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We investigate hole spin relaxation in the single- and multi-hole regime in a 2x2 germanium quantum dot array. We use radiofrequency (rf) charge sensing and observe Pauli Spin-Blockade (PSB) for every second interdot transition up to the (1,5)-(0,6) anticrossing, consistent with a standard Fock-Darwin spectrum. We find spin relaxation times $T_1$ as high as 32 ms for a quantum dot with single-hole occupation and 1.2 ms for a quantum dot occupied by five-holes, setting benchmarks for spin relaxation times for hole quantum dots. Furthermore, we investigate the qubit addressability and sensitivity to electric fields by measuring the resonance frequency dependence of each qubit on gate voltages. We are able to tune the resonance frequency over a large range for both the single and multi-hole qubit. Simultaneously, we find that the resonance frequencies are only weakly dependent on neighbouring gates, and in particular the five-hole qubit resonance frequency is more than twenty times as sensitive to its corresponding plunger gate. The excellent individual qubit tunability and long spin relaxation times make holes in germanium promising for addressable and high-fidelity spin qubits in dense two-dimensional quantum dot arrays for large-scale quantum information., Comment: 7 Pages (6 Main + 1 Supplementary Information) 5 Figures (4 Main, 1 Supplementary Information)

In the effort to develop disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing and transmitting quantum information. These devices leverage the special properties of holes in germanium, such as their inherently strong spin–orbit coupling and their ability to host superconducting pairing correlations. In this Review, we start by introducing the physics of holes in low-dimensional germanium structures, providing key insights from a theoretical perspective. We then examine the materials-science progress underpinning germanium-based planar heterostructures and nanowires. We go on to review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductor–semiconductor devices for hybrid quantum systems. We conclude by identifying the most promising avenues towards scalable quantum information processing in germanium-based systems. Germanium is a promising material to build quantum components for scalable quantum information processing. This Review examines progress in materials science and devices that has enabled key building blocks for germanium quantum technology, such as hole-spin qubits and superconductor–semiconductor hybrids.

Single-charge pumps are the main candidates for quantum-based standards of the unit ampere because they can generate accurate and quantized electric currents. In order to approach the metrological requirements in terms of both accuracy and speed of operation, in the past decade there has been a focus on semiconductor-based devices. The use of a variety of semiconductor materials enables the universality of charge pump devices to be tested, a highly desirable demonstration for metrology, with GaAs and Si pumps at the forefront of these tests. Here, we show that pumping can be achieved in a yet unexplored semiconductor, i.e. germanium. We realise a single-hole pump with a tunable-barrier quantum dot electrostatically defined at a Ge/SiGe heterostructure interface. We observe quantized current plateaux by driving the system with a single sinusoidal drive up to a frequency of 100 MHz. The operation of the prototype was affected by accidental formation of multiple dots, probably due to disorder potential, and random charge fluctuations. We suggest straightforward refinements of the fabrication process to improve pump characteristics in future experiments., 7 pages, 4 figures

A four-qubit quantum processor based on germanium hole spin quantum dots is presented. Universal quantum logic is demonstrated on qubits that are positioned in a two-by-two grid, revealing that spin qubits can be coupled in two dimensions. A two-by-two qubit quantum processor based on germanium hole spin quantum dots.

Quantum dots fabricated using techniques and materials that are compatible with semiconductor manufacturing are promising for quantum information processing. While great progress has been made toward high-fidelity control of quantum dots positioned in a linear arrangement, scalability along two dimensions is a key step toward practical quantum information processing. Here we demonstrate a two-dimensional quantum dot array where each quantum dot is tuned to single-charge occupancy, verified by simultaneous measuring with two integrated radio frequency charge sensors. We achieve this by using planar germanium quantum dots with low disorder and small effective mass, allowing the incorporation of dedicated barrier gates to control the coupling of the quantum dots. We demonstrate hole charge filling consistent with a Fock-Darwin spectrum and show that we can tune single-hole quantum dots from isolated quantum dots to strongly exchange coupled quantum dots. These results motivate the use of planar germanium quantum dots as building blocks for quantum simulation and computation., 7 pages, 4 figures

