Coherent long-distance displacement of individual electron spins

The SpinBus architecture for scaling spin qubits with electron shuttling

Quantum processor architectures must enable scaling to large qubit numbers while providing two-dimensional qubit connectivity and exquisite operation fidelities. For microwave-controlled semiconductor spin qubits, dense arrays have made considerable progress, but are still limited in size by wiring fan-out and exhibit significant crosstalk between qubits. To overcome these limitations, we introduce the SpinBus architecture, which uses electron shuttling to connect qubits and features low operating frequencies and enhanced qubit coherence. Device simulations for all relevant operations in the Si/SiGe platform validate the feasibility with established semiconductor patterning technology and operation fidelities exceeding 99.9%. Control using room temperature instruments can plausibly support at least 144 qubits, but much larger numbers are conceivable with cryogenic control circuits. Building on the theoretical feasibility of high-fidelity spin-coherent electron shuttling as key enabling factor, the SpinBus architecture may be the basis for a spin-based quantum processor that meets the scalability requirements for practical quantum computing.

Non-adiabatic quantum control of quantum dot arrays with fixed exchange using Cartan decomposition

In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin state transfer in long chains of singly occupied quantum dots in a non-adiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems in a systematic way, and use dynamical invariants to design smooth non-adiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we discuss the extensibility of our results to directed shuttling of spin states on two-dimensional lattices of quantum dots with fixed coupling. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Phase Transformation-Induced Quantum Dot States on the Bi/Si(111) Surface

Nanopatterns at near atomic dimensions with controllable quantum dot states (QDSs) are promising candidates for the continued downscaling of electronic devices. Herein, we report a phase transition-induced QD system achieved on the √3 × √3-Bi/Si(111) surface reconstruction, which points the way to a novel strategy on QDS implementation. Combining scanning tunneling microscopy, scanning tunneling spectroscopy, and density functional theory (DFT) calculations, the structure, energy dispersion, and size effect on band gap of the QDs are measured and verified. As-created QDs can be manipulated with a dot size down to 2 nm via Bi phase transformation, which, in turn, is triggered by thermal annealing at 700 K. The transition mechanism is also supported by our DFT calculations, and an empirical analytical model is developed to predict the transformation kinetics.

Distant spin entanglement via fast and coherent electron shuttling

In the quest for large-scale quantum computing, networked quantum computers offer a natural path towards scalability. While recent experiments have demonstrated nearest neighbour entanglement for electron spin qubits in semiconductors, on-chip long-distance entanglement could bring more versatility to connect quantum core units. Here, we employ the moving trapping potential of a surface acoustic wave to realize the controlled and coherent transfer of a pair of entangled electron spins between two distant quantum dots. The subsequent electron displacement induces coherent spin rotations, which drives spin quantum interferences. We observe high-contrast interference as a signature of the preservation of the entanglement all along the displacement procedure, which includes a separation of the two spins by a distance of 6 μm. This work opens the route towards fast on-chip deterministic interconnection of remote quantum bits in semiconductor quantum circuits.

Adiabatic quantum state transfer in a semiconductor quantum-dot spin chain

Semiconductor quantum-dot spin qubits are a promising platform for quantum computation, because they are scalable and possess long coherence times. In order to realize this full potential, however, high-fidelity information transfer mechanisms are required for quantum error correction and efficient algorithms. Here, we present evidence of adiabatic quantum-state transfer in a chain of semiconductor quantum-dot electron spins. By adiabatically modifying exchange couplings, we transfer single- and two-spin states between distant electrons in less than 127 ns. We also show that this method can be cascaded for spin-state transfer in long spin chains. Based on simulations, we estimate that the probability to correctly transfer single-spin eigenstates and two-spin singlet states can exceed 0.95 for the experimental parameters studied here. In the future, state and process tomography will be required to verify the transfer of arbitrary single qubit states with a fidelity exceeding the classical bound. Adiabatic quantum-state transfer is robust to noise and pulse-timing errors. This method will be useful for initialization, state distribution, and readout in large spin-qubit arrays for gate-based quantum computing. It also opens up the possibility of universal adiabatic quantum computing in semiconductor quantum-dot spin qubits.

