Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots

Universal control of four singlet-triplet qubits

The coherent control of interacting spins in semiconductor quantum dots is of strong interest for quantum information processing and for studying quantum magnetism from the bottom up. Here we present a 2 × 4 germanium quantum dot array with full and controllable interactions between nearest-neighbour spins. As a demonstration of the level of control, we define four singlet-triplet qubits in this system and show two-axis single-qubit control of each qubit and SWAP-style two-qubit gates between all neighbouring qubit pairs, yielding average single-qubit gate fidelities of 99.49(8)-99.84(1)% and Bell state fidelities of 73(1)-90(1)%. Combining these operations, we experimentally implement a circuit designed to generate and distribute entanglement across the array. A remote Bell state with a fidelity of 75(2)% and concurrence of 22(4)% is achieved. These results highlight the potential of singlet-triplet qubits as a competing platform for quantum computing and indicate that scaling up the control of quantum dot spins in extended bilinear arrays can be feasible.

Single Layer Control of Nanoscale Metal-Insulator Transition at the LaAlO3/SrTiO3 Interface

Modern quantum device fabrication often requires precisely adding and removing materials in situ at nanoscales, which is challenging for high-quality correlated oxide devices. In this work, we present a novel nanofabrication method that remotely controls the interfacial metal-insulator transition at the LaAlO3/SrTiO3 interface by selectively removing an LaAlO3 overlayer using a diamond tip. Remarkably, we observe a large force window within which single atomic layer precision of control is achievable. Our results confirm the critical thickness and charge transfer mechanism through a layer-by-layer removal process at the interface. Additionally, high-quality nanodevices, including nanochannels and single electron transistors, are successfully fabricated using this method. This nonvolatile and high-precision nanofabrication method provides a promising oxide platform for quantum engineering by harnessing the rich electron correlations at the nanoscale.

Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers.

A singlet-triplet hole-spin qubit in MOS silicon

Holes in silicon quantum dots are promising for spin qubit applications due to the strong intrinsic spin-orbit coupling. The spin-orbit coupling produces complex hole-spin dynamics, providing opportunities to further optimise spin qubits. Here, we demonstrate a singlet-triplet qubit using hole states in a planar metal-oxide-semiconductor double quantum dot. We demonstrate rapid qubit control with singlet-triplet oscillations up to 400 MHz. The qubit exhibits promising coherence, with a maximum dephasing time of 600 ns, which is enhanced to 1.3 μs using refocusing techniques. We investigate the magnetic field anisotropy of the eigenstates, and determine a magnetic field orientation to improve the qubit initialisation fidelity. These results present a step forward for spin qubit technology, by implementing a high quality singlet-triplet hole-spin qubit in planar architecture suitable for scaling up to 2D arrays of coupled qubits.

Entangling gates on degenerate spin qubits dressed by a global field

Semiconductor spin qubits represent a promising platform for future large-scale quantum computers owing to their excellent qubit performance, as well as the ability to leverage the mature semiconductor manufacturing industry for scaling up. Individual qubit control, however, commonly relies on spectral selectivity, where individual microwave signals of distinct frequencies are used to address each qubit. As quantum processors scale up, this approach will suffer from frequency crowding, control signal interference and unfeasible bandwidth requirements. Here, we propose a strategy based on arrays of degenerate spins coherently dressed by a global control field and individually addressed by local electrodes. We demonstrate simultaneous on-resonance driving of two degenerate qubits using a global field while retaining addressability for qubits with equal Larmor frequencies. Furthermore, we implement SWAP oscillations during on-resonance driving, constituting the demonstration of driven two-qubit gates. Significantly, our findings highlight how dressing can overcome the fragility of entangling gates between superposition states and increase their noise robustness. These results constitute a paradigm shift in qubit control in order to overcome frequency crowding in large-scale quantum computing.

Quantum Interference and Coherent Population Trapping in a Double Quantum Dot

Quantum interference is a natural consequence of wave-particle duality in quantum mechanics, and is widely observed at the atomic scale. One interesting manifestation of quantum interference is coherent population trapping (CPT), first proposed in three-level driven atomic systems and observed in quantum optical experiments. Here, we demonstrate CPT in a gate-defined semiconductor double quantum dot (DQD), with some unique twists as compared to the atomic systems. Specifically, we observe CPT in both driven and nondriven situations. We further show that CPT in a driven DQD could be used to generate adiabatic state transfer. Moreover, our experiment reveals a nontrivial modulation to the CPT caused by the longitudinal driving field, yielding an odd-even effect and a tunable CPT. Our results broaden the field of CPT, and open up the possibility of quantum simulation and quantum computation based on adiabatic passage in quantum dot systems.

