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Several domains of society will be disrupted once millions of high-quality qubits can be brought together to perform fault-tolerant quantum computing (FTQC). All quantum computing hardware available today is many orders of magnitude removed from the requirements for FTQC. The intimidating challenges associated with integrating such complex systems have already been addressed by the semiconductor industry -hence many qubit makers have retrofitted their technology to be CMOS-compatible. This compatibility, however, can have varying degrees ranging from the mere ability to fabricate qubits using a silicon wafer as a substrate, all the way to the co-integration of qubits with high-yield, low-power advanced electronics to control these qubits. Extrapolating the evolution of quantum processors to future systems, semiconductor spin qubits have unique advantages in this respect, making them one of the most serious contenders for large-scale FTQC. In this review, we focus on the overlap between state-of-the-art semiconductor spin qubit systems and CMOS industry Very Large-Scale Integration (VLSI) principles. We identify the main differences in spin qubit operation, material, and system requirements compared to well-established CMOS industry practices. As key players in the field are looking to collaborate with CMOS industry partners, this review serves to accelerate R&D towards the industrial scale production of FTQC processors., Comment: 36 pages, 5 figures

A key virtue of spin qubits is their sub-micron footprint, enabling a single silicon chip to host the millions of qubits required to execute useful quantum algorithms with error correction. With each physical qubit needing multiple control lines however, a fundamental barrier to scale is the extreme density of connections that bridge quantum devices to their external control and readout hardware. A promising solution is to co-locate the control system proximal to the qubit platform at milli-kelvin temperatures, wired-up via miniaturized interconnects. Even so, heat and crosstalk from closely integrated control have potential to degrade qubit performance, particularly for two-qubit entangling gates based on exchange coupling that are sensitive to electrical noise. Here, we benchmark silicon MOS-style electron spin qubits controlled via heterogeneously-integrated cryo-CMOS circuits with a low enough power density to enable scale-up. Demonstrating that cryo-CMOS can efficiently enable universal logic operations for spin qubits, we go on to show that mill-kelvin control has little impact on the performance of single- and two-qubit gates. Given the complexity of our milli-kelvin CMOS platform, with some 100-thousand transistors, these results open the prospect of scalable control based on the tight packaging of spin qubits with a chiplet style control architecture.

The fusion of non-Abelian anyons or topological defects is a fundamental operation in measurement-only topological quantum computation. In topological superconductors, this operation amounts to a determination of the shared fermion parity of Majorana zero modes. As a step towards this, we implement a single-shot interferometric measurement of fermion parity in indium arsenide-aluminum heterostructures with a gate-defined nanowire. The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of these quantum dots' quantum capacitance of up to 1 fF. Our quantum capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio of 1 in 3.7 $\mu$s at optimal flux values. From the time traces of the quantum capacitance measurements, we extract a dwell time in the two associated states that is longer than 1 ms at in-plane magnetic fields of approximately 2 T. These results are consistent with a measurement of the fermion parity encoded in a pair of Majorana zero modes that are separated by approximately 3 $\mu$m and subjected to a low rate of poisoning by non-equilibrium quasiparticles. The large capacitance shift and long poisoning time enable a parity measurement error probability of 1%., Comment: Added data on a second measurement of device A and a measurement of device B, expanded discussion of a trivial scenario. Refs added, author list updated

We present measurements and simulations of semiconductor-superconductor heterostructure devices that are consistent with the observation of topological superconductivity and Majorana zero modes. The devices are fabricated from high-mobility two-dimensional electron gases in which quasi-one-dimensional wires are defined by electrostatic gates. These devices enable measurements of local and non-local transport properties and have been optimized via extensive simulations to ensure robustness against non-uniformity and disorder. Our main result is that several devices, fabricated according to the design's engineering specifications, have passed the topological gap protocol defined in Pikulin et al. [arXiv:2103.12217]. This protocol is a stringent test composed of a sequence of three-terminal local and non-local transport measurements performed while varying the magnetic field, semiconductor electron density, and junction transparencies. Passing the protocol indicates a high probability of detection of a topological phase hosting Majorana zero modes as determined by large-scale disorder simulations. Our experimental results are consistent with a quantum phase transition into a topological superconducting phase that extends over several hundred millitesla in magnetic field and several millivolts in gate voltage, corresponding to approximately one hundred micro-electron-volts in Zeeman energy and chemical potential in the semiconducting wire. These regions feature a closing and re-opening of the bulk gap, with simultaneous zero-bias conductance peaks at both ends of the devices that withstand changes in the junction transparencies. The extracted maximum topological gaps in our devices are 20-60 $\mu$eV. This demonstration is a prerequisite for experiments involving fusion and braiding of Majorana zero modes., Comment: Final version

