Quantum Dot Arrays Research Articles

Tuning of paramagnetic and diamagnetic cavity photon excitations in a square array of quantum dots in a magnetic field

Tuning of paramagnetic and diamagnetic cavity photon excitations in a square array of quantum dots in a magnetic field

Monolithically Integrated Quantum Dots in a 22‐nm Fully Depleted Silicon‐on‐Insulator Process Operating at 3 K

ABSTRACTQuantum computers comprising large‐scale arrays of qubits will enable complex algorithms to be executed to provide a quantum advantage for practical applications. A prerequisite for this milestone is a power‐efficient qubit control and detection system operating at cryogenic temperatures. Implementing such systems in complementary metal‐oxide‐semiconductor (CMOS) technology offers clear advantages in terms of scalability. Here, we present a fully integrated quantum dot array in which silicon quantum wells are co‐located with control and detection circuitry on the same die in a commercial 22‐nm fully depleted silicon‐on‐insulator (FDSOI) process. Our system comprises a two‐dimensional quantum dot array, integrated with 8 detectors and 32 injectors, operating at 3 K inside a cryo‐cooler. The power consumption of the control and detection circuitry is 2.5 mW per qubit without body biasing. The design utilizes 0.8‐V nominal devices. The setup allows us to verify discrete charge injection control and detection at the quantum dot array and demonstrate the feasibility of this architecture for scaling up the existing quantum core to hundreds and thousands of physical qubits.

Impact of quantum information encoding and metallic leads on dynamical multipartite correlation formation in semiconductor quantum dot arrays.

This study investigates quantum information scrambling (QIS) in a semiconductor quantum dot array. Starting with the 1D Transverse Field Ising model, we expand to more relevant quasi-2D frameworks such as the Heisenberg chain, super-extended Fermi-Hubbard and hardcore Fermi-Hubbard models. Assessing their relevance to semiconductor spin-qubit quantum computers, simulations of multipartite entanglement formation examine qubit encoding strategies' fidelity, stability, and robustness, revealing trade-offs among these aspects. Furthermore, we investigate the weakly coupled metallic injector/detector (I/D) leads' significant impact on QIS behavior by employing Ω lead N-single orbital impurities weakly coupled Anderson models. We observe sign flips in spatiotemporal tripartite mutual information I3 which result in significant effects on dynamical quantum entanglement structures and their formation. Exploring carrier number effects, we identify optimal regions for QIS enhancement. Our findings emphasize the necessity of proper qubit encoding and I/D lead influence on quantum devices amidst noise and impurities.

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.

One-Dimensional Quantum Dot Array Integrated with Charge Sensors in an InAs Nanowire

One-Dimensional Quantum Dot Array Integrated with Charge Sensors in an InAs Nanowire

QArray: A GPU-accelerated constant capacitance model simulator for large quantum dot arrays

Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a 100 × 100100×100 pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.

Codebase release 1.3 for QArray

Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a 100 × 100100×100 pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.

Gate-driven transition temperatures of electron hopping behaviors in Hubbard bands formed by dopant-induced QD array in silicon nanowire

Abstract Dopant atoms confined in silicon nanoscale channel can be ionized to form quantum dots (QDs). Several dopant atoms couple with each other forming energy bands, where the electron hopping behavior can be described by the Hubbard model. This characteristic renders dopant-induced quantum dots particularly appealing for applications in nanoelectronic and quantum devices. Herein we study the gate-driven transition temperatures of electron hopping behavior in upper and lower Hubbard bands formed by dopant-induced QD array in junctionless silicon nanowire transistors. The gate-dependent transition temperatures are calculated for three stages of electron hopping behaviors including Efros-Shklovskii Variable Range Hopping (ES-VRH), Mott Variable Range Hopping (Mott-VRH) and Nearest Neighbor Hopping (NNH). Our experimental results indicate that the ES-VRH in arrays of dopant atoms occurs in the domination of a long-range Coulomb interaction, in which the hopping distance relies on the Coulomb gap. Furthermore, the localization length of ES-VRH can be modulated by gate voltages.Those factors lead to the significant difference of transition temperatures between the upper and lower Hubbard bands. In addition, we find that the source-drain bias voltage can effectively modulate the transition temperatures between VRH and NNH by thermal activation energies under different bias voltages Vds.

Highly Tunable 2D Silicon Quantum Dot Array with Coupling beyond Nearest Neighbors.