Electrical manipulation of the spins in phosphorene double quantum dots

We investigate electric dipole spin resonance (EDSR) induced by an oscillating electric field within a system of double quantum dots formed electrostatically in monolayer phosphorene. Apart from the observed anisotropy of effective masses, phosphorene has been predicted to exhibit anisotropic spin-orbit coupling. Here, we examine a system consisting of two electrons confined in double quantum dots. A single-band effective Hamiltonian together with the configuration interaction theory is implemented to simulate the time evolution of the ground state. We examine spin flips resulting from singlet-triplet transitions driven by external AC electric fields, both near and away from the Pauli blockade regime, revealing fast sub-nanosecond transition times. Furthermore, we analyze the impact of anisotropy by comparing dots arranged along a different crystal axis. The sub-harmonic multi-photon transitions and Landau-Zener-Stückelberg-Majorana transitions are discussed. We show modulation of spin-like and charge-like characteristics of the qubit through potential detuning.

Coherent phenomena and dynamics of lead halide perovskite nanocrystals for quantum information technologies

Solution-processed colloidal nanocrystals of lead halide perovskites have been intensively investigated in recent years in the context of optoelectronic devices, during which time their quantum properties have also begun to attract attention. Their unmatched ease of synthetic tunability and unique structural, optical and electronic properties, in conjunction with the confinement of carriers in three dimensions, have motivated studies on observing and controlling coherent light-matter interaction in these materials for quantum information technologies. This Review outlines the recent efforts and achievements in this direction. Particularly notable examples are the observation of coherent single-photon emission, evidence for superfluorescence and the realization of room-temperature coherent spin manipulation for ensemble samples, which have not been achieved for prototypical colloidal CdSe nanocrystals that have been under investigation for decades. This Review aims to highlight these results, point out the challenges ahead towards realistic applications and bring together the efforts of multidisciplinary communities in this nascent field.

Perfect Zeeman Anisotropy in Rotationally Symmetric Quantum Dots with Strong Spin-Orbit Interaction

In nanoscale structures with rotational symmetry, such as quantum rings, the orbital motion of electrons combined with a spin-orbit interaction can produce a very strong and anisotropic Zeeman effect. Since symmetry is sensitive to electric fields, ring-like geometries provide an opportunity to manipulate magnetic properties over an exceptionally wide range. In this work, we show that it is possible to form rotationally symmetric confinement potentials inside a semiconductor quantum dot, resulting in electron orbitals with large orbital angular momentum and strong spin-orbit interactions. We find complete suppression of Zeeman spin splitting for magnetic fields applied in the quantum dot plane, similar to the expected behavior of an ideal quantum ring. Spin splitting reappears as orbital interactions are activated with symmetry-breaking electric fields. For two valence electrons, representing a common basis for spin-qubits, we find that modulating the rotational symmetry may offer new prospects for realizing tunable protection and interaction of spin-orbital states.

Resonant exchange of chiral Majorana Fermions modulated by two parallel quantum dots

Resonant exchange of the chiral Majorana fermions (MFs) that is coupled to two parallel Majorana zero modes (MZMs) or two parallel quantum dots (QDs) is investigated. We find that, in the two QDs coupling case, the resonant exchange for the chiral MFs is analogous to that in the MZM coupling case. We further propose a circuit based on topological superconductor, which is formed by the proximity coupling of a quantum anomalous Hall insulator and a s-wave superconductor, to observe the resonant exchange of chiral MFs pairs. The numerical calculations show that the resonant transmission of the chiral MFs can be adjusted by varying the coupling parameters at superconductor phase differenceΔφ=π. It is particularly noteworthy that, by only modulating the coupling strength between the two QDs, the resonant exchange may be switched on or off. By adding another MZM, the non-Abelian braiding like operation can be realized. Therefore, our design scheme may provide another way for non-Abelian braiding operation of MFs and the findings may have potential application value in the realization of topological quantum computers.

Spin-resolved counting statistics as a sensitive probe of spin correlation in transport through a quantum dot spin valve

We investigate the noise in spin transport through a single quantum dot (QD) tunnel coupled to ferromagnetic (FM) electrodes with noncollinear magnetizations. Based on a spin-resolved quantum master equation, auto- and cross-correlations of spin-resolved currents are analyzed to reveal the underlying spin transport dynamics and characteristics for various polarizations. We find the currents of majority and minority spins could be strongly autocorrelated despite uncorrelated charge transfer. The interplay between tunnel coupling and the Coulomb interaction gives rise to an exchange magnetic field, leading to the precession of the accumulated spin in the QD. It strongly suppresses the bunching of spin tunneling events and results in a unique double-peak structure in the noise of the net spin current. The spin autocorrelation is found to be susceptible to magnetization alignments, which may serve as a sensitive tool to measure the magnetization directions between the FM electrodes.

