along one of the 〈110〉 directions, keeping a strained lattice in the perpendicular direction. Although individual defects cannot be directly observed, their implications to the resulting island registry are identified and discussed within the frame of half-loops propagations.

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.

Robust Single-Shot Spin Measurement with 99.5% Fidelity in a Quantum Dot Array

We demonstrate a new method for projective single-shot measurement of two electron spin states (singlet versus triplet) in an array of gate-defined lateral quantum dots in GaAs. The measurement has very high fidelity and is robust with respect to electric and magnetic fluctuations in the environment. It exploits a long-lived metastable charge state, which increases both the contrast and the duration of the charge signal distinguishing the two measurement outcomes. This method allows us to evaluate the charge measurement error and the spin-to-charge conversion error separately. We specify conditions under which this method can be used, and project its general applicability to scalable quantum dot arrays in GaAs or silicon.

Enhanced readout of spin states in double quantum dot

We investigate a spin-to-charge conversion mechanism which maps the spin singlet and triplet states to two charge states differing by one electron mediated by an intermediate metastable charge state. This mechanism allows us to observe fringes in the spin-unblocked region beyond the triplet transition line in the measurement of the exchange oscillations between singlet and triplet states in a four-electron double quantum dot. Moreover, these fringes are amplified and π-phase shifted, compared with those in the spin blockade region. Unlike the signal enhancement mechanism reported before which produces similar effects, this mechanism only requires one dot coupling to the lead, which is a commonly encountered case especially in imperfect devices. Besides, the crucial tunnel rate asymmetry is provided by the dependence on spin state, not by the asymmetric couplings to the leads. We also design a scheme to control the amplification process, which enables us to extract the relevant time parameters. This mechanism will have potential applications in future investigations of spin qubits.

Electrical Read-Out of a Single Spin Using an Exchange-Coupled Quantum Dot

We present an original way of continuously reading-out the state of a single electronic spin. Our detection scheme is based on an exchange interaction between the electronic spin and a nearby read-out quantum dot. The coupling between the two systems results in a spin-dependent conductance through the read-out dot and establishes an all electrical and nondestructive single spin detection. With conductance variations up to 4% and read-out fidelities greater than 99.5%, this method represents an alternative to systems for which spin-to-charge conversion cannot be implemented. Using a semiclassical approach, we present an asymmetric exchange coupling model in good agreement with our experimental results.

Split-gated point-contact for electrostatic confinement of transport in MoS2/h-BN hybrid structures

Electrostatically defined nanoscale devices on two-dimensional semiconductor heterostructures are the building blocks of various quantum electrical circuits. Owing to its atomically flat interfaces and the inherent two-dimensional nature, van der Waals heterostructures hold the advantage of large-scale uniformity, flexibility and portability over the conventional bulk semiconductor heterostructures. In this letter we show the operation of a split-gate defined point contact device on a MoS₂/h-BN heterostructure, the first step towards realizing electrostatically gated quantum circuits on van der Waals semiconductors. By controlling the voltage on the split-gate we are able to control and confine the electron flow in the device leading to the formation of the point contact. The formation of the point contact in our device is elucidated by the three characteristic regimes observed in the pinch-off curve; transport similar to the conventional FET, electrostatically confined transport and the tunneling dominated transport. We explore the role of the carrier concentration and the drain-source voltages on the pinch-off characteristics. We are able to tune the pinch-off characteristics by varying the back-gate voltage at temperatures ranging from 4 K to 300 K.

Atom-by-Atom Construction of a Quantum Device

Scanning tunneling microscopes (STMs) are conventionally used to probe surfaces with atomic resolution. Recent advances in STM include tunneling from spin-polarized and superconducting tips, time-domain spectroscopy, and the fabrication of atomically precise Si nanoelectronics. In this issue of ACS Nano, Tettamanzi et al. probe a single-atom transistor in silicon, fabricated using the precision of a STM, at microwave frequencies. While previous studies have probed such devices in the MHz regime, Tettamanzi et al. probe a STM-fabricated device at GHz frequencies, which enables excited-state spectroscopy and measurements of the excited-state lifetime. The success of this experiment will enable future work on quantum control, where the wave function must be controlled on a time scale that is much shorter than the decoherence time. We review two major approaches that are being pursued to develop spin-based quantum computers and highlight some recent progress in the atom-by-atom fabrication of donor-based devices in silicon. Recent advances in STM lithography may enable practical bottom-up construction of large-scale quantum devices.