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 wavefunctions in quantum dot systems, as long as they occupy neighbouring 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. We experimentally demonstrate direct exchange coupling and provide evidence for second neighbour mediated superexchange in a linear array of three single-electron spin qubits in silicon, inferred from the electron spin resonance frequency spectra. We confirm theoretically through atomistic modeling that the device geometry only allows for sizeable direct exchange coupling for neighbouring dots, while next nearest neighbour coupling cannot stem from the vanishingly small tail of the electronic wavefunction of the remote dots, and is only possible if mediated., 20 pages, 1.4MB, 4 figures

Solid-state qubits integrated on semiconductor substrates currently require at least one wire from every qubit to the control electronics, leading to a so-called wiring bottleneck for scaling. Demultiplexing via on-chip circuitry offers an effective strategy to overcome this bottleneck. In the case of gate-defined quantum dot arrays, specific static voltages need to be applied to many gates simultaneously to realize electron confinement. When a charge-locking structure is placed between the quantum device and the demultiplexer, the voltage can be maintained locally. In this study, we implement a switched-capacitor circuit for charge-locking and use it to float the plunger gate of a single quantum dot. Parallel plate capacitors, transistors, and quantum dot devices are monolithically fabricated on a Si/SiGe-based substrate to avoid complex off-chip routing. We experimentally study the effects of the capacitor and transistor size on the voltage accuracy of the floating node. Furthermore, we demonstrate that the electrochemical potential of the quantum dot can follow a 100 Hz pulse signal while the dot is partially floating, which is essential for applying this strategy in qubit experiments.

The prospect of building quantum circuits using advanced semiconductor manufacturing positions quantum dots as an attractive platform for quantum information processing. Extensive studies on various materials have led to demonstrations of two-qubit logic in gallium arsenide, silicon, and germanium. However, interconnecting larger numbers of qubits in semiconductor devices has remained an outstanding challenge. Here, we demonstrate a four-qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two-by-two array and obtain controllable coupling along both directions. Qubit logic is implemented all-electrically and the exchange interaction can be pulsed to freely program one-qubit, two-qubit, three-qubit, and four-qubit operations, resulting in a compact and high-connectivity circuit. We execute a quantum logic circuit that generates a four-qubit Greenberger-Horne-Zeilinger state and we obtain coherent evolution by incorporating dynamical decoupling. These results are an important step towards quantum error correction and quantum simulation with quantum dots., Comment: 7 pages, 5 figures, supplementary materials with 11 figures and 2 tables in separate file

Building a large-scale quantum computer requires the co-optimization of both the quantum bits (qubits) and their control electronics. By operating the CMOS control circuits at cryogenic temperatures (cryo-CMOS), and hence in close proximity to the cryogenic solid-state qubits, a compact quantum-computing system can be achieved, thus promising scalability to the large number of qubits required in a practical application. This work presents a cryo-CMOS microwave signal generator for frequency-multiplexed control of $4\times 32$ qubits (32 qubits per RF output). A digitally intensive architecture offering full programmability of phase, amplitude, and frequency of the output microwave pulses and a wideband RF front end operating from 2 to 20 GHz allow targeting both spin qubits and transmons. The controller comprises a qubit-phase-tracking direct digital synthesis (DDS) back end for coherent qubit control and a single-sideband (SSB) RF front end optimized for minimum leakage between the qubit channels. Fabricated in Intel 22-nm FinFET technology, it achieves a 48-dB SNR and 45-dB spurious-free dynamic range (SFDR) in a 1-GHz data bandwidth when operating at 3 K, thus enabling high-fidelity qubit control. By exploiting the on-chip 4096-instruction memory, the capability to translate quantum algorithms to microwave signals has been demonstrated by coherently controlling a spin qubit at both 14 and 18 GHz.

Cryogenic CMOS (cryo-CMOS) is a viable technology for the control interface of the large-scale quantum computers able to address non-trivial problems. In this paper, we demonstrate state-of-the-art cryo-CMOS circuits and systems for such application and we discuss the challenges still to be faced on the path towards practical quantum computers.

Perhaps the greatest challenge facing quantum computing hardware development is the lack of a high throughput electrical characterization infrastructure at the cryogenic temperatures required for qubit measurements. In this article, we discuss our efforts to develop such a line to guide 300mm spin qubit process development. This includes (i) working with our supply chain to create the required cryogenic high volume testing ecosystem, (ii) driving full wafer cryogenic testing for both transistor and quantum dot statistics, and (iii) utilizing this line to develop a quantum dot process resulting in key electrical data comparable to that from leading devices in literature, but with unprecedented yield and reproducibility.

