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.

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Silicon quantum electronics

Silicon is one of the most promising semiconductor materials for spin-based information processing devices. Its advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of a (28)Si form with no magnetic nuclei overcomes a primary source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than that achieved in isolated high-vacuum systems such as trapped ions. Here we examine electron spin coherence of donors in pure (28)Si material (residual (29)Si concentration <50 ppm) with donor densities of 10(14)-10(15) cm(-3). We elucidate three mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime T(2) up to 2 s. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. A magnetic field gradient suppresses such interactions, producing an extrapolated electron spin T(2) of 10 s at 1.8 K. These coherence lifetimes are without peer in the solid state and comparable to high-vacuum qubits, making electron spins of donors in silicon ideal components of quantum computers, or quantum memories for systems such as superconducting qubits.

Electron spin coherence exceeding seconds in high-purity 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 (31)P 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 (31)P 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 percent-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 (31)P donor, we find a nuclear spin coherence time of 60 milliseconds and a one-qubit gate control fidelity exceeding 98 percent. 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.

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

Quantum memories capable of storing and retrieving coherent information for extended times at room temperature would enable a host of new technologies. Electron and nuclear spin qubits using shallow neutral donors in semiconductors have been studied extensively but are limited to low temperatures (≲10 kelvin); however, the nuclear spins of ionized donors have the potential for high-temperature operation. We used optical methods and dynamical decoupling to realize this potential for an ensemble of phosphorous-31 donors in isotopically purified silicon-28 and observed a room-temperature coherence time of over 39 minutes. We further showed that a coherent spin superposition can be cycled from 4.2 kelvin to room temperature and back, and we report a cryogenic coherence time of 3 hours in the same system.

https://science.sciencemag.org/content/sci/342/6160/830.full.pdf

Room-Temperature Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon-28

Long-Lived Donors Quantum computing in materials such as silicon would simplify integration with existing electronic components; however, the coherence times of such qubits, especially at room temperature, are affected by the interaction with the busy environment of a solid. Eliminating isotopic impurities from the host material improves coherence times, as observed for qubits, based on the nuclear spin of neutral P donors in Si. Saeedi et al. (p. 830) modified this system by using charged P donors instead of neutral ones; by manipulating the states of the donors optically and using dynamical decoupling, the coherence time of the qubits was extended to 3 hours at cryogenic temperatures and 39 minutes at room temperature. Isotopically purified silicon is used to extend the coherence time of qubits based on phosphorus impurities. Quantum memories capable of storing and retrieving coherent information for extended times at room temperature would enable a host of new technologies. Electron and nuclear spin qubits using shallow neutral donors in semiconductors have been studied extensively but are limited to low temperatures (≲10 kelvin); however, the nuclear spins of ionized donors have the potential for high-temperature operation. We used optical methods and dynamical decoupling to realize this potential for an ensemble of phosphorous-31 donors in isotopically purified silicon-28 and observed a room-temperature coherence time of over 39 minutes. We further showed that a coherent spin superposition can be cycled from 4.2 kelvin to room temperature and back, and we report a cryogenic coherence time of 3 hours in the same system.

Supplementary Materials for Room-Temperature Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon-28

A metrological challenge is currently underway to replace the present definition of the kilogram by the mass of a certain number of silicon atoms. A prerequisite for this is that the Avogadro constant, N A , which defines the number of atoms in a mole, is determined with a relative uncertainty of better than 2 x 10- 8 . Silicon crystals are used for this determination, the difficulty arising thereby is the measurement of the average molar mass of natural Si. Consequently, a worldwide collaboration has been launched to produce ∼5 kg of 28 Si single crystal with an enrichment factor greater than 0.99985 and of sufficient chemical purity so that it can be used to determine N A with the targeted relative measurement uncertainty mentioned above. In the following, the development and first successful tests of all technological steps are reported, and the new equipment for the production of high-purity 28 Si with an enrichment of not less than 0.9999 is described. All steps are defined by a Technical Road Map (TRM28) mandatory for all partners, and all key results are measured by calibrated and certified means, e.g. the C content of the final material is less than 10 15 atoms/cm 3 and the specific resistance is in the range from 400 to 1000 Ωcm. New applications based on this highly enriched and purified 28 Si, and on 29 Si and 30 Si monocrystals produced in parallel, are reported briefly in the fields of solid state spectroscopy, spintronics, quantum computing, cooling of highly loaded SYS optics, superlattice structure (SLS), terahertz laser.

H.-J. Pohl

Papers

Enrichment of silicon for a better kilogram