Andrew S. Dzurak

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.

Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors

The past decade has seen remarkable progress in isolating and controlling quantum coherence using charges and spins in semiconductors. Quantum control has been established at room temperature, and electron spin coherence times now exceed several seconds, a nine–order-of-magnitude increase in coherence compared with the first semiconductor qubits. These coherence times rival those traditionally found only in atomic systems, ushering in a new era of ultracoherent spintronics. We review recent advances in quantum measurements, coherent control, and the generation of entangled states and describe some of the challenges that remain for processing quantum information with spins in semiconductors.

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.

Charge-based quantum computing using single donors in semiconductors

Solid-state quantum computer architectures with qubits encoded using single atoms are now feasible given recent advances in the atomic doping of semiconductors. Here we present a charge qubit consisting of two dopant atoms in a semiconductor crystal, one of which is singly ionized. Surface electrodes control the qubit and a radio-frequency single-electron transistor provides fast readout. The calculated single gate times, of order 50 ps or less, are much shorter than the expected decoherence time. We propose universal one- and two-qubit gate operations for this system and discuss prospects for fabrication and scale up.

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.

Density-Dependent Spin Polarization in Ultra-Low -Disorder Quantum Wires

There is controversy as to whether a one-dimensional (1D) electron gas can spin polarize in the absence of a magnetic field. Together with a simple model, we present conductance measurements on ultra-low-disorder quantum wires supportive of a spin polarization at B=0. A spin energy gap is indicated by the presence of a feature in the range (0.5-0.7)x2e(2)/h in conductance data. Importantly, it appears that the spin gap is not constant but a function of the electron density. Data obtained using a bias spectroscopy technique are consistent with the spin gap widening further as the Fermi level is increased.

Controlled shallow single-ion implantation in silicon using an active substrate for sub-20-keV ions

We demonstrate a method for the controlled implantation of single ions into a silicon substrate with energy of sub-20‐keV. The method is based on the collection of electron-hole pairs generated in the substrate by the impact of a single ion. We have used the method to implant single 14‐keV P31 ions through nanoscale masks into silicon as a route to the fabrication of devices based on single donors in silicon.