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.

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.

Bounds to electron spin qubit variability for scalable CMOS architectures.

Spins of electrons in silicon MOS quantum dots combine exquisite quantum properties and scalable fabrication. In the age of quantum technology, however, the metrics that crowned Si/SiO as the microelectronics standard need to be reassessed with respect to their impact upon qubit performance. We chart spin qubit variability due to the unavoidable atomic-scale roughness of the Si/SiO interface, compiling experiments across 12 devices, and develop theoretical tools to analyse these results.

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 scale. However, the operation of the large number of qubits required for advantageous quantum applications 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 higher.

Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields.

Efficient scaling and flexible control are key aspects of useful quantum computing hardware. Spins in semiconductors combine quantum information processing with electrons, holes or nuclei, control with electric or magnetic fields, and scalable coupling via exchange or dipole interaction. However, accessing large Hilbert space dimensions has remained challenging, due to the short-distance nature of the interactions.

Jellybean Quantum Dots in Silicon for Qubit Coupling and On-Chip Quantum Chemistry.

The small size and excellent integrability of silicon metal-oxide-semiconductor (SiMOS) quantum dot spin qubits make them an attractive system for mass-manufacturable, scaled-up quantum processors. Furthermore, classical control electronics can be integrated on-chip, in-between the qubits, if an architecture with sparse arrays of qubits is chosen. In such an architecture qubits are either transported across the chip via shuttling or coupled via mediating quantum systems over short-to-intermediate distances.

An electrically driven single-atom "flip-flop" qubit.

The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor.

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.

On-demand electrical control of spin qubits.

Once called a 'classically non-describable two-valuedness' by Pauli, the electron spin forms a qubit that is naturally robust to electric fluctuations. Paradoxically, a common control strategy is the integration of micromagnets to enhance the coupling between spins and electric fields, which, in turn, hampers noise immunity and adds architectural complexity. Here we exploit a switchable interaction between spins and orbital motion of electrons in silicon quantum dots, without a micromagnet.

Precision tomography of a three-qubit donor quantum processor in silicon.

Nuclear spins were among the first physical platforms to be considered for quantum information processing, because of their exceptional quantum coherence and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted P donor nuclei in a silicon nanoelectronic device.

Single-electron spin resonance in a nanoelectronic device using a global field.

Spin-based silicon quantum electronic circuits offer a scalable platform for quantum computation, combining the manufacturability of semiconductor devices with the long coherence times afforded by spins in silicon. Advancing from current few-qubit devices to silicon quantum processors with upward of a million qubits, as required for fault-tolerant operation, presents several unique challenges, one of the most demanding being the ability to deliver microwave signals for large-scale qubit control. Here, we demonstrate a potential solution to this problem by using a three-dimensional dielectric resonator to broadcast a global microwave signal across a quantum nanoelectronic circuit.

Bell-state tomography in a silicon many-electron artificial molecule.

An error-corrected quantum processor will require millions of qubits, accentuating the advantage of nanoscale devices with small footprints, such as silicon quantum dots. However, as for every device with nanoscale dimensions, disorder at the atomic level is detrimental to quantum dot uniformity. Here we investigate two spin qubits confined in a silicon double quantum dot artificial molecule.

A High-Sensitivity Charge Sensor for Silicon Qubits above 1 K.

Recent studies of silicon spin qubits at temperatures above 1 K are encouraging demonstrations that the cooling requirements for solid-state quantum computing can be considerably relaxed. However, qubit readout mechanisms that rely on charge sensing with a single-island single-electron transistor (SISET) quickly lose sensitivity due to thermal broadening of the electron distribution in the reservoirs. Here we exploit the tunneling between two quantized states in a double-island single-electron transistor (SET) to demonstrate a charge sensor with an improvement in the signal-to-noise ratio by an order of magnitude compared to a standard SISET, and a single-shot charge readout fidelity above 99% up to 8 K at a bandwidth greater than 100 kHz.

Exchange Coupling in a Linear Chain of Three Quantum-Dot Spin Qubits in Silicon.