Scaling up quantum dots to two-dimensional (2D) arrays is a crucial step for advancing semiconductor quantum computation. However, maintaining excellent tunability of quantum dot parameters, including both nearest-neighbor and next-nearest-neighbor couplings, during 2D scaling is challenging, particularly for silicon quantum dots due to their relatively small size. Here, we present a highly controllable and interconnected 2D quantum dot array in planar silicon, demonstrating independent control over electron fillings and the tunnel couplings of nearest-neighbor dots. More importantly, we also demonstrate the wide tuning of tunnel couplings between next-nearest-neighbor dots, which play a crucial role in 2D quantum dot arrays. This excellent tunability enables us to alter the coupling configuration of the array as needed. These results open up the possibility of utilizing silicon quantum dot arrays as versatile platforms for quantum computing and quantum simulation.

Nontrivial fusion of Majorana zero modes in interacting quantum-dot arrays

Motivated by recent experimental reports of Majorana zero modes (MZMs) in quantum-dot systems at the “sweet spot,” where the electronic hopping th is equal to the superconducting coupling Δ, we study the time-dependent spectroscopy corresponding to the fusion of MZMs. The term “nontrivial” refers to the fusion of Majoranas from different original pairs of MZMs, each with well-defined parities. We employ an experimentally accessible time-dependent real-space local density-of-states (LDOS) method to investigate the nontrivial MZM fusion outcomes in canonical chains and in a Y-shaped array of interacting electrons. In the case of quantum-dot chains where two pairs of MZMs are initially disconnected, after fusion we find equal-height peaks in the electron and hole components of the LDOS, signaling nontrivial fusion into both the vacuum I and fermion Ψ channels with equal weight. For π-junction quantum-dot chains, where the superconducting phase has opposite signs on the left and right portions of the chain, after the nontrivial fusion we observed the formation of an exotic two-site MZM near the center of the chain, coexisting with another single-site MZM. Furthermore, we also studied the fusion of three MZMs in the Y-shaped geometry. In this case, after the fusion we observed the novel formation of another exotic multisite MZM, with properties depending on the connection and geometry of the central region of the Y-shaped quantum-dot array. Published by the American Physical Society 2024

Topological boundary states in engineered quantum-dot molecules on the InAs(111)A surface: Odd numbers of quantum dots

Atom manipulation by scanning tunneling microscopy was used to construct quantum dots on the InAs(111)A surface. Each dot comprised six ionized indium adatoms. The positively charged adatoms create a confining potential acting on surface-state electrons, leading to the emergence of a bound state associated with the dot. By lining up the dots into N-dot chains with alternating tunnel coupling between them, quantum-dot molecules were constructed that revealed electronic boundary states as predicted by the Su-Schrieffer-Heeger (SSH) model of one-dimensional topological phases. Dot chains with odd N were constructed such that they host a single end or domain-wall state, allowing one to probe the localization of the boundary state on a given sublattice by scanning tunneling spectroscopy. We found probability density also on the forbidden sublattice together with an asymmetric energy spectrum of the chain-confined states. This deviation from the SSH model arises because the dots are charged and create a variation in on-site potential along the chain—which does not remove the boundary states but shifts their energy away from the midgap position. Our results demonstrate that topological boundary states can be created in quantum-dot arrays engineered with atomic-scale precision. Published by the American Physical Society 2024

High performance pixelated quantum dots array on Micro-LED by inkjet printing

Micro-LED display has risen to prominence in research and industry, distinguished by their numerous advantages. Quantum dots (QDs) film, serving as color conversion layers (CCLs) for Micro-LED, are considered a leading candidate for the next generation of displays, owing to their low power consumption and broad color gamut. Inkjet printing stands out as a feasible approach for crafting QDs CCLs. The essence of the process hinges on attaining a printed QDs film that boasts both uniformity and high-precision QDs array. However, the unstable printing of QDs ink significantly impacts the surface morphology of QDs arrays and the display performance of Micro-LEDs. Therefore, elucidating the mechanism behind the unstable printing of QDs in inkjet printing and fabricating QDs is of paramount importance. In this study, through the simulation of unstable printing with conventional QDs ink, we identified nozzle blockage and the rapid evaporation of low-boiling-point ink as the primary causes of unstable printing. This leads to aggregation and deposition of QDs, obstructing the nozzle and altering the fluid path. A novel binary organic composite ink was employed to print the QDs array on the substrate with ultra-stability, achieving a high yield and greatly reduced coffee-ring effect Micro-LED full-color display.