Electrons and holes confined in quantum dots define an excellent building block for quantum emergence, simulation, and computation. In order for quantum electronics to become practical, large numbers of quantum dots will be required, necessitating the fabrication of scaled structures such as linear and 2D arrays. Group IV semiconductors contain stable isotopes with zero nuclear spin and can thereby serve as excellent host for spins with long quantum coherence. Here we demonstrate group IV quantum dot arrays in silicon metal-oxide-semiconductor (SiMOS), strained silicon (Si/SiGe) and strained germanium (Ge/SiGe). We fabricate using a multi-layer technique to achieve tightly confined quantum dots and compare integration processes. While SiMOS can benefit from a larger temperature budget and Ge/SiGe can make ohmic contact to metals, the overlapping gate structure to define the quantum dots can be based on a nearly identical integration. We realize charge sensing in each platform, for the first time in Ge/SiGe, and demonstrate fully functional linear and two-dimensional arrays where all quantum dots can be depleted to the last charge state. In Si/SiGe, we tune a quintuple quantum dot using the N+1 method to simultaneously reach the few electron regime for each quantum dot. We compare capacitive cross talk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. These results constitute an excellent base for quantum computation with quantum dots and provide opportunities for each platform to be integrated with standard semiconductor manufacturing., Main text: 8 pages, 6 figures. Supporting Info: 5 pages, 3 figures

This paper presents a family of voltage references in standard 40-nm CMOS that exploits the temperature dependence of dynamic-threshold MOS, NMOS and PMOS transistors in weak inversion to enable operation over the ultra-wide temperature range from 4.2 K to 300 K. The proposed references achieve a temperature drift below 436 ppm/K over a statistically significant number of samples after a single-point trim and a supply regulation better than 1.7 %/V from a a supply as low as 0.99 V. These results demonstrate, for the first time, the generation of PVT-independent voltages over an ultra-wide temperature range using sub-1-V nanometer CMOS circuits, thus enabling the use of the proposed references in harsh environments, such as in space and quantum-computing applications.

Continuing advancements in quantum information processing have caused a paradigm shift from research mainly focused on testing the reality of quantum mechanics to engineering qubit devices with numbers required for practical quantum computation. One of the major challenges in scaling toward large-scale solid-state systems is the limited input/output (I/O) connectors present in cryostats operating at sub-kelvin temperatures required to execute quantum logic with high fidelity. This interconnect bottleneck is equally present in the device fabrication-measurement cycle, which requires high-throughput and cryogenic characterization to develop quantum processors. Here we multiplex quantum transport of two-dimensional electron gases at sub-kelvin temperatures. We use commercial off-the-shelf CMOS multiplexers to achieve an order of magnitude increase in the number of wires. Exploiting this technology, we accelerate the development of 300 mm epitaxial wafers manufactured in an industrial CMOS fab and report a remarkable electron mobility of (3.9 ± 0.6) × 105 cm2/Vs and percolation density of (6.9 ± 0.4) × 1010 cm−2, representing a key step toward large silicon qubit arrays. We envision that the demonstration will inspire the development of cryogenic electronics for quantum information, and because of the simplicity of assembly and versatility, we foresee widespread use of similar cryo-CMOS circuits for high-throughput quantum measurements and control of quantum engineered systems.

We investigate the structural and quantum transport properties of isotopically enriched Si28/SiO228 stacks deposited on 300-mm Si wafers in an industrial CMOS fab. Highly uniform films are obtained with an isotopic purity greater than 99.92%. Hall-bar transistors with an oxide stack comprising 10 nm of Si28O2 and 17 nm of Al2O3 (equivalent oxide thickness of 17 nm) are fabricated in an academic cleanroom. A critical density for conduction of 1.75×1011cm-2 and a peak mobility of 9800cm2/Vs are measured at a temperature of 1.7 K. The Si28/SiO228 interface is characterized by a roughness of Δ=0.4nm and a correlation length of Λ=3.4nm. An upper bound for valley splitting energy of 480μeV is estimated at an effective electric field of 9.5 MV/m. These results support the use of wafer-scale Si28/SiO228 as a promising material platform to manufacture industrial spin qubits.

