Silicon-based Quantum Computer Research Articles

Electric field dependence of spin qubit in a Si-MOS quantum dot

Abstract Valley, the intrinsic feature of silicon, is an inescapable subject in silicon-based quantum computing. At the spin-valley hotspot, both Rabi frequency and state relaxation rate are significantly enhanced. With protection against charge noise, the valley degree of freedom is also conceived to encode a qubit to realize noise-resistant quantum computing. Here, based on the spin qubit composed of one or three electrons, we characterize the intrinsic properties of valley in an isotopically enriched silicon quantum dot (QD) device. For one-electron qubit, we measure two electric-dipole spin resonance (EDSR) signals which are attributed to partial occupation of two valley states. The resonance frequencies of two EDSR signals have opposite electric field dependences. Moreover, we characterize the electric field dependence of the upper valley state based on three-electron qubit experiments. The difference of electric field dependences of two valleys is 52.02 MHz/V, which is beneficial for tuning qubit frequency to meet different experimental requirements. As an extension of electrical control spin qubits, the opposite electric field dependence is crucial for qubit addressability, individual single-qubit control and two-qubit gate approaches in scalable quantum computing.

Effect of high temperature annealing on cryogenic transport properties of silicon MOSFETs with a thin SiO2/HfO2 stacked dielectric

Quantum computing is expected to break the computing power bottleneck with the help of quantum superposition and quantum entanglement. In order to fabricate fault-tolerant quantum computers for encoding quantum information, it is important to improve the cryogenic mobility of silicon-based metal oxide semiconductor field effect transistors (MOSFETs) with a thin gate dielectric layer as much as possible. Based on a thin SiO2/HfO2 stacked dielectric, we investigate the effect of post-deposition annealing (PDA) temperature on the MOSFET cryogenic transport properties. The results show that silicon atoms will diffuse into the HfO2 to form silicates during PDA, leading to the HfO2 dielectric constant decrease. As the PDA temperature increases, the proportion of monoclinic hafnium oxide decreases and the tetragonal phase increases gradually. The oxygen vacancy content increases gradually, resulting in fixed charge density increases and the mobility decreases. The contribution of the forming gas annealing (FGA) to the mobility enhancement is clarified and the HfO2 recrystallization process is revealed from the perspective of long-time annealing. Finally, the mobility peak of silicon MOSFETs with thin SiO2/HfO2 dielectrics is enhanced to 1387 cm2(V·s)−1 at 1.6 K, which provides a technical pathway for the development of silicon-based quantum computation.

Thin films of silicon nitride deposited at room temperature by non-reactive magnetron sputtering: radiofrequency power and deposition time influence on the formation of α-Si3N4 and its optical properties

Silicon nitride’s excellent electronic and optical properties have positioned it as an indispensable element in silicon-based photonic platforms and photonic quantum computing. Chemical Vapor Deposition (CVD) and Plasma Enhanced CVD (PECVD) techniques predominate in high-performance silicon nitride thin film manufacture. Unfortunately, Chemical Vapor Deposition and Plasma Enhanced CVD are expensive techniques that use hazardous gases and very high substrate temperatures. In this work, we used the sputtering technique to grow α-Si3N4 thin films at room temperature. We identified that by applying radiofrequency powers between 30 and 50 W combined with deposition times below 120 min, we could achieve the growth of silicon nitride (SiNX) films with uniformly distributed crystalline particles, limited formation of clusters, and minimal alterations in atomic ordering. The Volmer-Weber model governs the film’s growth, which favors its continuity and surface roughness. The optical bandgaps of our SiNX films ranged from 2.3 to 3.9 eV, and their RMS roughness never exceeded 4 nm. We observed a quasi-linear deposition rate concerning radiofrequency power and deposition time, whereby we were able to grow SiNX films controllably and reproducibly with thicknesses ranging from 45 to 500 nm.

Probing the Atomic Arrangement of Subsurface Dopants in a Silicon Quantum Device Platform.

