Spin-based Quantum Computation Research Articles

Scalable Atomic Arrays for Spin-Based Quantum Computers in Silicon.

Semiconductor spin qubits combine excellent quantum performance with the prospect of manufacturing quantum devices using industry-standard metal-oxide-semiconductor (MOS) processes. This applies also to ion-implanted donor spins, which further afford exceptional coherence times and large Hilbert space dimension in their nuclear spin. Here multiple strategies are demonstrated and integrated to manufacture scale-up donor-based quantum computers. 31PF2 molecule implants are used to triple the placement certainty compared to 31P ions, while attaining 99.99% confidence in detecting the implant. Similar confidence is retained by implanting heavier atoms such as 123Sb and 209Bi, which represent high-dimensional qudits for quantum information processing, while Sb2 molecules enable deterministic formation of closely-spaced qudits. The deterministic formation of regular arrays of donor atoms with 300nm spacing is demonstrated, using step-and-repeat implantation through a nano aperture. These methods cover the full gamut of technological requirements for the construction of donor-based quantum computers in silicon.

Ultrafast spin dynamics in magnetic trimer and tetramer clusters: a step towards prototypic spin-SHIFT registers

Ultrafast magnetic dynamics is a necessary ingredient for magnetic recording and ultrafast information processing. The shift functionality, although not mandatory for Boolean logic, is always implemented in CMOS CPUs and therefore must be also present in magnetic logic. In this respect, using ab initio calculations we show ultrafast spin dynamics in molecular clusters such as Co3 +CO and Ni4. In this work, we establish that clusters with magnetic atoms can provide a theoretical toolbox for efficient spin charge dynamics whose operation time can range up to a few picoseconds. The prime underlying mechanism for all spin manipulation scenarios in the above mentioned clusters are laser-induced Λ processes where the laser parameters are fully optimized using a genetic algorithm. In general, a structural asymmetry enforces substantial spin localization on the active centers of both magnetic clusters. Keeping in mind the shift functionality, we theoretically suggest a series of spin-transfer scenarios between the Co and Ni atoms in each of these two clusters independently to construct a 3-bit and a 4-bit cyclic spin-SHIFT register, respectively. The maximum operational time for both logic devices is 2 ps, which is much faster than the response time of conventional spintronic devices. Additionally, for a better understanding of the transfer cycles, their feasibility and reversibility are also investigated through the analysis of the optical spectra of the related states. Our results provide important theoretical guidance for ultrafast spin manipulation in molecular structures as well as their potential spin functionality, and thus step closer to the realization of future spin-based logic devices and quantum computation. This effectively motivates the investigation and precise establishment of the shift functionality in magnetic trimers and tetramers.

Performance of high impedance resonators in dirty dielectric environments

High-impedance resonators are a promising contender for realizing long-distance entangling gates between spin qubits. Often, the fabrication of spin qubits relies on the use of gate dielectrics which are detrimental to the quality of the resonator. Here, we investigate loss mechanisms of high-impedance NbTiN resonators in the vicinity of thermally grown SiO2 and Al2O3 fabricated by atomic layer deposition. We benchmark the resonator performance in elevated magnetic fields and at elevated temperatures and find that the internal quality factors are limited by the coupling between the resonator and two-level systems of the employed oxides. Nonetheless, the internal quality factors of high-impedance resonators exceed 103 in all investigated oxide configurations which implies that the dielectric configuration would not limit the performance of resonators integrated in a spin-qubit device. Because these oxides are commonly used for spin qubit device fabrication, our results allow for straightforward integration of high-impedance resonators into spin-based quantum processors. Hence, these experiments pave the way for large-scale, spin-based quantum computers.

Baseband Control of Superconducting Qubits with Shared Microwave Drives

Accurate control of qubits is the central requirement for building functional quantum processors. For the current superconducting quantum processor, high-fidelity control of qubits is mainly based on independently calibrated microwave pulses, which could differ from each other in frequencies, amplitudes, and phases. With this control strategy, the needed physical resource could be challenging, especially when scaling up to large-scale quantum processors is considered. Inspired by Kane's proposal for spin-based quantum computing, here, we explore theoretically the possibility of baseband flux control of superconducting qubits with only shared and always-on microwave drives. In our strategy, qubits are by default far detuned from the drive during system idle periods, qubit readout and baseband flux-controlled two-qubit gates can thus be realized with minimal impacts from the always-on drive. By contrast, during working periods, qubits are tuned on resonance with the drive and single-qubit gates can be realized. Therefore, universal qubit control can be achieved with only baseband flux pulses and always-on shared microwave drives. We apply this strategy to the qubit architecture where tunable qubits are coupled via a tunable coupler, and the analysis shows that high-fidelity qubit control is possible. Besides, the baseband control strategy needs fewer physical resources, such as control electronics and cooling power in cryogenic systems, than that of microwave control. Of note, the flexibility of baseband flux control could be employed for addressing the nonuniformity issue of superconducting qubits, potentially allowing the realization of multiplexing and cross-bar technologies and thus controlling large numbers of qubits with fewer control lines. We thus expect that baseband control with shared microwave drives can help build large-scale superconducting quantum processors.