Universal Control of Symmetric States Using Spin Squeezing

The manipulation of quantum many-body systems is a crucial goal in quantum science. Entangled quantum states that are symmetric under qubits permutation are of growing interest. Yet, the creation and control of symmetric states has remained a challenge. Here, we introduce a method to universally control symmetric states, proposing a scheme that relies solely on coherent rotations and spin squeezing. We present protocols for the creation of different symmetric states including Schrödinger's cat and Gottesman-Kitaev-Preskill states. The obtained symmetric states can be transferred to traveling photonic states via spontaneous emission, providing a powerful approach for engineering desired quantum photonic states.

An elementary review on basic principles and developments of qubits for quantum computing

An elementary review on principles of qubits and their prospects for quantum computing is provided. Due to its rapid development, quantum computing has attracted considerable attention as a core technology for the next generation and has demonstrated its potential in simulations of exotic materials, molecular structures, and theoretical computer science. To achieve fully error-corrected quantum computers, building a logical qubit from multiple physical qubits is crucial. The number of physical qubits needed depends on their error rates, making error reduction in physical qubits vital. Numerous efforts to reduce errors are ongoing in both existing and emerging quantum systems. Here, the principle and development of qubits, as well as the current status of the field, are reviewed to provide information to researchers from various fields and give insights into this promising technology.

High-fidelity spin qubit operation and algorithmic initialization above 1 K

The encoding of qubits in semiconductor spin carriers has been recognized as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale1-10. However, the operation of the large number of qubits required for advantageous quantum applications11-13 will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 K, at which the cooling power is orders of magnitude higher14-18. Here we tune up and operate spin qubits in silicon above 1 K, with fidelities in the range required for fault-tolerant operations at these temperatures19-21. We design an algorithmic initialization protocol to prepare a pure two-qubit state even when the thermal energy is substantially above the qubit energies and incorporate radiofrequency readout to achieve fidelities up to 99.34% for both readout and initialization. We also demonstrate single-qubit Clifford gate fidelities up to 99.85% and a two-qubit gate fidelity of 98.92%. These advances overcome the fundamental limitation that the thermal energy must be well below the qubit energies for the high-fidelity operation to be possible, surmounting a main obstacle in the pathway to scalable and fault-tolerant quantum computation.

Strong coupling between a microwave photon and a singlet-triplet qubit

Combining superconducting resonators and quantum dots has triggered tremendous progress in quantum information, however, attempts at coupling a resonator to even charge parity spin qubits have resulted only in weak spin-photon coupling. Here, we integrate a zincblende InAs nanowire double quantum dot with strong spin-orbit interaction in a magnetic-field resilient, high-quality resonator. The quantum confinement in the nanowire is achieved using deterministically grown wurtzite tunnel barriers. Our experiments on even charge parity states and at large magnetic fields, allow us to identify the relevant spin states and to measure the spin decoherence rates and spin-photon coupling strengths. We find an anti-crossing between the resonator mode in the single photon limit and a singlet-triplet qubit with a spin-photon coupling strength of g/2π = 139 ± 4 MHz. This coherent coupling exceeds the resonator decay rate κ/2π = 19.8 ± 0.2 MHz and the qubit dephasing rate γ/2π = 116 ± 7 MHz, putting our system in the strong coupling regime.

Microwave quantum diode

The fragile nature of quantum circuits is a major bottleneck to scalable quantum applications. Operating at cryogenic temperatures, quantum circuits are highly vulnerable to amplifier backaction and external noise. Non-reciprocal microwave devices such as circulators and isolators are used for this purpose. These devices have a considerable footprint in cryostats, limiting the scalability of quantum circuits. As a proof-of-concept, here we report a compact microwave diode architecture, which exploits the non-linearity of a superconducting flux qubit. At the qubit degeneracy point we experimentally demonstrate a significant difference between the power levels transmitted in opposite directions. The observations align with the proposed theoretical model. At - 99 dBm input power, and near the qubit-resonator avoided crossing region, we report the transmission rectification ratio exceeding 90% for a 50 MHz wide frequency range from 6.81 GHz to 6.86 GHz, and over 60% for the 250 MHz range from 6.67 GHz to 6.91 GHz. The presented architecture is compact, and easily scalable towards multiple readout channels, potentially opening up diverse opportunities in quantum information, microwave read-out and optomechanics.

Josephson Junction π-0 Transition Induced by Orbital Hybridization in a Double Quantum Dot

In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.

Pulse-controlled qubit in semiconductor double quantum dots

We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.

Coherent charge oscillations in a bilayer graphene double quantum dot

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and [Formula: see text] charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield [Formula: see text] average values in the range of 400-500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.