Quantum gates between spin qubits can be implemented leveraging the natural Heisenberg exchange interaction between two electrons in contact with each other. This interaction is controllable by electrically tailoring the overlap between electronic wave functions in quantum dot systems, as long as they occupy neighboring dots. An alternative route is the exploration of superexchange-the coupling between remote spins mediated by a third idle electron that bridges the distance between quantum dots.

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

Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single-donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second.

Controllable freezing of the nuclear spin bath in a single-atom spin qubit.

The quantum coherence and gate fidelity of electron spin qubits in semiconductors are often limited by nuclear spin fluctuations. Enrichment of spin-zero isotopes in silicon markedly improves the dephasing time [Formula: see text], which, unexpectedly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom P qubit in enriched Si, we show that the abnormally long [Formula: see text] is due to the freezing of the dynamics of the residual Si nuclei, caused by the electron-nuclear hyperfine interaction.

Coherent electrical control of a single high-spin nucleus in silicon.

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers and demonstrations of quantum search and factoring algorithms.

A silicon quantum-dot-coupled nuclear spin qubit.

Single nuclear spins in the solid state are a potential future platform for quantum computing, because they possess long coherence times and offer excellent controllability. Measurements can be performed via localized electrons, such as those in single atom dopants or crystal defects. However, establishing long-range interactions between multiple dopants or defects is challenging.

Gate-based single-shot readout of spins in silicon.

Electron spins in silicon quantum dots provide a promising route towards realizing the large number of coupled qubits required for a useful quantum processor. For the implementation of quantum algorithms and error detection, qubit measurements are ideally performed in a single shot, which is presently achieved using on-chip charge sensors, capacitively coupled to the quantum dots. However, as the number of qubits is increased, this approach becomes impractical due to the footprint and complexity of the charge sensors, combined with the required proximity to the quantum dots.

Gigahertz Single-Electron Pumping Mediated by Parasitic States.

In quantum metrology, semiconductor single-electron pumps are used to generate accurate electric currents with the ultimate goal of implementing the emerging quantum standard of the ampere. Pumps based on electrostatically defined tunable quantum dots (QDs) have thus far shown the most promising performance in combining fast and accurate charge transfer. However, at frequencies exceeding approximately 1 GHz the accuracy typically decreases.

A dressed spin qubit in silicon.

Coherent dressing of a quantum two-level system provides access to a new quantum system with improved properties-a different and easily tunable level splitting, faster control and longer coherence times. In our work we investigate the properties of the dressed, donor-bound electron spin in silicon, and assess its potential as a quantum bit in scalable architectures. The two dressed spin-polariton levels constitute a quantum bit that can be coherently driven with an oscillating magnetic field, an oscillating electric field, frequency modulation of the driving field or a simple detuning pulse.

Electrically controlling single-spin qubits in a continuous microwave field.

Large-scale quantum computers must be built upon quantum bits that are both highly coherent and locally controllable. We demonstrate the quantum control of the electron and the nuclear spin of a single (31)P atom in silicon, using a continuous microwave magnetic field together with nanoscale electrostatic gates. The qubits are tuned into resonance with the microwave field by a local change in electric field, which induces a Stark shift of the qubit energies.

Bell's inequality violation with spins in silicon.

Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.

Pauli Spin Blockade of Heavy Holes in a Silicon Double Quantum Dot.

In this work, we study hole transport in a planar silicon metal-oxide-semiconductor based double quantum dot. We demonstrate Pauli spin blockade in the few hole regime and map the spin relaxation induced leakage current as a function of interdot level spacing and magnetic field. With varied interdot tunnel coupling, we can identify different dominant spin relaxation mechanisms.

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping.

As mass-produced silicon transistors have reached the nano-scale, their behavior and performances are increasingly affected, and often deteriorated, by quantum mechanical effects such as tunneling through single dopants, scattering via interface defects, and discrete trap charge states. However, progress in silicon technology has shown that these phenomena can be harnessed and exploited for a new class of quantum-based electronics. Among others, multi-layer-gated silicon metal-oxide-semiconductor (MOS) technology can be used to control single charge or spin confined in electrostatically-defined quantum dots (QD).