Acceptor-based qubit in silicon with tunable strain

Long coherence time and compatibility with semiconductor fabrication make spin qubits in silicon an attractive platform for quantum computing. In recent years, hole spin qubits are being developed as they have the advantages of weak coupling to nuclear spin noise and strong spin-orbit coupling (SOC), in constructing high-fidelity quantum gates. However, there are relatively few studies on the hole spin qubits in a single acceptor, which requires only low density of the metallic gates. In particular, the investigation of flexible tunability using controllable strain for fault-tolerant quantum gates of acceptor-based qubits is still lacking. Here, we study the tunability of electric dipole spin resonance (EDSR) of acceptor-based hole spin qubits with controllable strain. The flexible tunability of LH-HH splitting and spin-hole coupling (SHC) with the two kinds of strain can avoid high electric field at the "sweet spot", and the operation performance of the acceptor qubits could be optimized. Longer relaxation time or stronger EDSR coupling at low electric field can be obtained. Moreover, with asymmetric strain, two "sweet spots" are induced and may merge together, and form a second-order "sweet spot". As a result, the quality factor $Q$ can reach $10^{4}$ for single-qubit operation, with high tolerance for the electric field variation. Furthermore, the two-qubit operation of acceptor qubits based on dipole-dipole interaction is discussed for high-fidelity two-qubit gates. The tunability of spin qubit properties in acceptor via strain could provide promising routes for spin-based quantum computing.

Single-Shot Readout of Multiple Donor Electron Spins with a Gate-Based Sensor

Proposals for large-scale semiconductor spin-based quantum computers require high-fidelity single-shot qubit readout to perform error correction and read out qubit registers at the end of a computation. However, as devices scale to larger qubit numbers integrating readout sensors into densely packed qubit chips is a critical challenge. Two promising approaches are minimizing the footprint of the sensors, and extending the range of each sensor to read more qubits. Here we show high-fidelity single-shot electron spin readout using a nanoscale single-lead quantum dot (SLQD) sensor that is both compact and capable of reading multiple qubits. Our gate-based SLQD sensor is deployed in an all-epitaxial silicon donor spin-qubit device, and we demonstrate single-shot readout of three 31P donor quantum dot electron spins with a maximum fidelity of 95%. Importantly, in our device the quantum dot confinement potentials are provided inherently by the donors, removing the need for additional metallic confinement gates and resulting in strong capacitive interactions between sensor and donor quantum dots. Our results are consistent with a 1/d1.4 scaling of the capacitive coupling between sensor and 31P dots (where d is the sensor-dot distance), compared to 1/d2.5−3.0 in gate-defined quantum dot devices. Due to the small qubit size and strong capacitive interactions in all-epitaxial donor devices, we estimate a single sensor can achieve single-shot readout of approximately 15 qubits in a linear array, compared to 3–4 qubits for a similar sensor in a gate-defined quantum dot device. Our results highlight the potential for spin-qubit devices with significantly reduced sensor densities.Received 19 October 2021Revised 19 August 2022Accepted 4 January 2023DOI:https://doi.org/10.1103/PRXQuantum.4.010319Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum information with solid state qubitsQuantum metrologyQuantum Information

Three-dimensional fourier imaging of thousands of individual solid-state quantum bits – a tool for spin-based quantum technology

Nitrogen vacancies in diamond (NVs) are frequently considered as possible candidates to constitute the building blocks of spin-based quantum computers. The main caveats to this approach are the lack of a reliable process to accurately place many NVs in close proximity to each other (∼10–20 nm) to enable an adequate spin-spin interaction; and the inability to read out and selectively manipulate the quantum states of many such closely spaced NVs. A possible approach to overcome these issues includes the following: (i) making use of a diamond dense with NVs in random (‘as-produced’) 3D positions; (ii) mapping out their individual locations at high spatial resolution (in 3D); (iii) employing techniques for selective spin manipulation based on the mapped 3D locations of the NVs; and (iv) making use of imaging techniques to read out the quantum state of the NVs. Within this grand vision, we present here a tool that can support this scheme—namely, an approach to the efficient high accuracy 3D mapping of many thousands of individual NVs in a diamond via magnetic resonance imaging (MRI). In the present work, the NVs’ spacings and the corresponding imaging resolution are in the submicron-scale, but the same approach can be scaled down to support a resolution lower than 10 nm in diamonds with dense NVs, as is required for practical quantum computing applications.

Micromagnet design for addressable fast spin manipulations in a 2 × 2 quantum dot array

The scaling up of semiconductor quantum dots to two-dimensional arrays is attracting considerable interest for use in large-scale spin-based quantum computation. One of the fundamental technologies to be realized in the two-dimensional arrays of quantum dots is the coherent manipulations of individual electron spins. In this work, we report on a micromagnet design that generates stray magnetic fields that can be used for spin manipulations via electric dipole spin resonance in a 2 × 2 quantum dot array. We consider a micromagnet with lower symmetry than that typically used in the case of linear dot arrays and optimize its dimensions to produce a maximum stray field gradient while maintaining Zeeman splitting differences sufficiently large among the four dots to permit qubit addressability. The optimized field gradient is around 60% smaller than that used in linear dot arrays, but it is still large enough for spin manipulation experiments. Our result represents an important step toward the experimental realization of spin-qubit operations in two-dimensional arrays of quantum dots.