Single PbS colloidal quantum dot transistors

Colloidal quantum dots are sub-10 nm semiconductors treated with liquid processes, rendering them attractive candidates for single-electron transistors operating at high temperatures. However, there have been few reports on single-electron transistors using colloidal quantum dots due to the difficulty in fabrication. In this work, we fabricated single-electron transistors using single oleic acid-capped PbS quantum dot coupled to nanogap metal electrodes and measured single-electron tunneling. We observed dot size-dependent carrier transport, orbital-dependent electron charging energy and conductance, electric field modulation of the electron confinement potential, and the Kondo effect, which provide nanoscopic insights into carrier transport through single colloidal quantum dots. Moreover, the large charging energy in small quantum dots enables single-electron transistor operation even at room temperature. These findings, as well as the commercial availability and high stability, make PbS quantum dots promising for the development of quantum information and optoelectronic devices, particularly room-temperature single-electron transistors with excellent optical properties.

Quantum Phase Transition in Magnetic Nanographenes on a Lead Superconductor

Quantum spins, also known as spin operators that preserve SU(2) symmetry, lack a specific orientation in space and are hypothesized to display unique interactions with superconductivity. However, spin-orbit coupling and crystal field typically cause a significant magnetic anisotropy in d/f shell spins on surfaces. Here, we fabricate atomically precise S = 1/2 magnetic nanographenes on Pb(111) through engineering sublattice imbalance in the graphene honeycomb lattice. Through tuning the magnetic exchange strength between the unpaired spin and Cooper pairs, a quantum phase transition from the singlet to the doublet state has been observed, consistent with the quantum spin models. From our calculations, the particle-hole asymmetry is induced by the Coulomb scattering potential and gives a transition point about kBTk ≈ 1.6Δ. Our work demonstrates that delocalized π electron magnetism hosts highly tunable magnetic bound states, which can be further developed to study the Majorana bound states and other rich quantum phases of low-dimensional quantum spins on superconductors.

Electric control of spin transitions at the atomic scale

Electric control of spins has been a longstanding goal in the field of solid state physics due to the potential for increased efficiency in information processing. This efficiency can be optimized by transferring spintronics to the atomic scale. We present electric control of spin resonance transitions in single TiH molecules by employing electron spin resonance scanning tunneling microscopy (ESR-STM). We find strong bias voltage dependent shifts in the ESR signal of about ten times its line width. We attribute this to the electric field in the tunnel junction, which induces a displacement of the spin system changing the g-factor and the effective magnetic field of the tip. We demonstrate direct electric control of the spin transitions in coupled TiH dimers. Our findings open up new avenues for fast coherent control of coupled spin systems and expands on the understanding of spin electric coupling.

Single-Gate In-Transistor Readout of Current Superposition and Collapse Utilizing Quantum Tunneling and Ferroelectric Switching

In nanostructure assemblies, the superposition of current paths forms microscopic electric circuits, and different circuit networks produce varying results, particularly when utilized as transistor channels for computing applications. However, the intricate nature of assembly networks and the winding paths of commensurate currents hinder standard circuit modeling. Inspired by the quantum collapse of superposition states for information decoding in quantum circuits, the implementation of analogous current path collapse to facilitate the detection of microscopic circuits by modifying their network topology is explored. Here, the superposition and collapse of current paths in gate-all-around polysilicon nanosheet arrays are demonstrated to enrich the computational resources within transistors by engineering the channel length and quantity. Switching the ferroelectric polarization of Hf0.5 Zr0.5 O2 gate dielectric, which drives these transistors out-of-equilibrium, decodes the output polymorphism through circuit topological modifications. Furthermore, a protocol for the single-electron readout of ferroelectric polarization is presented with tailoring the channel coherence. The introduction of lateral path superposition results into intriguing metal-to-insulator transitions due to transient behavior of ferroelectric switching. This ability to adjust the current networks within transistors and their interaction with ferroelectric polarization in polycrystalline nanostructures lays the groundwork for generating diverse current characteristics as potential physical databases for optimization-based computing.

Coherent optical control of a superconducting microwave cavity via electro-optical dynamical back-action

Recent quantum technologies have established precise quantum control of various microscopic systems using electromagnetic waves. Interfaces based on cryogenic cavity electro-optic systems are particularly promising, due to the direct interaction between microwave and optical fields in the quantum regime. Quantum optical control of superconducting microwave circuits has been precluded so far due to the weak electro-optical coupling as well as quasi-particles induced by the pump laser. Here we report the coherent control of a superconducting microwave cavity using laser pulses in a multimode electro-optical device at millikelvin temperature with near-unity cooperativity. Both the stationary and instantaneous responses of the microwave and optical modes comply with the coherent electro-optical interaction, and reveal only minuscule amount of excess back-action with an unanticipated time delay. Our demonstration enables wide ranges of applications beyond quantum transductions, from squeezing and quantum non-demolition measurements of microwave fields, to entanglement generation and hybrid quantum networks.