Many important phenomena in quantum devices are dynamic, meaning that they cannot be studied using time-averaged measurements alone. Experiments that measure such transient effects are collectively known as fast readout. One of the most useful techniques in fast electrical readout is radio-frequency reflectometry, which can measure changes in impedance (both resistive and reactive) even when their duration is extremely short, down to a microsecond or less. Examples of reflectometry experiments, some of which have been realised and others so far only proposed, include projective measurements of qubits and Majorana devices for quantum computing, real-time measurements of mechanical motion and detection of non-equilibrium temperature fluctuations. However, all of these experiments must overcome the central challenge of fast readout: the large mismatch between the typical impedance of quantum devices (set by the resistance quantum) and of transmission lines (set by the impedance of free space). Here, we review the physical principles of radio-frequency reflectometry and its close cousins, measurements of radio-frequency transmission and emission. We explain how to optimise the speed and sensitivity of a radio-frequency measurement, and how to incorporate new tools such as superconducting circuit elements and quantum-limited amplifiers into advanced radio-frequency experiments. Our aim is three-fold: to introduce the readers to the technique, to review the advances to date and to motivate new experiments in fast quantum device dynamics. Our intended audience includes experimentalists in the field of quantum electronics who want to implement radio-frequency experiments or improve them, together with physicists in related fields who want to understand how the most important radio-frequency measurements work., Comment: Review paper. 64 pages main text, 15 pages supplementary. 47 figures in main text, 5 in the supplementary

The rapidly growing quantum information science and engineering (QISE) industry will require both quantum-aware and quantum-proficient engineers at the bachelor's level. We provide a roadmap for building a quantum engineering education program to satisfy this need. For quantum-aware engineers, we describe how to design a first quantum engineering course accessible to all STEM students. For the education and training of quantum-proficient engineers, we detail both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors. We propose that such programs typically require only three or four newly developed courses that complement existing engineering and science classes available on most larger campuses. We describe a conceptual quantum information science course for implementation at any post-secondary institution, including community colleges and military schools. QISE presents extraordinary opportunities to work towards rectifying issues of inclusivity and equity that continue to be pervasive within engineering. We present a plan to do so and describe how quantum engineering education presents an excellent set of education research opportunities. Finally, we outline a hands-on training plan on quantum hardware, a key component of any quantum engineering program, with a variety of technologies including optics, atoms and ions, cryogenic and solid-state technologies, nanofabrication, and control and readout electronics. Our recommendations provide a flexible framework that can be tailored for academic institutions ranging from teaching and undergraduate-focused two- and four-year colleges to research-intensive universities., Comment: 25 pages, 2 figures

Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon., Comment: Roadmap article with contributed sections and subsections on: 1. Metrology and sensing 2. Quantum light sources, cavities and detectors 3. Quantum computing with spins 4. Nano and opto-mechanics 5. Low-dimensional systems 6. Molecular devices 7. Nanoplasmonics (47 pages, 25 figures). Contains arXiv:1907.02625, arXiv:1907.07087, arXiv:2001.11119, arXiv:2011.13907

Quantum information processing systems rely on a broad range of microwave technologies and have spurred development of microwave devices and methods in new operating regimes. Here we review the use of microwave signals and systems in quantum computing, with specific reference to three leading quantum computing platforms: trapped atomic ion qubits, spin qubits in semiconductors, and superconducting qubits. We highlight some key results and progress in quantum computing achieved through the use of microwave systems, and discuss how quantum computing applications have pushed the frontiers of microwave technology in some areas. We also describe open microwave engineering challenges for the construction of large-scale, fault-tolerant quantum computers., Comment: Invited review article, to appear in IEEE Journal of Microwaves. 29 pages, 13 figures, $10^{6}$ to $10^{11}$ Hz

We analyze a readout scheme for Majorana qubits based on dispersive coupling to a resonator. We consider two variants of Majorana qubits: the Majorana transmon and the Majorana box qubit. In both cases, the qubit-resonator interaction can produce sizeable dispersive shifts in the MHz range for reasonable system parameters, allowing for submicrosecond readout with high fidelity. For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qubits. In contrast, Majorana box qubits only recover an approximately QND readout mechanism in the dispersive limit where the resonator detuning is large. We also compare dispersive readout to longitudinal readout for the Majorana box qubit. We show that the latter gives faster and higher fidelity readout for reasonable parameters, while having the additional advantage of being manifestly QND, and so may prove to be a better readout mechanism for these systems.