High-density structures of subsurface phosphorus dopants in silicon continue to garner interest as a silicon-based quantum computer platform; however, a much-needed confirmation of their dopant arrangement has been lacking. In this work, we take advantage of the chemical specificity of X-ray photoelectron diffraction to obtain the precise structural configuration of P dopants in subsurface Si:P δ-layers. The growth of δ-layer systems with different levels of doping is carefully studied and verified using X-ray photoelectron spectroscopy and low-energy electron diffraction. Subsequent diffraction measurements reveal that in all cases, the subsurface dopants primarily substitute with Si atoms from the host material. Furthermore, no signs of carrier-inhibiting P-P dimerization can be observed. Our observations not only settle a nearly decade-long debate about the dopant arrangement but also demonstrate how X-ray photoelectron diffraction is surprisingly well suited for studying subsurface dopant structure. This work thus provides valuable input for an updated understanding of the behavior of Si:P δ-layers and the modeling of their derived quantum devices.

Single-electron pump in a quantum dot array for silicon quantum computers

It is necessary to load single electrons into individual quantum dots (QDs) in an array for implementing fully scalable silicon-based quantum computers. However, this single-electron loading would be impacted by the variability of the QD characteristics, and suppressing this variability is highly challenging even in the state-of-the-art silicon front-end process. Here, we used a single-electron pump (SEP) for loading single electrons into a QD array as a preparatory step to use electrons as spin qubits. We used parallel gates in the QD array as a SEP and demonstrated 100 MHz operation with an accuracy of 99% at 4 K. By controlling the timing of a subsequent gate synchronously as a shutter, we found that the jitter representing electron transfer was less than 10 ns, which would be acceptable for a typical operating speed of around 1 MHz for silicon qubits.

Superconducting and Silicon-Based Semiconductor Quantum Computers: A review

Quantum computers are based on the theory of quantum mechanics, and their powerful parallel data processing capability is expected to solve many mathematical problems that too are difficult to be handled by classical computers. Especially with the increase of data processing volume, the quantum advantage is more obvious. Among the many physical systems for quantum computers, superconducting quantum circuit and semiconductor quantum dot computers show amazing potential due to their compatibility with traditional integrated circuit process technology and ultrashort gating time of nanoseconds. Superconducting qubits consisting of Josephson junctions and superconducting coplanar capacitors are easily integrated into a large scale for their simple circuit structure and conventional semiconductor process compatibility. Semiconductor qubits made from isotopically purified silicon (Si)-based materials greatly suppress nuclear spin noise, and decoherence times of ultralong milliseconds can be achieved. In this article, we systematically describe the challenges faced by superconducting qubits and semiconductor qubits in hot issues such as error correction and decoherence and look into the future development of superconducting quantum computers and Si-based semiconductor quantum computers.

Current Status and Future Development of Quantum Computation

Quantum computation, as part of the broader field of quantum information, represents an assembly of concepts and techniques that concern the nature and processing of information based on quantum mechanics. Quantum computation utilizes unique resources such as quantum superposition and quantum entanglement to encode and process information and has been proved to be dominantly advantageous over classical computation on certain important scientific and engineering problems. Potential applications of quantum computation are expected to influence future information technology and many other related fields deeply and significantly. In this article, we briefly review the history of quantum computation, including how its fundamental ideas and concepts came into being and the development of its significant theories and algorithms. We also discuss the status and outlook of several representative technical routes in this field, including superconducting quantum computation, distributed superconducting quantum computation, photonic quantum computation, trapped-ion quantum computation, silicon-based quantum computation, as well as other systems. Furthermore, by analyzing certain common issues faced by all routes, we propose some thoughts and suggestions for future development of quantum computation in China. We particularly emphasize the following: reinforcement of strategic planning at a national level, establishment of a research team of high caliber, and boost of relevant fundamental research and development of core techniques and critical instruments.