Quantum phase transitions and cat states in cavity-coupled quantum dots

We study double quantum dots coupled to a quasistatic cavity mode with high mode-volume compression allowing for strong light-matter coupling. Besides the cavity-mediated interaction, electrons in different double quantum dots interact with each other via dipole-dipole (Coulomb) interaction. There is a first-order cavity-induced ferroelectric quantum phase transition when the attractive dipolar interaction is smaller than the critical value defined by the energy splitting in DQDs and a smooth transition, otherwise. We show that, in the smooth transition region, both the ground and the first excited states of an array of double quantum dots are cat states. Such states are actively discussed as high-fidelity qubits for quantum computing, and thus our proposal provides a platform for semiconductor implementation of such qubits. We also calculate gauge-invariant observables such as the net dipole moment, the optical conductivity, and the absorption spectrum beyond the semiclassical approximation. The results are robust against cavity losses and variations of system parameters. Published by the American Physical Society 2024

Coupling and characterization of a Si/SiGe triple quantum dot array with a microwave resonator

Abstract Scaling up spin qubits in silicon-based quantum dots is one of the pivotal challenges in achieving large-scale semiconductor quantum computation. To satisfy the connectivity requirements and reduce the lithographic complexity, utilizing the qubit array structure and the circuit quantum electrodynamics (cQED) architecture together is expected to be a feasible scaling scheme. A triple-quantum dot (TQD) coupled with a superconducting resonator is regarded as a basic cell to demonstrate this extension scheme. In this article, we investigate a system consisting of a silicon TQD and a high-impedance TiN coplanar waveguide (CPW) resonator. The TQD can couple to the resonator via the right double-quantum dot (RDQD), which reaches the strong coupling regime with a charge–photon coupling strength of g 0/(2π) = 175 MHz. Moreover, we illustrate the high tunability of the TQD through the characterization of stability diagrams, quadruple points (QPs), and the quantum cellular automata (QCA) process. Our results contribute to fostering the exploration of silicon-based qubit integration.

Impact of interface traps on charge noise and low-density transport properties in Ge/SiGe heterostructures

Hole spins in Ge/SiGe heterostructures have emerged as an interesting qubit platform with favourable properties such as fast electrical control and noise-resilient operation at sweet spots. However, commonly observed gate-induced electrostatic disorder, drifts, and hysteresis hinder reproducible tune-up of SiGe-based quantum dot arrays. Here, we study Hall bar and quantum dot devices fabricated on Ge/SiGe heterostructures and present a consistent model for the origin of gate hysteresis and its impact on transport metrics and charge noise. As we push the accumulation voltages more negative, we observe non-monotonous changes in the low-density transport metrics, attributed to the induced gradual filling of a spatially varying density of charge traps at the SiGe-oxide interface. With each gate voltage push, we find local activation of a transient low-frequency charge noise component that completely vanishes again after 30 hours. Our results highlight the resilience of the SiGe material platform to interface-trap-induced disorder and noise and pave the way for reproducible tuning of larger multi-dot systems.

Photoluminescence of dense arrays of InGaPAs/InGaAs quantum dots formed by substitution of group V elements

One drawback of self-organized quantum dots is their low optical gain. The development of new shaping methods that would allow higher gain, for example, due to a higher surface density of the QD array, remains an important task to date. In the present work, arrays of quantum dots have been formed by substituting phosphorous atoms with arsenic ones in a thin InGaP epilayer. Based on transmission electron microscopy data, the surface density was estimated to be about 1.3 × 1012 cm−2, which is one of the highest values for quantum dots on GaAs. The influence of an additional InGaAs epilayer (quantum well) on the luminescence properties of quantum dots was investigated in a wide temperature range and different optical pumping levels. It was found that placing the quantum well under the layer of quantum dots has little effect on the central emission wavelength, while quantum dots covered with the InGaAs demonstrate a strong red shift of the luminescence spectrum. A transition from a nonequilibrium to an equilibrium distribution of charge carriers over quantum-dot states, related to the lateral transport of charge carriers over quantum dot array, similar to that previously observed in In(Ga)As Stranski-Krastanow quantum dots, was revealed. This is manifested in a change in temperature dependencies of the linewidth and peak position of the photoluminescence band. For the structures under study, this transition occurs at a temperature of about 125 K. Rapid thermal annealing of the structures allows to increase the integrated photoluminescence intensity of quantum dots up to 4 times, while the maximum of the spectrum remains almost unchanged, provided that the annealing temperature does not exceed 620 °C.