Atomically engineered electron spin lifetimes of 30 s in silicon

Scaling up to large arrays of donor-based spin qubits for quantum computation will require the ability to perform high-fidelity readout of multiple individual spin qubits. Recent experiments have shown that the limiting factor for high-fidelity readout of many qubits is the lifetime of the electron spin. We demonstrate the longest reported lifetimes (up to 30 s) of any electron spin qubit in a nanoelectronic device. By atomic-level engineering of the electron wave function within phosphorus atom quantum dots, we can minimize spin relaxation in agreement with recent theoretical predictions. These lifetimes allow us to demonstrate the sequential readout of two electron spin qubits with fidelities as high as 99.8%, which is above the surface code fault-tolerant threshold. This work paves the way for future experiments on multiqubit systems using donors in silicon.

Quantum state readout of individual quantum dots by electrostatic force detection

Electric charge detection by atomic force microscopy (AFM) with single-electron resolution (e-EFM) is a promising way to investigate the electronic level structure of individual quantum dots (QDs). The oscillating AFM tip modulates the energy of the QDs, causing single electrons to tunnel between QDs and an electrode. The resulting oscillating electrostatic force changes the resonant frequency and damping of the AFM cantilever, enabling electrometry with a single-electron sensitivity. Quantitative electronic level spectroscopy is possible by sweeping the bias voltage. Charge stability diagram can be obtained by scanning the AFM tip around the QD. e-EFM technique enables to investigate individual colloidal nanoparticles and self-assembled QDs without nanoscale electrodes. e-EFM is a quantum electromechanical system where the back-action of a tunneling electron is detected by AFM; it can also be considered as a mechanical analog of admittance spectroscopy with a radio frequency resonator, which is emerging as a promising tool for quantum state readout for quantum computing. In combination with the topography imaging capability of the AFM, e-EFM is a powerful tool for investigating new nanoscale material systems which can be used as quantum bits.

Electron Spin Resonance at the Level of 10^{4} Spins Using Low Impedance Superconducting Resonators

We report on electron spin resonance measurements of phosphorus donors localized in a 200  μm^{2} area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design, we are able to detect around 2×10^{4} spins with a signal-to-noise ratio of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1-10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Because of the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell.

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.

Coherent spin-exchange via a quantum mediator

Coherent interactions at a distance provide a powerful tool for quantum simulation and computation. The most common approach to realize an effective long-distance coupling 'on-chip' is to use a quantum mediator, as has been demonstrated for superconducting qubits and trapped ions. For quantum dot arrays, which combine a high degree of tunability with extremely long coherence times, the experimental demonstration of the time evolution of coherent spin-spin coupling via an intermediary system remains an important outstanding goal. Here, we use a linear triple-quantum-dot array to demonstrate a coherent time evolution of two interacting distant spins via a quantum mediator. The two outer dots are occupied with a single electron spin each, and the spins experience a superexchange interaction through the empty middle dot, which acts as mediator. Using single-shot spin readout, we measure the coherent time evolution of the spin states on the outer dots and observe a characteristic dependence of the exchange frequency as a function of the detuning between the middle and outer dots. This approach may provide a new route for scaling up spin qubit circuits using quantum dots, and aid in the simulation of materials and molecules with non-nearest-neighbour couplings such as MnO (ref. 27), high-temperature superconductors and DNA. The same superexchange concept can also be applied in cold atom experiments.

Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities

We construct an error-detected block, assisted by the quantum-dot spins in double-sided optical microcavities. With this block, we propose three error-detected schemes for the deterministic generation, the complete analysis, and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom of two-photon systems. In these schemes, the errors can be detected, which can improve their fidelities largely, far different from other previous schemes assisted by the interaction between the photon and the QD-cavity system. Our scheme for the deterministic generation of hyperentangled two-photon systems can be performed by repeat until success. These features make our schemes more useful in high-capacity quantum communication with hyperentanglement in the future.

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.

Signatures of Hyperfine, Spin-Orbit, and Decoherence Effects in a Pauli Spin Blockade

We detect in real time interdot tunneling events in a weakly coupled two-electron double quantum dot in GaAs. At finite magnetic fields, we observe two characteristic tunneling times T_{d} and T_{b}, belonging to, respectively, a direct and a blocked (spin-flip-assisted) tunneling. The latter corresponds to the lifting of a Pauli spin blockade, and the tunneling times ratio η=T_{b}/T_{d} characterizes the blockade efficiency. We find pronounced changes in the behavior of η upon increasing the magnetic field, with η increasing, saturating, and increasing again. We explain this behavior as due to the crossover of the dominant blockade-lifting mechanism from the hyperfine to spin-orbit interactions and due to a change in the contribution of the charge decoherence.

Measuring the Degeneracy of Discrete Energy Levels Using a GaAs/AlGaAs Quantum Dot

We demonstrate an experimental method for measuring quantum state degeneracies in bound state energy spectra. The technique is based on the general principle of detailed balance and the ability to perform precise and efficient measurements of energy-dependent tunneling-in and -out rates from a reservoir. The method is realized using a GaAs/AlGaAs quantum dot allowing for the detection of time-resolved single-electron tunneling with a precision enhanced by a feedback control. It is thoroughly tested by tuning orbital and spin degeneracies with electric and magnetic fields. The technique also lends itself to studying the connection between the ground-state degeneracy and the lifetime of the excited states.

Transport, shot noise, and topology in AC-driven dimer arrays

We analyze an AC-driven dimer chain connected to a strongly biased electron source and drain. It turns out that the resulting transport exhibits fingerprints of topology. They are particularly visible in the driving-induced current suppression and the Fano factor. Thus, shot noise measurements provide a topological phase diagram as a function of the driving parameters. The observed phenomena can be explained physically by a mapping to an effective time-independent Hamiltonian and the emergence of edge states. Moreover, by considering quantum dissipation, we determine the requirements for the coherence properties in a possible experimental realization. For the computation of the zero-frequency noise, we develop an efficient method based on matrix-continued fractions.

Gate fidelity and coherence of an electron spin in an Si/SiGe quantum dot with micromagnet

The gate fidelity and the coherence time of a quantum bit (qubit) are important benchmarks for quantum computation. We construct a qubit using a single electron spin in an Si/SiGe quantum dot and control it electrically via an artificial spin-orbit field from a micromagnet. We measure an average single-qubit gate fidelity of ∼99% using randomized benchmarking, which is consistent with dephasing from the slowly evolving nuclear spins in the substrate. The coherence time measured using dynamical decoupling extends up to ∼400 μs for 128 decoupling pulses, with no sign of saturation. We find evidence that the coherence time is limited by noise in the 10-kHz to 1-MHz range, possibly because charge noise affects the spin via the micromagnet gradient. This work shows that an electron spin in an Si/SiGe quantum dot is a good candidate for quantum information processing as well as for a quantum memory, even without isotopic purification.

A Multifunctional Biomaterial with NIR Long Persistent Phosphorescence, Photothermal Response and Magnetism

There are many reports on long persistent phosphors (LPPs) applied in bioimaging. However, there are few reports on LPPs applied in photothermal therapy (PTT), and an integrated system with multiple functions of diagnosis and therapy. In this work, we fabricate effective multifunctional phosphors Zn3 Ga2 SnO8 : Cr(3+) , Nd(3+) , Gd(3+) with NIR persistent phosphorescence, photothermal response and magnetism. Such featured materials can act as NIR optical biolabels and magnetic resonance imaging (MRI) contrast agents for tracking the early cancer cells, but also as photothermal therapeutic agent for killing the cancer cells. This new multifunctional biomaterial is expected to open a new possibility of setting up an advanced imaging-guided therapy system featuring a high resolution for bioimaging and low side effects for the photothermal ablation of tumors.