Dielectrics for Two-Dimensional Transition-Metal Dichalcogenide Applications

Despite over a decade of intense research efforts, the full potential of two-dimensional transition-metal dichalcogenides continues to be limited by major challenges. The lack of compatible and scalable dielectric materials and integration techniques restrict device performances and their commercial applications. Conventional dielectric integration techniques for bulk semiconductors are difficult to adapt for atomically thin two-dimensional materials. This review provides a brief introduction into various common and emerging dielectric synthesis and integration techniques and discusses their applicability for 2D transition metal dichalcogenides. Dielectric integration for various applications is reviewed in subsequent sections including nanoelectronics, optoelectronics, flexible electronics, valleytronics, biosensing, quantum information processing, and quantum sensing. For each application, we introduce basic device working principles, discuss the specific dielectric requirements, review current progress, present key challenges, and offer insights into future prospects and opportunities.

Wigner-molecularization-enabled dynamic nuclear polarization

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau-Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering.

Ultrafast and Electrically Tunable Rabi Frequency in a Germanium Hut Wire Hole Spin Qubit

Hole spin qubits based on germanium (Ge) have strong tunable spin-orbit interaction (SOI) and ultrafast qubit operation speed. Here we report that the Rabi frequency (f_Rabi) of a hole spin qubit in a Ge hut wire (HW) double quantum dot (DQD) is electrically tuned through the detuning energy (ϵ) and middle gate voltage (V_M). f_Rabi gradually decreases with increasing ϵ; on the contrary, f_Rabi is positively correlated with V_M. We attribute our results to the change of electric field on SOI and the contribution of the excited state in quantum dots to f_Rabi. We further demonstrate an ultrafast f_Rabi exceeding 1.2 GHz, which indicates the strong SOI in our device. The discovery of an ultrafast and electrically tunable f_Rabi in a hole spin qubit has potential applications in semiconductor quantum computing.

Strain-induced ordered Ge(Si) hut wires on patterned Si (001) substrates

Ge/Si nanowires are predicted to be a promising platform for spin and even topological qubits. While for large-scale integration of these devices, nanowires with fully controlled positions and arrangements are a prerequisite. Here, we have reported ordered Ge hut wires by multilayer heteroepitaxy on patterned Si (001) substrates. Self-assembled GeSi hut wire arrays are orderly grown inside patterned trenches with post growth surface flatness. Such embedded GeSi wires induce tensile strain on the Si surface, which results in preferential nucleation of Ge nanostructures. Ordered Ge nano-dashes, disconnected wires and continuous wires are obtained correspondingly by tuning the growth conditions. These site-controlled Ge nanowires on a flattened surface lead to the ease of fabrication and large-scale integration of nanowire quantum devices.

Pseudo-Qutrit Formed by Two Interacting Identical Spins (s = 1/2) in a Variable External Magnetic Field

An analytical solution is obtained for the problem of two interacting, identical but separated spin 1/2 particles in a time-dependent external magnetic field, in a general case. The solution involves isolating the pseudo-qutrit subsystem from a two-qubit system. It is shown that the quantum dynamics of a pseudo-qutrit system with a magnetic dipole-dipole interaction can be described clearly and accurately in an adiabatic representation, using a time-dependent basis set. The transition probabilities between the energy levels for an adiabatically varying magnetic field, which follows the Landau-Majorana-Stuckelberg-Zener (LMSZ) model within a short time interval, are illustrated in the appropriate graphs. It is shown that for close energy levels and entangled states, the transition probabilities are not small and strongly depend on the time. These results provide insight into the degree of entanglement of two spins (qubits) over time. Furthermore, the results are applicable to more complex systems with a time-dependent Hamiltonian.

Coherence Characteristics of a GaAs Single Heavy-Hole Spin Qubit Using a Modified Single-Shot Latching Readout Technique

We present an experimental study of the coherence properties of a single heavy-hole spin qubit formed in one quantum dot of a gated GaAs/AlGaAs double quantum dot device. We use a modified spin-readout latching technique in which the second quantum dot serves both as an auxiliary element for a fast spin-dependent readout within a 200 ns time window and as a register for storing the spin-state information. To manipulate the single-spin qubit, we apply sequences of microwave bursts of various amplitudes and durations to make Rabi, Ramsey, Hahn-echo, and CPMG measurements. As a result of the qubit manipulation protocols combined with the latching spin readout, we determine and discuss the achieved qubit coherence times: T1, TRabi, T2*, and T2CPMG vs. microwave excitation amplitude, detuning, and additional relevant parameters.

Combining n-MOS Charge Sensing with p-MOS Silicon Hole Double Quantum Dots in a CMOS platform

Holes in silicon quantum dots are receiving attention due to their potential as fast, tunable, and scalable qubits in semiconductor quantum circuits. Despite this, challenges remain in this material system including difficulties using charge sensing to determine the number of holes in a quantum dot, and in controlling the coupling between adjacent quantum dots. We address these problems by fabricating an ambipolar complementary metal-oxide-semiconductor (CMOS) device using multilayer palladium gates. The device consists of an electron charge sensor adjacent to a hole double quantum dot. We demonstrate control of the spin state via electric dipole spin resonance. We achieve smooth control of the interdot coupling rate over 1 order of magnitude and use the charge sensor to perform spin-to-charge conversion to measure the hole singlet-triplet relaxation time of 11 μs for a known hole occupation. These results provide a path toward improving the quality and controllability of hole spin-qubits.