The control interface of a large-scale quantum computer will likely require electronic sub-systems that operate in close proximity to the qubits, at deep cryogenic temperatures. Here, we report the low-temperature performance of custom cryo-CMOS band-gap reference circuits designed to provide stable voltages and currents on-chip, independent of local temperature fluctuations. Our circuits are fabricated in 0.35 um silicon Germanium (SiGe) BiCMOS and 28 nm Fully Depleted Silicon On Insulator (FDSOI) CMOS processes, and we compare the performance of each. Beyond their specific application as low-power references, these circuits are ideal test-vehicles for developing design approaches that mitigate the adverse effects of cryogenic temperatures on circuit performance.

The characteristic impedance of a microwave transmission line is typically constrained to a value $Z_0$ = 50 $ \Omega$, in-part because of the low impedance of free space and the limited range of permittivity and permeability realizable with conventional materials. Here we suggest the possibility of constructing high-impedance transmission lines by exploiting the plasmonic response of edge states associated with the quantum Hall effect in gated devices. We analyze various implementations of quantum Hall transmission lines based on distributed networks and lumped-element circuits, including a detailed account of parasitic capacitance and Coulomb drag effects, which can modify device performance. We additionally conceive of a meta-material structure comprising arrays of quantum Hall droplets and analyze its unusual properties. The realization of such structures holds promise for efficiently wiring-up quantum circuits on chip, as well as engineering strong coupling between semiconductor qubits and microwave photons.

The hyperpolarization of nuclear spins can enable powerful imaging and sensing techniques provided the hyperpolarization is sufficiently long-lived. Recent experiments on nanodiamond $^{13}$C nuclear spins demonstrate that relaxation times can be extended by three orders of magnitude by building up dynamic nuclear polarization (DNP) through the driving of electron-nuclear flip-flop processes at defect centers. This finding raises the question of whether the nuclear spin coherence times are also impacted by this hyperpolarization process. Here, we theoretically examine the effect of DNP on the nuclear spin coherence times as a function of the hyperpolarization drive time. We do this by developing a microscopic theory of DNP in a nuclear spin ensemble coupled to microwave-driven defect centers in solids and subject to spin diffusion mediated by internuclear dipolar interactions. We find that, similarly to relaxation times, the nuclear spin coherence times can be increased substantially by a few orders of magnitude depending on the driving time. Our theoretical model and results will be useful for current and future experiments on enhancing nuclear spin coherence times via DNP., Comment: 13 pages, 11 figures. Replaced by version accepted in Phys. Rev. B

Surface-functionalized nanomaterials can act as theranostic agents that detect disease and track biological processes using hyperpolarized magnetic resonance imaging (MRI). Candidate materials are sparse however, requiring spinful nuclei with long spin-lattice relaxation (T1) and spin-dephasing times (T2), together with a reservoir of electrons to impart hyperpolarization. Here, we demonstrate the versatility of the nanodiamond material system for hyperpolarized 13C MRI, making use of its intrinsic paramagnetic defect centers, hours-long nuclear T1 times, and T2 times suitable for spatially resolving millimeter-scale structures. Combining these properties, we enable a new imaging modality that exploits the phase-contrast between spins encoded with a hyperpolarization that is aligned, or anti-aligned with the external magnetic field. The use of phase-encoded hyperpolarization allows nanodiamonds to be tagged and distinguished in an MRI based on their spin-orientation alone, and could permit the action of specific bio-functionalized complexes to be directly compared and imaged., Comment: Supplemental Material available via email

Nanodiamonds are of interest as nontoxic substrates for targeted drug delivery and as highly biostable fluorescent markers for cellular tracking. Beyond optical techniques however, options for noninvasive imaging of nanodiamonds in vivo are severely limited. Here, we demonstrate that the Overhauser effect, a proton-electron double resonance technique developed to detect free radicals in vivo, can enable high contrast magnetic resonance imaging (MRI) of nanodiamonds in water at room temperature and ultra-low magnetic field. The technique transfers spin polarization from paramagnetic impurities at nanodiamond surfaces to $^1$H spins in the surrounding water solution, creating MRI contrast on-demand. We further examine the conditions required for maximum enhancement as well as the ultimate sensitivity of the technique. The ability to perform continuous hyperpolarization via the Overhauser mechanism, in combination with excellent in vivo stability, raises the possibility of performing noninvasive tracking of nanodiamonds over indefinitely long periods of time.

