Andrea Morello

A single-atom electron spin qubit in silicon

A single atom is the prototypical quantum system, and a natural candidate for a quantum bit, or qubit—the elementary unit of a quantum computer. Atoms have been successfully used to store and process quantum information in electromagnetic traps, as well as in diamond through the use of the nitrogen–vacancy-centre point defect. Solid-state electrical devices possess great potential to scale up such demonstrations from few-qubit control to larger-scale quantum processors. Coherent control of spin qubits has been achieved in lithographically defined double quantum dots in both GaAs (refs 3–5) and Si (ref. 6). However, it is a formidable challenge to combine the electrical measurement capabilities of engineered nanostructures with the benefits inherent in atomic spin qubits. Here we demonstrate the coherent manipulation of an individual electron spin qubit bound to a phosphorus donor atom in natural silicon, measured electrically via single-shot read-out. We use electron spin resonance to drive Rabi oscillations, and a Hahn echo pulse sequence reveals a spin coherence time exceeding 200 µs. This time should be even longer in isotopically enriched 28Si samples. Combined with a device architecture that is compatible with modern integrated circuit technology, the electron spin of a single phosphorus atom in silicon should be an excellent platform on which to build a scalable quantum computer.

Silicon quantum electronics

This review describes recent groundbreaking results in Si, Si/SiGe, and dopant-based quantum dots, and it highlights the remarkable advances in Si-based quantum physics that have occurred in the past few years. This progress has been possible thanks to materials development of Si quantum devices, and the physical understanding of quantum effects in silicon. Recent critical steps include the isolation of single electrons, the observation of spin blockade, and single-shot readout of individual electron spins in both dopants and gated quantum dots in Si. Each of these results has come with physics that was not anticipated from previous work in other material systems. These advances underline the significant progress toward the realization of spin quantum bits in a material with a long spin coherence time, crucial for quantum computation and spintronics.

A two-qubit logic gate in silicon

Quantum computation requires qubits that can be coupled in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates. Many physical realizations of qubits exist, including single photons, trapped ions, superconducting circuits, single defects or atoms in diamond and silicon, and semiconductor quantum dots, with single-qubit fidelities that exceed the stringent thresholds required for fault-tolerant quantum computing. Despite this, high-fidelity two-qubit gates in the solid state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits, owing to the difficulties of coupling qubits and dephasing in semiconductor systems. Here we present a two-qubit logic gate, which uses single spins in isotopically enriched silicon and is realized by performing single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the Loss–DiVincenzo proposal. We realize CNOT gates via controlled-phase operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is used in the two-qubit controlled-phase gate. By independently reading out both qubits, we measure clear anticorrelations in the two-spin probabilities of the CNOT gate.

An addressable quantum dot qubit with fault-tolerant control-fidelity

Exciting progress towards spin-based quantum computing has recently been made with qubits realized using nitrogen-vacancy centres in diamond and phosphorus atoms in silicon. For example, long coherence times were made possible by the presence of spin-free isotopes of carbon and silicon. However, despite promising single-atom nanotechnologies, there remain substantial challenges in coupling such qubits and addressing them individually. Conversely, lithographically defined quantum dots have an exchange coupling that can be precisely engineered, but strong coupling to noise has severely limited their dephasing times and control fidelities. Here, we combine the best aspects of both spin qubit schemes and demonstrate a gate-addressable quantum dot qubit in isotopically engineered silicon with a control fidelity of 99.6%, obtained via Clifford-based randomized benchmarking and consistent with that required for fault-tolerant quantum computing. This qubit has dephasing time T2* = 120 μs and coherence time T2 = 28 ms, both orders of magnitude larger than in other types of semiconductor qubit. By gate-voltage-tuning the electron g*-factor we can Stark shift the electron spin resonance frequency by more than 3,000 times the 2.4 kHz electron spin resonance linewidth, providing a direct route to large-scale arrays of addressable high-fidelity qubits that are compatible with existing manufacturing technologies.

Storing quantum information for 30 seconds in a nanoelectronic device

The spin of an electron or a nucleus in a semiconductor naturally implements the unit of quantum information--the qubit. In addition, because semiconductors are currently used in the electronics industry, developing qubits in semiconductors would be a promising route to realize scalable quantum information devices. The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms, or charge and spin fluctuations arising from defects in oxides and interfaces. For materials such as silicon, enrichment of the spin-zero (28)Si isotope drastically reduces spin-bath decoherence. Experiments on bulk spin ensembles in (28)Si crystals have indeed demonstrated extraordinary coherence times. However, it remained unclear whether these would persist at the single-spin level, in gated nanostructures near amorphous interfaces. Here, we present the coherent operation of individual (31)P electron and nuclear spin qubits in a top-gated nanostructure, fabricated on an isotopically engineered (28)Si substrate. The (31)P nuclear spin sets the new benchmark coherence time (>30 s with Carr-Purcell-Meiboom-Gill (CPMG) sequence) of any single qubit in the solid state and reaches >99.99% control fidelity. The electron spin CPMG coherence time exceeds 0.5 s, and detailed noise spectroscopy indicates that--contrary to widespread belief--it is not limited by the proximity to an interface. Instead, decoherence is probably dominated by thermal and magnetic noise external to the device, and is thus amenable to further improvement.