We fabricate Josephson field-effect transistors in germanium quantum wells contacted by superconducting aluminum and demonstrate supercurrents carried by holes that extend over junction lengths of several micrometers. In superconducting quantum point contacts we observe discretization of supercurrent, as well as Fabry-Perot resonances, demonstrating ballistic transport. The magnetic field dependence of the supercurrent follows a clear Fraunhofer-like pattern, and Shapiro steps appear upon microwave irradiation. Multiple Andreev reflections give rise to conductance enhancement and evidence a transparent interface, confirmed by analyzing the excess current. These demonstrations of ballistic superconducting transport are promising for hybrid quantum technology in germanium. A© 2019 American Physical Society.

The promise of quantum computation with quantum dots has stimulated widespread research. Still, a platform that can combine excellent control with fast and high-fidelity operation is absent. Here, we show single and two-qubit operations based on holes in germanium. A high degree of control over the tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder and by working in a virtual gate space. Spin-orbit coupling obviates the need for microscopic elements and enables rapid qubit control with Rabi frequencies exceeding 100 MHz and a single-qubit fidelity of 99.3 %. We demonstrate fast two-qubit CX gates executed within 75 ns and minimize decoherence by operating at the charge symmetry point. Planar germanium thus matured within one year from a material that can host quantum dots to a platform enabling two-qubit logic, positioning itself as a unique material to scale up spin qubits for quantum information., 6 pages, 5 figures

Qubits based on quantum dots have excellent prospects for scalable quantum technology due to their inherent compatibility with standard semiconductor manufacturing. While early on it was recognized that holes may offer a multitude of favourable properties for fast and scalable quantum control, research thus far has remained almost exclusively restricted to the simpler electron system. However, recent developments with holes have led to separate demonstrations of single-shot readout and fast quantum logic, albeit only in the multi-hole regime. Here, we establish a single-hole spin qubit in germanium and demonstrate the integration of single-shot readout and quantum control. Moreover, we make use of Pauli spin blockade, allowing to arbitrarily set the qubit resonance frequency, while providing large readout windows. We deplete a planar germanium double quantum dot to the last hole, confirmed by radio-frequency reflectrometry charge sensing, and achieve single-shot spin readout. To demonstrate the integration of the readout and qubit operation, we show Rabi driving on both qubits and find remarkable electric control over their resonance frequencies. Finally, we analyse the spin relaxation time, which we find to exceed one millisecond, setting the benchmark for hole-based spin qubits. The ability to coherently manipulate a single hole spin underpins the quality of strained germanium and defines an excellent starting point for the construction of novel quantum hardware., Comment: 6 pages, 4 figures

Buried-channel semiconductor heterostructures are an archetype material platform for the fabrication of gated semiconductor quantum devices. Sharp confinement potential is obtained by positioning the channel near the surface; however, nearby surface states degrade the electrical properties of the starting material. Here, a 2D hole gas of high mobility (5 × 105 cm2 V−1 s−1) is demonstrated in a very shallow strained germanium (Ge) channel, which is located only 22 nm below the surface. The top-gate of a dopant-less field effect transistor controls the channel carrier density confined in an undoped Ge/SiGe heterostructure with reduced background contamination, sharp interfaces, and high uniformity. The high mobility leads to mean free paths ≈ 6 µm, setting new benchmarks for holes in shallow field effect transistors. The high mobility, along with a percolation density of 1.2 × 1011cm−2, light effective mass (0.09me), and high effective g-factor (up to 9.2) highlight the potential of undoped Ge/SiGe as a low-disorder material platform for hybrid quantum technologies.

Quantum computing is on the verge of a transition from fundamental research to practical applications. Yet, to make the step to large-scale quantum computation, an extensible qubit system has to be developed. In classical semiconductor technology, this was made possible by the invention of the integrated circuit, which allowed to interconnect large numbers of components without having to solder to each and every one of them. Similarly, we expect that the scaling of interconnections and control lines with the number of qubits will be a central bottleneck in creating large-scale quantum technology. Here, we define the quantum Rent exponent p to quantify the progress in overcoming this challenge at different levels throughout the quantum computing stack. We further discuss the concept of quantum extensibility as an indicator of a platform’s potential to reach the large quantum volume needed for universal quantum computing and review extensibility limits faced by different qubit implementations on the way towards truly large-scale qubit systems.