Single-electron Spin Resonance in a Quadruple Quantum Dot

Electron spins in semiconductor quantum dots are good candidates of quantum bits for quantum information processing. Basic operations of the qubit have been realized in recent years: initialization, manipulation of single spins, two qubit entanglement operations, and readout. Now it becomes crucial to demonstrate scalability of this architecture by conducting spin operations on a scaled up system. Here, we demonstrate single-electron spin resonance in a quadruple quantum dot. A few-electron quadruple quantum dot is formed within a magnetic field gradient created by a micro-magnet. We oscillate the wave functions of the electrons in the quantum dots by applying microwave voltages and this induces electron spin resonance. The resonance energies of the four quantum dots are slightly different because of the stray field created by the micro-magnet and therefore frequency-resolved addressable control of each electron spin resonance is possible.

A fault-tolerant addressable spin qubit in a natural silicon quantum dot

Fault-tolerant quantum computing requires high-fidelity qubits. This has been achieved in various solid-state systems, including isotopically purified silicon, but is yet to be accomplished in industry-standard natural (unpurified) silicon, mainly as a result of the dephasing caused by residual nuclear spins. This high fidelity can be achieved by speeding up the qubit operation and/or prolonging the dephasing time, that is, increasing the Rabi oscillation quality factor Q (the Rabi oscillation decay time divided by the π rotation time). In isotopically purified silicon quantum dots, only the second approach has been used, leaving the qubit operation slow. We apply the first approach to demonstrate an addressable fault-tolerant qubit using a natural silicon double quantum dot with a micromagnet that is optimally designed for fast spin control. This optimized design allows access to Rabi frequencies up to 35 MHz, which is two orders of magnitude greater than that achieved in previous studies. We find the optimum Q = 140 in such high-frequency range at a Rabi frequency of 10 MHz. This leads to a qubit fidelity of 99.6% measured via randomized benchmarking, which is the highest reported for natural silicon qubits and comparable to that obtained in isotopically purified silicon quantum dot-based qubits. This result can inspire contributions to quantum computing from industrial communities.

Fast spin information transfer between distant quantum dots using individual electrons

Transporting ensembles of electrons over long distances without losing their spin polarization is an important benchmark for spintronic devices. It usually requires injecting and probing spin-polarized electrons in conduction channels using ferromagnetic contacts or optical excitation. In parallel with this development, important efforts have been dedicated to achieving control of nanocircuits at the single-electron level. The detection and coherent manipulation of the spin of a single electron trapped in a quantum dot are now well established. Combined with the recently demonstrated control of the displacement of individual electrons between two distant quantum dots, these achievements allow the possibility of realizing spintronic protocols at the single-electron level. Here, we demonstrate that spin information carried by one or two electrons can be transferred between two quantum dots separated by a distance of 4 μm with a classical fidelity of 65%. We show that at present it is limited by spin flips occurring during the transfer procedure before and after electron displacement. Being able to encode and control information in the spin degree of freedom of a single electron while it is being transferred over distances of a few micrometres on nanosecond timescales will pave the way towards 'quantum spintronics' devices, which could be used to implement large-scale spin-based quantum information processing.

Optical Blocking of Electron Tunneling into a Single Self-Assembled Quantum Dot

Time-resolved resonance fluorescence (RF) is used to analyze electron tunneling between a single self-assembled quantum dot (QD) and an electron reservoir. In equilibrium, the RF intensity reflects the average electron occupation of the QD and exhibits a gate voltage dependence that is given by the Fermi distribution in the reservoir. In the time-resolved signal, however, we find that the relaxation rate for electron tunneling is, surprisingly, independent of the occupation in the charge reservoir-in contrast to results from all-electrical transport measurements. Using a master equation approach, which includes both the electron tunneling and the optical excitation or recombination, we are able to explain the experimental data by optical blocking, which also reduces the electron tunneling rate when the QD is occupied by an exciton.