High-fidelity readout and control of a nuclear spin qubit in silicon

Detection of nuclear spin precession is critical for a wide range of scientific techniques that have applications in diverse fields including analytical chemistry, materials science, medicine and biology. Fundamentally, it is possible because of the extreme isolation of nuclear spins from their environment. This isolation also makes single nuclear spins desirable for quantum-information processing, as shown by pioneering studies on nitrogen-vacancy centres in diamond. The nuclear spin of a 31P donor in silicon is very promising as a quantum bit: bulk measurements indicate that it has excellent coherence times and silicon is the dominant material in the microelectronics industry. Here we demonstrate electrical detection and coherent manipulation of a single 31P nuclear spin qubit with sufficiently high fidelities for fault-tolerant quantum computing. By integrating single-shot readout of the electron spin with on-chip electron spin resonance, we demonstrate quantum non-demolition and electrical single-shot readout of the nuclear spin with a readout fidelity higher than 99.8 per cent—the highest so far reported for any solid-state qubit. The single nuclear spin is then operated as a qubit by applying coherent radio-frequency pulses. For an ionized 31P donor, we find a nuclear spin coherence time of 60 milliseconds and a one-qubit gate control fidelity exceeding 98 per cent. These results demonstrate that the dominant technology of modern electronics can be adapted to host a complete electrical measurement and control platform for nuclear-spin-based quantum-information processing.

Transport Spectroscopy of Single Phosphorus Donors in a Silicon Nanoscale Transistor

We have developed nanoscale double-gated field-effect-transistors for the study of electron states and transport properties of single deliberately implanted phosphorus donors. The devices provide a high-level of control of key parameters required for potential applications in nanoelectronics. For the donors, we resolve transitions corresponding to two charge states successively occupied by spin down and spin up electrons. The charging energies and the Lande g-factors are consistent with expectations for donors in gated nanostructures.

Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting

Although silicon is a promising material for quantum computation, the degeneracy of the conduction band minima (valleys) must be lifted with a splitting sufficient to ensure the formation of well-defined and long-lived spin qubits. Here we demonstrate that valley separation can be accurately tuned via electrostatic gate control in a metal-oxide-semiconductor quantum dot, providing splittings spanning 0.3-0.8 meV. The splitting varies linearly with applied electric field, with a ratio in agreement with atomistic tight-binding predictions. We demonstrate single-shot spin read-out and measure the spin relaxation for different valley configurations and dot occupancies, finding one-electron lifetimes exceeding 2 s. Spin relaxation occurs via phonon emission due to spin-orbit coupling between the valley states, a process not previously anticipated for silicon quantum dots. An analytical theory describes the magnetic field dependence of the relaxation rate, including the presence of a dramatic rate enhancement (or hot-spot) when Zeeman and valley splittings coincide.

Architecture for high-sensitivity single-shot readout and control of the electron spin of individual donors in silicon

We describe a method to control and detect in single-shot the electron spin state of an individual donor in silicon with greatly enhanced sensitivity. A silicon-based Single-Electron Transistor (SET) allows for spin-dependent tunneling of the donor electron directly into the SET island during the read-out phase. Simulations show that the charge transfer signals are typically \Delta q > 0.2 e - over an order of magnitude larger than achievable with metallic SETs on the SiO2 surface. A complete spin-based qubit structure is obtained by adding a local Electron Spin Resonance line for coherent spin control. This architecture is ideally suited to demonstrate and study the coherent properties of donor electron spins, but can be expanded and integrated with classical control electronics in the context of scale-up.

Observation of the single-electron regime in a highly tunable silicon quantum dot

We report on low-temperature electronic transport measurements of a silicon metal-oxidesemiconductor quantum dot, with independent gate control of electron densities in the leads and the quantum dot island. This architecture allows the dot energy levels to be probed without affecting the electron density in the leads and vice versa. Appropriate gate biasing enables the dot occupancy to be reduced to the single-electron level, as evidenced by magnetospectroscopy measurements of the ground state of the first two charge transitions. Independent gate control of the electron reservoirs also enables discrimination between excited states of the dot and density of states modulations in the leads.