The widespread use of nanodiamond as a biomedical platform for drug-delivery, imaging, and sub-cellular tracking applications stems from their non-toxicity and unique quantum mechanical properties. Here, we extend this functionality to the domain of magnetic resonance, by demonstrating that the intrinsic electron spins on the nanodiamond surface can be used to hyperpolarize adsorbed liquid compounds at room temperature. By combining relaxation measurements with hyperpolarization, spins on the surface of the nanodiamond can be distinguished from those in the bulk liquid. These results are likely of use in signaling the controlled release of pharmaceutical payloads.

We describe progress and initial results achieved towards the goal of developing integrated multi-conductor arrays of shielded controlled-impedance flexible superconducting transmission lines with ultra-miniature cross sections and wide bandwidths (dc to >10 GHz) over meter-scale lengths. Intended primarily for use in future scaled-up quantum computing systems, such flexible thin-film Nb/polyimide ribbon cables provide a physically compact and ultra-low thermal conductance alternative to the rapidly increasing number of discrete coaxial cables that are currently used by quantum computing experimentalists to transmit signals between the low-temperature stages (from ~ 4 K down to ~ 20 mK) of a dilution refrigerator. S-parameters are presented for 2-metal layer Nb microstrip structures with lengths ranging up to 550 mm. Weakly coupled open-circuit microstrip resonators provided a sensitive measure of the overall transmission line loss as a function of frequency, temperature, and power. Two common polyimide dielectrics, one conventional and the other photo-definable (PI-2611 and HD-4100, respectively) were compared. Our most striking result, not previously reported to our knowledge, was that the dielectric loss tangents of both polyimides are remarkably low at deep cryogenic temperatures, typically 100$\times$ smaller than corresponding room temperature values. This enables fairly long-distance transmission of microwave signals without excessive attenuation and permits usefully high rf power levels to be transmitted without creating excessive dielectric heating. We observed loss tangents as low as 2.2$\times$10$^{-5}$ at 20 mK. Our fabrication techniques could be extended to more complex structures such as multiconductor, multi-layer stripline or rectangular coax, and integrated attenuators and thermalization structures., Comment: 22 pages, 10 figures (included)

The use of hyperpolarized agents in magnetic resonance (MR), such as 13C-labeled compounds, enables powerful new imaging and detection modalities that stem from a 10,000-fold boost in signal. A major challenge for the future of the hyperpolarizaton technique is the inherently short spin relaxation times, typically < 60 seconds for 13C liquid-state compounds, which limit the time that the signal remains boosted. Here, we demonstrate that 1.1% natural abundance 13C spins in synthetic nanodiamond (ND) can be hyperpolarized at cryogenic and room temperature without the use of toxic free- radicals, and, owing to their solid-state environment, exhibit relaxation times exceeding 1 hour. Combined with the already established applications of NDs in the life-sciences as inexpensive fluorescent markers and non-cytotoxic substrates for gene and drug delivery, these results extend the theranostic capabilities of nanoscale diamonds into the domain of hyperpolarized MR., Comment: Supplemental Material available on request

We consider the absorption of microwaves by a quantum Hall droplet. We show that the number and velocities of charged edge modes can be directly measured from a droplet of known shape. In contrast to standard transport measurements, different edge equilibration regimes can be accessed in the same device. If there is a quantum point contact in the droplet, then quasiparticle properties, including braiding statistics, can be observed. Their effects are manifested as modulations of the microwave absorption spectrum that are, notably, first-order in the tunneling amplitude at the point contact.

Coupled electron spins in semiconductor double quantum dots hold promise as the basis for solid-state qubits. To date, most experiments have used III-V materials, in which coherence is limited by hyperfine interactions. Ge/Si heterostructure nanowires seem ideally suited to overcome this limitation: the predominance of spin-zero nuclei suppresses the hyperfine interaction and chemical synthesis creates a clean and defect-free system with highly controllable properties. Here we present a top gate-defined double quantum dot based on Ge/Si heterostructure nanowires with fully tunable coupling between the dots and to the leads. We also demonstrate a novel approach to charge sensing in a one-dimensional nanostructure by capacitively coupling the double dot to a single dot on an adjacent nanowire. The double quantum dot and integrated charge sensor serve as an essential building block required to form a solid-state spin qubit free of nuclear spin., Comment: Related work at http://marcuslab.harvard.edu and http://cmliris.harvard.edu