The spin states of electrons confined in semiconductor quantum dots form a promising platform for quantum computation. Recent studies of silicon CMOS qubits have shown coherent manipulation of electron spin states with extremely high fidelity. However, manipulation of single electron spins requires large oscillatory magnetic fields to be generated on-chip, making it difficult to address individual qubits when scaling up to multi-qubit devices. The spin-orbit interaction allows spin states to be controlled with electric fields, which act locally and are easier to generate. While the spin-orbit interaction is weak for electrons in silicon, valence band holes have an inherently strong spin-orbit interaction. However, creating silicon quantum dots in which a single hole can be localised, in an architecture that is suitable for scale-up to a large number of qubits, is a challenge. Here we report a silicon quantum dot, with an integrated charge sensor, that can be operated down to the last hole. We map the spin states and orbital structure of the first six holes, and show they follow the Fock-Darwin spectrum. We also find that hole-hole interactions are extremely strong, reducing the two-hole singlet-triplet splitting by 90% compared to the single particle level spacing of 3.5 meV. These results provide a route to single hole spin quantum bits in a planar silicon CMOS architecture., 7 pages, 3 figures

Quantum computing's value proposition of an exponential speedup in computing power for certain applications has propelled a vast array of research across the globe. While several different physical implementations of device level qubits are being investigated, semiconductor spin qubits have many similarities to scaled transistors. In this article, we discuss the device/integration of full 300mm based spin qubit devices. This includes the development of (i) a 28 Si epitaxial module ecosystem for growing isotopically pure substrates with among the best Hall mobility at these oxide thicknesses, (ii) a custom 300mm qubit testchip and integration/device line, and (iii) a novel dual nested gate integration process for creating quantum dots.

We investigate the effect of the valley degree of freedom on Pauli-spin blockade readout of spin qubits in silicon. The valley splitting energy sets the singlet-triplet splitting and thereby constrains the detuning range. The valley phase difference controls the relative strength of the intra- and inter-valley tunnel couplings, which, in the proposed Pauli-spin blockade readout scheme, couple singlets and polarized triplets, respectively. We find that high-fidelity readout is possible for a wide range of phase differences, while taking into account experimentally observed valley splittings and tunnel couplings. We also show that the control of the valley splitting together with the optimization of the readout detuning can compensate the effect of the valley phase difference. To increase the measurement fidelity and extend the relaxation time we propose a latching protocol that requires a triple quantum dot and exploits weak long-range tunnel coupling. These opportunities are promising for scaling spin qubit systems and improving qubit readout fidelity, 8 pages, 6 figures

We identify the presence of monoatomic steps at the Si/SiGe or Si/SiO$_2$ interface as a dominant source of variations in the dephasing time of Si quantum dot (QD) spin qubits. First, using atomistc tight-binding calculations we show that the g-factors and their Stark shifts undergo variations due to these steps. We compare our theoretical predictions with experiments on QDs at a Si/SiO$_2$ interface, in which we observe significant differences in Stark shifts between QDs in two different samples. We also experimentally observe variations in the $g$-factors of one-electron and three-electron spin qubits realized in three neighboring QDs on the same sample, at a level consistent with our calculations. The dephasing times of these qubits also vary, most likely due to their varying sensitivity to charge noise, resulting from different interface conditions. More importantly, from our calculations we show that by employing the anisotropic nature of the spin-orbit interaction (SOI) in a Si QD, we can minimize and control these variations. Ultimately, we predict that the dephasing times of the Si QD spin qubits will be anisotropic and can be improved by at least an order of magnitude, by aligning the external DC magnetic field towards specific crystal directions., 5 pages, 3 figures, Supplemental Material (3 pages, 2 figures)

A two-qubit quantum processor in a silicon device is demonstrated, which can perform the Deutsch–Josza algorithm and the Grover search algorithm. The development of platforms for spin-based quantum computing continues apace. The individual components of such a system have been the subject of much investigation, and they have been assembled to implement specific quantum-computational algorithms. Thomas Watson and colleagues have now taken such component integration and control to the next level. Using two single-electron-spin qubits in a silicon-based double quantum dot, they realize a system that can be simply programmed to perform different quantum algorithms on demand. Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing1,2. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform3,4,5. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations6,7,8,9. However, as seen with small-scale demonstrations of quantum computers using other types of qubit10,11,12,13, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch–Josza algorithm and the Grover search algorithm—canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85–89 per cent and concurrences of 73–82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