New progress of silicon-based semiconductor quantum computation

<sec>Spin qubits in silicon-based semiconductor quantum dots have become one of the prominent candidates for realizing fault-tolerant quantum computing due to their long coherence time, good controllability, and compatibility with modern advanced integrated circuit manufacturing processes. In recent years, due to the remarkable advances in silicon-based materials, the structure of quantum dot and its fabrication process, and qubit manipulation technology, the great progress of high-fidelity state preparation and readout, single- and two-qubit gates of spin qubits for silicon based semiconductor quantum computation has been achieved. The control fidelities for single- and two-qubit gates all exceed 99%—fault tolerance threshold required by the surface code known for its exceptionally high tolerance to errors. In this paper, we briefly introduce the basic concepts of silicon-based semiconductor quantum dots, discuss the state-of-art technologies used to improve the fidelities of single- and two-qubit gates, and finally highlight the research directions that should be focused on.</sec><sec>This paper is organized as follows. Firstly, we introduce three major types of quantum dot (QD) devices fabricated on different silicon-based substrates, including Si/SiGe heterojunction and Si/SiO<sub>2</sub>. The spin degree of electron or nucleus hosted in QD can be encoded into spin qubits. Electron spin qubits can be thermally initialized to ground state by using an electron reservoirs, and can be read out by spin-charge conversion mechanism: energy-selective readout (Elzerman readout) with reservoirs or Pauli spin blockade (PSB) without reservoirs. Additionally, high fidelity single-shot readout has been demonstrated by using radio-frequency gate reflectometry combined with the PSB, which has unique advantages in large-scale qubit array. To coherently control the spin qubits, electron dipole resonance (ESR) or electron dipole spin resonance (EDSR) for electron and nuclear magnetic resonance (NMR) for nucleus are introduced. With the help of isotope purification greatly improving the dephasing time of qubit and fast single-qubit manipulation based on EDSR, fidelity above 99.9% can be reached. For the two-qubit gates based on exchange interaction between electron spins, the strength of interaction <inline-formula><tex-math id="M1">\begin{document}$ J $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.png"/></alternatives></inline-formula> combined with Zeeman energy difference <inline-formula><tex-math id="M2">\begin{document}$ \Delta {E}_{z} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.png"/></alternatives></inline-formula> determines the energy levels of system, which lead to the different two-qubit gates, such as controlled-Z (CZ), controlled-Rotation (CROT), and the square root of the SWAP gate (<inline-formula><tex-math id="M3">\begin{document}$ \sqrt{\rm{S}\rm{W}\rm{A}\rm{P}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.png"/></alternatives></inline-formula>) gates. In order to improve the fidelity of two-qubit gates, a series of key technologies is used experimentally, they being isotope purification, symmetry operation, careful Hamiltonian engineering, and gate set tomography. Fidelity of two-qubit gates exceeding 99% has been demonstrated for electron spin qubits in Si/SiGe quantum dots and nuclear spin qubits in donors. These advances have pushed the silicon-based spin qubit platform to become a major stepping stone towards fault-tolerant quantum computation. Finally, we discuss the future study of spin qubits, that is, how to effectively expand the number of qubits, and many other problems to be explored and solved.</sec>

CMOS-based cryogenic control of silicon quantum circuits.

The most promising quantum algorithms require quantum processors that host millions of quantum bits when targeting practical applications1. A key challenge towards large-scale quantum computation is the interconnect complexity. In current solid-state qubit implementations, an important interconnect bottleneck appears between the quantum chip in a dilution refrigerator and the room-temperature electronics. Advanced lithography supports the fabrication of both control electronics and qubits in silicon using technology compatible with complementary metal oxide semiconductors (CMOS)2. When the electronics are designed to operate at cryogenic temperatures, they can ultimately be integrated with the qubits on the same die or package, overcoming the 'wiring bottleneck'3-6. Here we report a cryogenic CMOS control chip operating at 3 kelvin, which outputs tailored microwave bursts to drive silicon quantum bits cooled to 20 millikelvin. We first benchmark the control chip and find an electrical performance consistent with qubit operations of 99.99 per cent fidelity, assuming ideal qubits. Next, we use it to coherently control actual qubits encoded in the spin of single electrons confined in silicon quantum dots7-9 and find that the cryogenic control chip achieves the same fidelity as commercial instruments at room temperature. Furthermore, we demonstrate the capabilities of the control chip by programming a number of benchmarking protocols, as well as the Deutsch-Josza algorithm10, on a two-qubit quantum processor. These results open up the way towards a fully integrated, scalable silicon-based quantum computer.