Towards scalable cryogenic quantum dot biasing using memristor-based DC sources

Cryogenic memristor-based DC sources offer a promising avenue for in situ biasing of quantum dot arrays. In this study, we present experimental results and discuss the scaling potential for such DC sources. We first demonstrate the operation of a commercial discrete operational amplifier down to ▪ which is used on the DC source prototype. Then, the tunability of the memristor-based DC source is validated by performing several ▪-DC sweeps with a resolution of ▪ at room temperature and at ▪. Additionally, the DC source prototype exhibits a limited output drift of ▪ at ▪. This showcases the potential of memristor-based DC sources for quantum dot biasing. Limitations in power consumption and voltage resolution using discrete components highlight the need for a fully integrated and scalable complementary metal–oxide–semiconductor-based (CMOS-based) approach. To address this, we propose to monolithically co-integrate emerging non-volatile memories (eNVMs) and ▪ CMOS circuitry. Simulations reveal a reduction in power consumption, down to ▪ per DC source and in footprint. This allows for the integration of up to one million eNVM-based DC sources at the ▪ stage of a dilution fridge, paving the way for near term large-scale quantum computing applications.

Operating semiconductor quantum processors with hopping spins.

Qubits that can be efficiently controlled are essential for the development of scalable quantum hardware. Although resonant control is used to execute high-fidelity quantum gates, the scalability is challenged by the integration of high-frequency oscillating signals, qubit cross-talk, and heating. Here, we show that by engineering the hopping of spins between quantum dots with a site-dependent spin quantization axis, quantum control can be established with discrete signals. We demonstrate hopping-based quantum logic and obtain single-qubit gate fidelities of 99.97%, coherent shuttling fidelities of 99.992% per hop, and a two-qubit gate fidelity of 99.3%, corresponding to error rates that have been predicted to allow for quantum error correction. We also show that hopping spins constitute a tuning method by statistically mapping the coherence of a 10-quantum dot system. Our results show that dense quantum dot arrays with sparse occupation could be developed for efficient and high-connectivity qubit registers.

Miniaturized Sniffing Device based on an Array of Fluorescent Carbon Quantum Dots and Metallic Nanoclusters Efficiently Identifies Hematologic Malignancy in Adults.

The study demonstrates the potential of an optical nose made by depositing an array of fluorescent nanomaterials on a paper substrate for the early detection of leukemia in adults. This is based on the fact that blood volatile organic compounds (VOCs) are useful leukemia biomarkers. The integrated design was miniaturized and comprised both sensing zones and a sample holding zone, which were installed on a small sheet of paper within a miniature cubic reaction chamber fabricated by using 3D printing technology. The sensing device, comprising seven fluorescent sensing elements, namely, metal nanoclusters, quantum dots, and carbon dots was capable of detecting VOCs in the blood headspace and providing a colorimetric signature that could discriminate between blood samples from healthy and cancerous individuals. A total of 70 new leukemia cases and 51 healthy controls aged 20-50 years were studied. The device required a 60 μL portion of the blood sample and reacted to blood VOCs after 3 h when kept at 50 °C. The imaging data from the device was processed by linear discriminant analysis, and the results confirmed efficient identification of patient samples from healthy samples with 100% accuracy. Overall, the array system is noninvasive (or minimally invasive), portable, fast, inexpensive, and requires only a small amount of blood sample.

Efficient characterization of a double quantum dot using the Hubbard model

Semiconductor quantum dots are favorable candidates for quantum information processing due to their long coherence time and potential scalability. However, the calibration and characterization of interconnected quantum dot arrays have proven to be challenging tasks. One method to characterize the configuration of such an array involves using the Hubbard model. In this paper, we present an efficient characterization algorithm that efficiently extracts the Hubbard model parameters, including tunnel coupling and capacitive coupling energy, from experimental stability diagrams. Leveraging the dual-annealing optimizer, we determine the set of Hubbard parameters that best characterize the experimental data. We compare our method with an alternate, well-established measure of tunnel coupling and find good agreement within the investigated regime. Our extracted tunnel couplings range from 69 to 517 μeV, and we discuss the limiting factors of our method.