We investigate the magnetic field and temperature dependence of the single-electron spin lifetime in silicon quantum dots and find a lifetime of 2.8 ms at a temperature of 1.1 K. We develop a model based on spin-valley mixing and find that Johnson noise and two-phonon processes limit relaxation at low and high temperature respectively. We also investigate the effect of temperature on charge noise and find a linear dependence up to 4 K. These results contribute to the understanding of relaxation in silicon quantum dots and are promising for qubit operation at elevated temperatures., 8 pages, 6 figures

The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle electrons as a mechanism for on-chip flying qubits. In order to increase the number of qubits to the thousands or millions of qubits needed for practical quantum information we present an architecture based on shared control and a scalable number of lines. Crucially, the control lines define the qubit grid, such that no local components are required. Our design enables qubit coupling beyond nearest neighbors, providing prospects for non-planar quantum error correction protocols. Fabrication is based on a three-layer design to define qubit and tunnel barrier gates. We show that a double stripline on top of the structure can drive high-fidelity single-qubit rotations. Qubit addressability and readout are enabled by self-aligned inhomogeneous magnetic fields induced by direct currents through superconducting gates. Qubit coupling is based on the exchange interaction, and we show that parallel two-qubit gates can be performed at the detuning noise insensitive point. While the architecture requires a high level of uniformity in the materials and critical dimensions to enable shared control, it stands out for its simplicity and provides prospects for large-scale quantum computation in the near future., Comment: 13 pages, 7 figures

Superconductors and semiconductors are crucial platforms in the field of quantum computing. They can be combined to hybrids, bringing together physical properties that enable the discovery of new emergent phenomena and provide novel strategies for quantum control. The involved semiconductor materials, however, suffer from disorder, hyperfine interactions or lack of planar technology. Here we realise an approach that overcomes these issues altogether and integrate gate-defined quantum dots and superconductivity into a material system with strong spin-orbit coupling. In our germanium heterostructures, heavy holes with mobilities exceeding 500,000 cm$^2$/Vs are confined in shallow quantum wells that are directly contacted by annealed aluminium leads. We demonstrate gate-tunable superconductivity and find a characteristic voltage $I_cR_n$ that exceeds 10 $\mu$V. Germanium therefore has great promise for fast and coherent quantum hardware and, being compatible with standard manufacturing, could become a leading material in the quantum revolution., Comment: 7 pages, 5 figures

We theoretically model the spin-orbit interaction in silicon quantum dot devices, relevant for quantum computation and spintronics. Our model is based on a modified effective mass approach with spin-valley boundary conditions, derived from the interface symmetry under presence of perpendicular to the interface electric field. The g-factor renormalization in the two lowest valley states is explained by the interface-induced spin-orbit 2D (3D) interaction, favoring intervalley spin-flip tunneling over intravalley processes. We show that the quantum dot level structure makes only negligible higher order effects to the g-factor. We calculate the g-factor as a function of the magnetic field direction, which is sensitive to the interface symmetry. We identify spin-qubit dephasing sweet spots at certain directions of the magnetic field, where the g-factor renormalization is zeroed: these include perpendicular to the interface magnetic field, and also in-plain directions, the latter being defined by the interface-induced spin-orbit constants. The g-factor dependence on electric field opens the possibility for fast all-electric manipulation of an encoded, few electron spin-qubit, without the need of a nanomagnet or a nuclear spin-background. Our approach of an almost fully analytic theory allows for a deeper physical understanding of the importance of spin-orbit coupling to silicon spin qubits., Comment: 19 pages, 3 figures, Updated and added new estimations and references

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar architectures. Recently we made a proposal for a large scale quantum processor~[Li et al. arXiv:1711.03807 (2017)] to be implemented in silicon quantum dots. This system features a crossbar control architecture which limits parallel single qubit control, but allows the scheme to overcome control scaling issues that form a major hurdle to large scale quantum computing systems. In this work, we develop a language that makes it possible to easily map quantum circuits to crossbar systems, taking into account their architecture and control limitations. Using this language we show how to map well known quantum error correction codes such as the planar surface and color codes in this limited control setting with only a small overhead in time. We analyze the logical error behavior of this surface code mapping for estimated experimental parameters of the crossbar system and conclude that logical error suppression to a level useful for real quantum computation is feasible., 29 + 9 pages, 13 figures, 9 tables, 8 algorithms and 3 big boxes. Comments are welcome