The sub-band structure of atomically sharp dopant profiles in silicon

The downscaling of silicon-based structures and proto-devices has now reached the single-atom scale, representing an important milestone for the development of a silicon-based quantum computer. One especially notable platform for atomic-scale device fabrication is the so-called Si:P δ-layer, consisting of an ultra-dense and sharp layer of dopants within a semiconductor host. Whilst several alternatives exist, it is on the Si:P platform that many quantum proto-devices have been successfully demonstrated. Motivated by this, both calculations and experiments have been dedicated to understanding the electronic structure of the Si:P δ-layer platform. In this work, we use high-resolution angle-resolved photoemission spectroscopy to reveal the structure of the electronic states which exist because of the high dopant density of the Si:P δ-layer. In contrast to published theoretical work, we resolve three distinct bands, the most occupied of which shows a large anisotropy and significant deviation from simple parabolic behaviour. We investigate the possible origins of this fine structure, and conclude that it is primarily a consequence of the dielectric constant being large (ca. double that of bulk Si). Incorporating this factor into tight-binding calculations leads to a major revision of band structure; specifically, the existence of a third band, the separation of the bands, and the departure from purely parabolic behaviour. This new understanding of the band structure has important implications for quantum proto-devices which are built on the Si:P δ-layer platform.

Improving mobility of silicon metal-oxide–semiconductor devices for quantum dots by high vacuum activation annealing

To improve mobility of fabricated silicon metal-oxide–semiconductor (MOS) quantum devices, forming gas annealing is a common method used to mitigate the effects of disorder at the Si/SiO2 interface. However, the importance of activation annealing is usually ignored. Here, we show that a high vacuum environment for implantation activation is beneficial for improving mobility compared to nitrogen atmosphere. Low-temperature transport measurements of Hall bars show that peak mobility can be improved by a factor of two, reaching using high vacuum annealing during implantation activation. Moreover, the charge stability diagram of a single quantum dot is mapped, with no visible disturbance caused by disorder, suggesting the possibility of fabricating high-quality quantum dots on commercial wafers. Our results may provide valuable insights into device optimization in silicon-based quantum computing.

Variability and Fidelity Limits of Silicon Quantum Gates Due to Random Interface Charge Traps

Silicon offers an attractive material platform for hardware realization of quantum computing. In this study, a microscopic stochastic simulation method is developed to model the effect of random interface charge traps in silicon metal-oxide-semiconductor (MOS) quantum gates. The statistical results show that by using a fast two-qubit gate in isotopically purified silicon, the two-qubit silicon-based quantum gates have the fidelity >98% with a probability of 75% for the state-of-the-art MOS interface quality. By using a composite gate pulse, the fidelity can be further improved to >99.5% with the 75% probability. The variations between the quantum gate devices, however, are largely due to the small number of traps per device. The results highlight the importance of variability consideration due to random charge traps and potential to improve fidelity in silicon-based quantum computing.

Single-Shot Spin Readout in Semiconductors Near the Shot-Noise Sensitivity Limit

New highly sensitive detectors can read the state of a single-spin qubit in microseconds with 97% accuracy, providing a realistic path toward robust error correction in silicon-based quantum computation.

Toward a silicon-based quantum computer.

A controlled NOT gate for two quantum bits is demonstrated with a strained-silicon device

Silicon CMOS architecture for a spin-based quantum computer

Recent advances in quantum error correction codes for fault-tolerant quantum computing and physical realizations of high-fidelity qubits in multiple platforms give promise for the construction of a quantum computer based on millions of interacting qubits. However, the classical-quantum interface remains a nascent field of exploration. Here, we propose an architecture for a silicon-based quantum computer processor based on complementary metal-oxide-semiconductor (CMOS) technology. We show how a transistor-based control circuit together with charge-storage electrodes can be used to operate a dense and scalable two-dimensional qubit system. The qubits are defined by the spin state of a single electron confined in quantum dots, coupled via exchange interactions, controlled using a microwave cavity, and measured via gate-based dispersive readout. We implement a spin qubit surface code, showing the prospects for universal quantum computation. We discuss the challenges and focus areas that need to be addressed, providing a path for large-scale quantum computing.