Coherent control of individual electron spins in a two-dimensional quantum dot array

The coherent manipulation of individual quantum objects organized in arrays is a prerequisite to any scalable quantum information platform. The cumulated efforts to control electron spins in quantum dot arrays have permitted the recent realization of quantum simulators and multielectron spin-coherent manipulations. Although a natural path to resolve complex quantum-matter problems and to process quantum information, two-dimensional (2D) scaling with a high connectivity of such implementations remains undemonstrated. Here we demonstrate the 2D coherent control of individual electron spins in a 3 × 3 array of tunnel-coupled quantum dots. We focus on several key quantum functionalities: charge-deterministic loading and displacement, local spin readout and local coherent exchange manipulation between two electron spins trapped in adjacent dots. This work lays some of the foundations to exploit a 2D array of electron spins for quantum simulation and information processing.

Coherent electron displacement for quantum information processing using attosecond single cycle pulses

Coherent electron displacement is a conventional strategy for processing quantum information, as it enables to interconnect distinct sites in a network of atoms. The efficiency of the processing relies on the precise control of the mechanism, which has yet to be established. Here, we theoretically demonstrate a new route to drive the electron displacement on a timescale faster than that of the dynamical distortion of the electron wavepacket by utilizing attosecond single-cycle pulses. The characteristic feature of these pulses relies on a vast momentum transfer to an electron, leading to its displacement following a unidirectional path. The scenario is illustrated by revealing the spatiotemporal nature of the displaced wavepacket encoding a quantum superposition state. We map out the associated phase information and retrieve it over long distances from the origin. Moreover, we show that a sequence of such pulses applied to a chain of ions enables attosecond control of the directionality of the coherent motion of the electron wavepacket back and forth between the neighbouring sites. An extension to a two-electron spin state demonstrates the versatility of the use of these pulses. Our findings establish a promising route for advanced control of quantum states using attosecond single-cycle pulses, which pave the way towards ultrafast processing of quantum information as well as imaging.

Conditional teleportation of quantum-dot spin states

Among the different platforms for quantum information processing, individual electron spins in semiconductor quantum dots stand out for their long coherence times and potential for scalable fabrication. The past years have witnessed substantial progress in the capabilities of spin qubits. However, coupling between distant electron spins, which is required for quantum error correction, presents a challenge, and this goal remains the focus of intense research. Quantum teleportation is a canonical method to transmit qubit states, but it has not been implemented in quantum-dot spin qubits. Here, we present evidence for quantum teleportation of electron spin qubits in semiconductor quantum dots. Although we have not performed quantum state tomography to definitively assess the teleportation fidelity, our data are consistent with conditional teleportation of spin eigenstates, entanglement swapping, and gate teleportation. Such evidence for all-matter spin-state teleportation underscores the capabilities of exchange-coupled spin qubits for quantum-information transfer.

Despite recent demonstrations of coherent spin-state transfer in arrays of spin qubits via exchange interaction, all-matter spin-state teleportation is still out of reach. Here the authors provide evidence for conditional teleportation of quantum-dot spin states, entanglement swapping, and gate teleportation.

Single-photon emission from single-electron transport in a SAW-driven lateral light-emitting diode

The long-distance quantum transfer between electron-spin qubits in semiconductors is important for realising large-scale quantum computing circuits. Electron-spin to photon-polarisation conversion is a promising technology for achieving free-space or fibre-coupled quantum transfer. In this work, using only regular lithography techniques on a conventional 15 nm GaAs quantum well, we demonstrate acoustically-driven generation of single photons from single electrons, without the need for a self-assembled quantum dot. In this device, a single electron is carried in a potential minimum of a surface acoustic wave (SAW) and is transported to a region of holes to form an exciton. The exciton then decays and creates a single optical photon within 100 ps. This SAW-driven electroluminescence, without optimisation, yields photon antibunching with g⁽²⁾(0) = 0.39 ± 0.05 in the single-electron limit (g⁽²⁾(0) = 0.63 ± 0.03 in the raw histogram). Our work marks the first step towards electron-to-photon (spin-to-polarisation) qubit conversion for scaleable quantum computing architectures.

Electron-spin to photon-polarisation conversion is a promising technology for achieving free-space or fibre coupled quantum transfer. Here, the authors demonstrate acoustically-driven single photons from single electrons, without the need for self-assembled quantum dots, using a SAW-driven lateral n-i-p junction.