Geometrical and magnetic properties of small titanium and chromium clusters on monolayer hexagonal boron nitride

Magnetic clusters on an insulating substrate are potential candidates for spin-based quantum devices. Here we investigate the geometric, electronic, and magnetic structures of small Ti and Cr clusters, from dimers to pentamers, adsorbed on a single-layer hexagonal boron nitride (h-BN) sheet within the framework of density functional theory. The stable adsorption configurations of the Ti clusters and Cr clusters composed of the same number of atoms are found to be totally different from each other. The difference in their bonding mechanisms has been revealed by the density of states and the charge density difference of the corresponding adsorption systems. While chemical bonds are formed between the Ti atoms and the supporting sheet, the Cr clusters are found in the physisorption state on the substrate. In addition, it is shown that the h-BN sheet is energetically favorable for building three-dimensional Ti clusters. These findings support the use of h-BN as a suitable decoupling substrate for manipulation of quantum spin states in small transition metal (TM) clusters and fabrication of devices based on them.

The Use of Exchange Coupled Atom Qubits as Atomic-Scale Magnetic Field Sensors

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 individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubit gates.

Colloquium: Advances in automation of quantum dot devices control

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

Robust electron spin qubit control in a nanowire double quantum dot

Robust and efficient manipulation of electron spin qubits in quantum dots is of great significance for the reliable realization of quantum computers and execution of quantum algorithms. In this paper, we study the robust control on a singlet-triplet qubit based on inverse engineering, one technique of shortcuts to adiabaticity (STA), in a nanowire double quantum dot in the presence of magnetic field and strong spin-orbit coupling. The optimization of STA with respect to the systematic errors, contributed from the control field and the perturbative interaction, is explored. Moreover, we also apply optimal control techniques combining with STA, referred to as robust inverse optimization, to design optimal control fields and optimal operation time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Tunable Superconducting Coupling of Quantum Dots via Andreev Bound States in Semiconductor-Superconductor Nanowires

Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this Letter, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to individually control both the coupling mediated by Cooper pairs and by single electrons by changing the properties of the Andreev bound states with easily accessible experimental parameters. In addition, the problem of coupling suppression is greatly mitigated. We also propose how to experimentally extract the coupling strengths from resonant current in a three-terminal junction. Our proposal will enable future experiments that have not been possible so far.

Variable-Barrier Quantum Coulomb Blockade Effect in Nanoscale Transistors

Current-voltage characteristics of a quantum dot in double-barrier configuration, as formed in the nanoscale channel of silicon transistors, were analyzed both experimentally and theoretically. Single electron transistors (SET) made in a SOI-FET configuration using silicon quantum dot as well as phosphorus donor quantum dots were experimentally investigated. These devices exhibited a quantum Coulomb blockade phenomenon along with a detectable effect of variable tunnel barriers. To replicate the experimental results, we developed a generalized formalism for the tunnel-barrier dependent quantum Coulomb blockade by modifying the rate-equation approach. We qualitatively replicate the experimental results with numerical calculation using this formalism for two and three energy levels participated in the tunneling transport. The new formalism supports the features of most of the small-scaled SET devices.

Entropy Measurement of a Strongly Coupled Quantum Dot

The spin 1/2 entropy of electrons trapped in a quantum dot has previously been measured with great accuracy, but the protocol used for that measurement is valid only within a restrictive set of conditions. Here, we demonstrate a novel entropy measurement protocol that is universal for arbitrary mesoscopic circuits and apply this new approach to measure the entropy of a quantum dot hybridized with a reservoir. The experimental results match closely to numerical renormalization group (NRG) calculations for small and intermediate coupling. For the largest couplings investigated in this Letter, NRG calculations predict a suppression of spin entropy at the charge transition due to the formation of a Kondo singlet, but that suppression is not observed in the experiment.

A Pair of Coupled Waveguides as a Classical Analogue for a Solid-State Qubit

We have determined conditions when a pair of coupled waveguides, a common element for integrated room-temperature photonics, can act as a qubit based on a system with a double-well potential. Moreover, we have used slow-varying amplitude approximation (SVA) for the "classical" wave equation to study the propagation of electromagnetic beams in a couple of dielectric waveguides both analytically and numerically. As a part of an extension of the optical-mechanical analogy, we have considered examples of "quantum operations" on the electromagnetic wave state in a pair of waveguides. Furthermore, we have provided examples of "quantum-mechanical" calculations of nonlinear transfer functions for the implementation of the considered element in optical neural networks.