A photonic platform for donor spin qubits in silicon.

Donor spins in silicon are highly competitive qubits for upcoming quantum technologies, offering complementary metal-oxide semiconductor compatibility, coherence (T2) times of minutes to hours, and simultaneous initialization, manipulation, and readout fidelities near ~99.9%. This allows for many quantum error correction protocols, which will be essential for scale-up. However, a proven method of reliably coupling spatially separated donor qubits has yet to be identified. We present a scalable silicon-based platform using the unique optical properties of "deep" chalcogen donors. For the prototypical 77Se+ donor, we measure lower bounds on the transition dipole moment and excited-state lifetime, enabling access to the strong coupling limit of cavity quantum electrodynamics using known silicon photonic resonator technology and integrated silicon photonics. We also report relatively strong photon emission from this same transition. These results unlock clear pathways for silicon-based quantum computing, spin-to-photon conversion, photonic memories, integrated single-photon sources, and all-optical switches.

Ultralow-Noise Atomic-Scale Structures for Quantum Circuitry in Silicon

The atomically precise doping of silicon with phosphorus (Si:P) using scanning tunneling microscopy (STM) promises ultimate miniaturization of field effect transistors. The one-dimensional (1D) Si:P nanowires are of particular interest, retaining exceptional conductivity down to the atomic scale, and are predicted as interconnects for a scalable silicon-based quantum computer. Here, we show that ultrathin Si:P nanowires form one of the most-stable electrical conductors, with the phenomenological Hooge parameter of low-frequency noise being as low as ≈10(-8) at 4.2 K, nearly 3 orders of magnitude lower than even carbon-nanotube-based 1D conductors. A in-built isolation from the surface charge fluctuations due to encapsulation of the wires within the epitaxial Si matrix is the dominant cause for the observed suppression of noise. Apart from quantum information technology, our results confirm the promising prospects for precision-doped Si:P structures in atomic-scale circuitry for the 11 nm technology node and beyond.

A silicon-based surface code quantum computer

AbstractIndividual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.

On the nuclear magnetic resonance frequency of phosphorus donor atom in a silicon-based quantum computer

The nuclear magnetic resonance (NMR) frequency of a single qubit structure of Kane’s solid-state quantum computer is investigated by using the perturbation theory. With higher-order excited states (up to 3d modes) included in our calculation, the perturbation frequencies and energies are obtained numerically. To compute for arbitrary A gate geometries, the perturbation potential inside the qubit structure is determined through an electromagnetic simulation method. Calculations show that the potential distributions for realistic A gate geometries are far from linear ones. Our results show that the A gate voltage has a much more effective control over the NMR frequency of the phosphorus nucleus than that previously shown. Using our method, arbitrary A gate structures of any shapes or geometries can be engineered for the realization of a solid-state scalable quantum computer. We also investigate an alternative A gate structure using SiGe as the insulation barrier. Our study shows that this A gate structure o...

Qubit addressing using hyperfine-interaction control by an electric field in a magnetic crystal

We demonstrate experimentally the hyperfine-interaction control by an electric field, which is the operating principle of the addressable qubit operation in a silicon-based solid-state quantum computer in a new quantum computer system, a magnetic crystal. The transferred hyperfine field at a ${\mathrm{F}}^{\ensuremath{-}}$ nucleus caused by neighboring ${\mathrm{Mn}}^{2+}$ electron spins in an antiferromagnetic ${\mathrm{MnF}}_{2}$ single crystal was measured by $^{19}\mathrm{F}$ nuclear magnetic resonance (NMR) with an external electric field applied along the [110] crystal direction. The electric field splits the $^{19}\mathrm{F}$ NMR peak into two resolved lines that come from the F nuclei located at geometrically equivalent sites. A line splitting of 56 kHz was achieved at an electric field of 3.4 V/$\ensuremath{\mu}$m. One of the ${\mathrm{F}}^{\ensuremath{-}}$ nuclear spins could be flipped selectively by a composite radio-frequency pulse while leaving the other unchanged, thereby demonstrating qubit addressing via electric field control of the hyperfine interaction.