Theoretical Study on Spin-Selective Coherent Electron Transfer in a Quantum Dot Array

Recently, we proposed the spin-selective coherent electron transfer in a silicon-quantum-dot array. It requires temporal tuning of two pulses of an oscillating magnetic field and gate voltage control. This paper proposes a simpler method that requires a single pulse of oscillating magnetic field and gate voltage control. We examined the robustness of the control against the error in the pulse amplitude and the effect of the excited states relaxation to the control efficiency. In addition, we propose a novel control method based on a shortcuts-to-adiabaticity protocol, which utilizes two pulses but requires temporal control of the pulse amplitude for only one of them. We compared their efficiencies under the effect of realistic pulse amplitude errors and relaxation.

Sound-driven single-electron transfer in a circuit of coupled quantum rails

Surface acoustic waves (SAWs) strongly modulate the shallow electric potential in piezoelectric materials. In semiconductor heterostructures such as GaAs/AlGaAs, SAWs can thus be employed to transfer individual electrons between distant quantum dots. This transfer mechanism makes SAW technologies a promising candidate to convey quantum information through a circuit of quantum logic gates. Here we present two essential building blocks of such a SAW-driven quantum circuit. First, we implement a directional coupler allowing to partition a flying electron arbitrarily into two paths of transportation. Second, we demonstrate a triggered single-electron source enabling synchronisation of the SAW-driven sending process. Exceeding a single-shot transfer efficiency of 99%, we show that a SAW-driven integrated circuit is feasible with single electrons on a large scale. Our results pave the way to perform quantum logic operations with flying electron qubits.

Coherent spin-state transfer via Heisenberg exchange

Quantum information science has the potential to revolutionize modern technology by providing resource-efficient approaches to computing¹, communication² and sensing³. Although the physical qubits in a realistic quantum device will inevitably suffer errors, quantum error correction creates a path to fault-tolerant quantum information processing⁴. Quantum error correction, however, requires that individual qubits can interact with many other qubits in the processor. Engineering such high connectivity can pose a challenge for platforms such as electron spin qubits⁵, which naturally favour linear arrays. Here we present an experimental demonstration of the transmission of electron spin states via the Heisenberg exchange interaction in an array of spin qubits. Heisenberg exchange coupling-a direct manifestation of the Pauli exclusion principle, which prevents any two electrons with the same spin state from occupying the same orbital-tends to swap the spin states of neighbouring electrons. By precisely controlling the wavefunction overlap between electrons in a semiconductor quadruple quantum dot array, we generate a series of coherent SWAP operations to transfer both single-spin and entangled states back and forth in the array without moving any electrons. Because the process is scalable to large numbers of qubits, state transfer through Heisenberg exchange will be useful for multi-qubit gates and error correction in spin-based quantum computers.

Shuttling a single charge across a one-dimensional array of silicon quantum dots

Significant advances have been made towards fault-tolerant operation of silicon spin qubits, with single qubit fidelities exceeding 99.9%, several demonstrations of two-qubit gates based on exchange coupling, and the achievement of coherent single spin-photon coupling. Coupling arbitrary pairs of spatially separated qubits in a quantum register poses a significant challenge as most qubit systems are constrained to two dimensions with nearest neighbor connectivity. For spins in silicon, new methods for quantum state transfer should be developed to achieve connectivity beyond nearest-neighbor exchange. Here we demonstrate shuttling of a single electron across a linear array of nine series-coupled silicon quantum dots in ~50 ns via a series of pairwise interdot charge transfers. By constructing more complex pulse sequences we perform parallel shuttling of two and three electrons at a time through the array. These experiments demonstrate a scalable approach to physically transporting single electrons across large silicon quantum dot arrays.

Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot

In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines fidelity loss in spin transport from multiple perspectives. We first study incoherent fidelity loss due to hyperfine and spin-orbit interaction. We calculate fidelity loss due to the random Overhauser field from hyperfine interaction, and spin relaxation rate due to spin-orbit interaction in a wide range of experimental parameters with a focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We then analyze systematic errors due to non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-Stückelberg interference to achieve high-fidelity spin transport at a higher speed. At last, we study another systematic error caused by the correction to the electron g-factor from the double dot potential, which can lead to a notable phase error. In all, our results should provide a useful guidance for future experiments on coherent electron spin transport.

Coherent control of single electrons: a review of current progress

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

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.