Charge detection of a quantum dot under different tunneling barrier symmetries and bias voltages

We report the realization of a coupled quantum dot (QD) system containing two single QDs made in two adjacent InAs nanowires. One QD (sensor QD) was used as a charge sensor to detect the charge state transitions in the other QD (target QD). We investigated the effect of the tunneling barrier asymmetry of the target QD on the detection visibility of the charge state transitions in the target QD. The charge stability diagrams of the target QD under different configurations of barrier-gate voltages were simultaneously measured via the direct signals of electron transport through the target QD and via the detection signals of the charge state transitions in the target QD revealed by the sensor QD. We find that the complete Coulomb diamond boundaries of the target QD and the transport processes involving the excited states in the target QD can be observed in the transconductance signals of the sensor QD only when the tunneling barriers of the target QD are nearly symmetric. These observations were explained by analyzing the effect of the ratio of the two tunneling rates on the electron transport processes through the target QD. Our results imply that it is important to consider the symmetry of the tunnel couplings when constructing a charge sensor integrated QD device.

A multimode photodetector with polarization-dependent near-infrared responsivity using the tunable split-dual gates control

As the limited carrier densities in atomic thin materials can be well controlled by electrostatic gates, p-n junctions based on two-dimensional materials in the coplanar split-gate configuration can work as photodetectors or light-emitting diodes. These coplanar gates can be fabricated in a simple one-step lithography process and are frequently used in hybrid integration with on-chip optical structures. However, the polarization-dependent responsivity of such a configuration is less explored in the near-infrared band, and a clear understanding is still missing. Here we fabricate near-infrared tunable multiple modes twisted bilayer graphene photodetector enabled by the coplanar split-gate control and confirm that the photothermoelectric effect governs the photovoltage mechanism of the p-n junction mode. Our study also elucidates that the discrepancy of the responsivities under different linear polarizations is owing to the different cavity modes and provides a valuable example for designing chip-integrated optoelectronic devices.

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Design of coplanar split-gated controlled multimode near-infrared photodetector

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Verification of the photothermoelectric mechanism of the p-n junction

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Understanding the reason for the polarization-dependent responsivity

A shuttling-based two-qubit logic gate for linking distant silicon quantum processors

Control of entanglement between qubits at distant quantum processors using a two-qubit gate is an essential function of a scalable, modular implementation of quantum computation. Among the many qubit platforms, spin qubits in silicon quantum dots are promising for large-scale integration along with their nanofabrication capability. However, linking distant silicon quantum processors is challenging as two-qubit gates in spin qubits typically utilize short-range exchange coupling, which is only effective between nearest-neighbor quantum dots. Here we demonstrate a two-qubit gate between spin qubits via coherent spin shuttling, a key technology for linking distant silicon quantum processors. Coherent shuttling of a spin qubit enables efficient switching of the exchange coupling with an on/off ratio exceeding 1000, while preserving the spin coherence by 99.6% for the single shuttling between neighboring dots. With this shuttling-mode exchange control, we demonstrate a two-qubit controlled-phase gate with a fidelity of 93%, assessed via randomized benchmarking. Combination of our technique and a phase coherent shuttling of a qubit across a large quantum dot array will provide feasible path toward a quantum link between distant silicon quantum processors, a key requirement for large-scale quantum computation.

A coherent quantum link between distant quantum processors is desirable for scaling up of quantum computation. Noiri et al. demonstrate a strategy to link distant quantum processors in silicon, by implementing a shuttling-based two-qubit gate between spin qubits in a Si/SiGe triple quantum dot.

Optical measurement of electron spins in quantum dots: quantum Zeno effects

We describe theoretically the effects of the quantum back action under the continuous optical measurement of electron spins in quantum dots. We consider the system excitation by elliptically polarized light close to the trion resonance, which allows for simultaneous spin orientation and measurement. We microscopically demonstrate that the nuclei-induced spin relaxation can be both suppressed and accelerated by the continuous spin measurement due to the quantum Zeno and anti-Zeno effects, respectively. Our theoretical predictions can be directly compared with the future experimental results and straightforwardly generalized for pump-probe experiments.

Ramped measurement technique for robust high-fidelity spin qubit readout

State preparation and measurement of single-electron spin qubits typically rely on spin-to-charge conversion where a spin-dependent charge transition of the electron is detected by a coupled charge sensor. For high-fidelity, fast readout, this process requires that the qubit energy is much larger than the temperature of the system limiting the temperature range for measurements. Here, we demonstrate an initialization and measurement technique that involves voltage ramps rather than static voltages allowing us to achieve state-to-charge readout fidelities above 99% for qubit energies almost half that required by traditional methods. This previously unidentified measurement technique is highly relevant for achieving high-fidelity electron spin readout at higher temperature operation and offers a number of pragmatic benefits compared to traditional energy-selective readout such as real-time dynamic feedback and minimal alignment procedures.