Semiconductor spins are one of the few qubit realizations that remain a serious candidate for the implementation of large-scale quantum circuits. Excellent scalability is often argued for spin qubits defined by lithography and controlled via electrical signals, based on the success of conventional semiconductor integrated circuits. However, the wiring and interconnect requirements for quantum circuits are completely different from those for classical circuits, as individual DC, pulsed and in some cases microwave control signals need to be routed from external sources to every qubit. This is further complicated by the requirement that these spin qubits currently operate at temperatures below 100 mK. Here we review several strategies that are considered to address this crucial challenge in scaling quantum circuits based on electron spin qubits. Key assets of spin qubits include the potential to operate at 1 to 4 K, the high density of quantum dots or donors combined with possibilities to space them apart as needed, the extremely long spin coherence times, and the rich options for integration with classical electronics based on the same technology., 13 pages, 4 figures

We define single electron spin qubits in a silicon metal-oxide-semiconductor double quantum dot system. By mapping the qubit resonance frequency as a function of a gate-induced electric field, the spectrum reveals an anticrossing that is consistent with an intervalley spin-orbit coupling. We fit the data from which we extract an intervalley coupling strength of 43 MHz. In addition, we observe a narrow resonance near the primary qubit resonance when we operate the device in the (1,1) charge configuration. The experimental data are consistent with a simulation involving two weakly exchanged-coupled spins with a Zeeman energy difference of 1 MHz, of the same order as the Rabi frequency. We conclude that the narrow resonance is the result of driven transitions between the T- and T+ triplet states, using an electron spin resonance signal of frequency located halfway between the resonance frequencies of the two individual spins. The findings presented here offer an alternative method of implementing two-qubit gates, of relevance to the operation of larger-scale spin qubit systems.

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., Realisation of large-scale quantum computation requires both error correction capability and a large number of qubits. Here, the authors propose to use a CMOS-compatible architecture featuring a spin qubit surface code and individual qubit control via floating memory gate electrodes.

Quantum processors rely on classical electronic controllers to manipulate and read out the quantum state. As the performance of the quantum processor improves, non-idealities in the classical controller can become the performance bottleneck for the whole quantum computer. To prevent such limitation, this paper presents a systematic study of the impact of the classical electrical signals on the qubit fidelity. All operations, i.e. single-qubit rotations, two-qubit gates and read-out, are considered, in the presence of errors in the control electronics, such as static, dynamic, systematic and random errors. Although the presented study could be extended to any qubit technology, it currently focuses on single-electron spin qubits, because of several advantages, such as purely electrical control and long coherence times, and for their potential for large-scale integration. As a result of this study, detailed electrical specifications for the classical control electronics for a given qubit fidelity can be derived, as demonstrated with specific case studies. We also discuss the effect on qubit fidelity of the performance of the general-purpose room-temperature equipment that is typically employed to control the few qubits available today. Ultimately, we show that tailor-made electronic controllers can achieve significantly lower power, cost and size, as required to support the scaling up of quantum computers.

The electrical control of single spin qubits based on semiconductor quantum dots is of great interest for scalable quantum computing since electric fields provide an alternative mechanism for qubit control compared with magnetic fields and can also be easier to produce. Here we outline the mechanism for a drastic enhancement in the electrically-driven spin rotation frequency for silicon quantum dot qubits in the presence of a step at a heterointerface. The enhancement is due to the strong coupling between the ground and excited states which occurs when the electron wave function overcomes the potential barrier induced by the interface step. We theoretically calculate single qubit gate times tπ of 170 ns for a quantum dot confined at a silicon/silicon-dioxide interface. The engineering of such steps could be used to achieve fast electrical rotation and entanglement of spin qubits despite the weak spin-orbit coupling in silicon.

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 31P 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. This method, known as A-gate control, preserves the excellent coherence times and gate fidelities of isolated spins, and can be extended to arbitrarily many qubits without requiring multiple microwave sources., Main paper: 13 pages, 4 figures. Supplementary information: 25 pages, 13 figures