Enhanced Spin Coherence of a Self-Assembled Quantum Dot Molecule at the Optimal Electrical Bias

A pair of coupled dots with one electron in each dot can provide improvements in spin coherence, particularly at an electrical bias called the "sweet spot," but few measurements have been performed on self-assembled dots in this regime. Here, we directly measure the T_{2}^{*} coherence time of the singlet-triplet states in this system as a function of bias and magnetic field, obtaining a maximum T_{2}^{*} of 60 ns, more than an order of magnitude higher than an electron spin in a single quantum dot. Our results uncover two main dephasing mechanisms: electrical noise away from the sweet spot, and a magnetic field dependent interaction with nuclear spins due to a difference in g factors.

Spin relaxation in a single-electron graphene quantum dot

The relaxation time of a single-electron spin is an important parameter for solid-state spin qubits, as it directly limits the lifetime of the encoded information. Thanks to the low spin-orbit interaction and low hyperfine coupling, graphene and bilayer graphene (BLG) have long been considered promising platforms for spin qubits. Only recently, it has become possible to control single-electrons in BLG quantum dots (QDs) and to understand their spin-valley texture, while the relaxation dynamics have remained mostly unexplored. Here, we report spin relaxation times (T₁) of single-electron states in BLG QDs. Using pulsed-gate spectroscopy, we extract relaxation times exceeding 200 μs at a magnetic field of 1.9 T. The T₁ values show a strong dependence on the spin splitting, promising even longer T₁ at lower magnetic fields, where our measurements are limited by the signal-to-noise ratio. The relaxation times are more than two orders of magnitude larger than those previously reported for carbon-based QDs, suggesting that graphene is a potentially promising host material for scalable spin qubits.

Graphene has long been considered to be a promising host for spin qubits, however a demonstration of long spin relaxation times for a potential qubit has been lacking. Here, the authors report the electrical measurement of the single-electron spin relaxation time exceeding 200 μs in a bilayer graphene quantum dot.

Low-Temperature Characteristics of Nanowire Network Demultiplexer for Qubit Biasing

In current quantum computers, most qubit control electronics are connected to the qubit chip inside the cryostat by cables at room temperature. This poses a challenge when scaling the quantum chip to an increasing number of qubits. We present a lateral nanowire network 1-to-4 demultiplexer design fabricated by selective area grown InGaAs on InP, suitable for on chip routing of DC current for qubit biasing. We have characterized the device at cryogenic temperatures, and at 40 mK the device exhibits a minimum inverse subthreshold slope of 2 mV/dec, which is encouraging for low power operation. At low drain bias, the transmission breaks up into several resonance peaks due to a rough conduction band edge; this is qualitatively explained by a simple model based on a 1D real space tight-binding nonequilibrium Green's functions model.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Complete Mapping of Interacting Charging States in Single Coupled Colloidal Quantum Dot Molecules

Colloidal quantum dots (CQDs), major building blocks in modern optoelectronic devices, have so far been synthesized with only one emission center where the exciton resides. Recent development of coupled colloidal quantum dots molecules (CQDM), where two core-shell CQDs are fused to form two emission centers in close proximity, allows exploration of how charge carriers in one CQD affect the charge carriers in the other CQD. Cryogenic single particle spectroscopy reveals that while CQD monomers manifest a simple emission spectrum comprising a main emission peak with well-defined phonon sidebands, CQDMs exhibit a complex spectrum with multiple peaks that are not all spaced according to the known phonon frequencies. Based on complementary emission polarization and time-resolved analysis, this is assigned to fluorescence of the two coupled emission centers. Moreover, the complex peak structure shows correlated spectral diffusion indicative of the coupling between the two emission centers. Utilizing Schrödinger-Poisson self-consistent calculations, we directly map the spectral behavior, alternating between neutral and charged states of the CQDM. Spectral shifts related to electrostatic interaction between a charged emission center and the second emission center are thus fully mapped. Furthermore, effects of moving surface charges are identified, whereby the emission center proximal to the charge shows larger shifts. Instances where the two emission centers are negatively charged simultaneously are also identified. Such detailed mapping of charging states is enabled by the coupling within the CQDM and its anisotropic structure. This understanding of the coupling interactions is progress toward quantum technology and sensing applications based on CQDMs.

Two-qubit silicon quantum processor with operation fidelity exceeding 99

Silicon spin qubits satisfy the necessary criteria for quantum information processing. However, a demonstration of high-fidelity state preparation and readout combined with high-fidelity single- and two-qubit gates, all of which must be present for quantum error correction, has been lacking. We use a two-qubit Si/SiGe quantum processor to demonstrate state preparation and readout with fidelity greater than 97%, combined with both single- and two-qubit control fidelities exceeding 99%. The operation of the quantum processor is quantitatively characterized using gate set tomography and randomized benchmarking. Our results highlight the potential of silicon spin qubits to become a dominant technology in the development of intermediate-scale quantum processors.