Coherent control of electron spin qubits in silicon using a global field

Silicon spin qubits promise to leverage the extraordinary progress in silicon nanoelectronic device fabrication over the past half century to deliver large-scale quantum processors. Despite the scalability advantage of using silicon technology, realising a quantum computer with the millions of qubits required to run some of the most demanding quantum algorithms poses several outstanding challenges, including how to control many qubits simultaneously. Recently, compact 3D microwave dielectric resonators were proposed as a way to deliver the magnetic fields for spin qubit control across an entire quantum chip using only a single microwave source. Although spin resonance of individual electrons in the globally applied microwave field was demonstrated, the spins were controlled incoherently. Here we report coherent Rabi oscillations of single electron spin qubits in a planar SiMOS quantum dot device using a global magnetic field generated off-chip. The observation of coherent qubit control driven by a dielectric resonator establishes a credible pathway to achieving large-scale control in a spin-based quantum computer.

Spin manipulation and decoherence in a quantum dot mediated by a synthetic spin–orbit coupling of broken T-symmetry

The electrical control of a spin qubit in a quantum dot (QD) relies on spin–orbit coupling (SOC), which could be either intrinsic to the underlying crystal lattice or heterostructure, or extrinsic via, for example, a micro-magnet. In experiments, micromagnets have been used as a synthetic SOC to enable strong coupling of a spin qubit in quantum dots with electric fields. Here we study theoretically the spin relaxation, pure dephasing, spin manipulation, and spin–photon coupling of an electron in a QD due to the synthetic SOC induced spin–orbit mixing. We find qualitative difference in the spin dynamics in the presence of a synthetic SOC compared with the case of the intrinsic SOC. Specifically, spin relaxation due to the synthetic SOC and deformation potential phonon emission (or Johnson noise) shows (or B 0) dependence with the magnetic field, which is in contrast with the (or ) dependence in the case of the intrinsic SOC. Moreover, charge noise induces fast spin dephasing to the first order of the synthetic SOC, which is in sharp contrast with the negligible spin pure dephasing in the case of the intrinsic SOC. These qualitative differences are attributed to the broken time-reversal symmetry (T-symmetry) of the synthetic SOC. An SOC with broken T-symmetry (such as the synthetic SOC from a micro-magnet) eliminates the ‘Van Vleck cancellation’ and causes a finite longitudinal spin–electric coupling that allows the longitudinal coupling between spin and electric field, and in turn allows spin pure dephasing. Finally, through proper choice of magnetic field orientation, the electric-dipole spin resonance via the synthetic SOC can be improved with potential applications in spin-based quantum computing.

Pulse engineering of a global field for robust and universal quantum computation

Global control strategies for arrays of qubits are a promising pathway to scalable quantum computing. A continuous-wave global field provides decoupling of the qubits from background noise. However, this approach is limited by variability in the parameters of individual qubits in the array. Here we show that by modulating a global field simultaneously applied to the entire array, we are able to encode qubits that are less sensitive to the statistical scatter in qubit resonance frequency and microwave amplitude fluctuations, which are problems expected in a large scale system. We name this approach the SMART (Sinusoidally Modulated, Always Rotating and Tailored) qubit protocol. We show that there exist optimal modulation conditions for qubits in a global field that robustly provide improved coherence times. We discuss in further detail the example of spins in silicon quantum dots, in which universal one- and two-qubit control is achieved electrically by controlling the spin-orbit coupling of individual qubits and the exchange coupling between spins in neighbouring dots. This work provides a high-fidelity qubit operation scheme in a global field, significantly improving the prospects for scalability of spin-based quantum computer architectures.

Spin-valley coupling in single-electron bilayer graphene quantum dots

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the K and K^{prime} states below 20 μeV.

Single-electron spin resonance in a nanoelectronic device using a global field.

Spin-based silicon quantum electronic circuits offer a scalable platform for quantum computation, combining the manufacturability of semiconductor devices with the long coherence times afforded by spins in silicon. Advancing from current few-qubit devices to silicon quantum processors with upward of a million qubits, as required for fault-tolerant operation, presents several unique challenges, one of the most demanding being the ability to deliver microwave signals for large-scale qubit control. Here, we demonstrate a potential solution to this problem by using a three-dimensional dielectric resonator to broadcast a global microwave signal across a quantum nanoelectronic circuit. Critically, this technique uses only a single microwave source and is capable of delivering control signals to millions of qubits simultaneously. We show that the global field can be used to perform spin resonance of single electrons confined in a silicon double quantum dot device, establishing the feasibility of this approach for scalable spin qubit control.

Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules

The electronic structure of magnetic lanthanide atoms is fascinating from a fundamental perspective. They have electrons in a submerged open 4f shell lying beneath a filled 6s shell with strong relativistic correlations leading to a large magnetic moment and large electronic orbital angular momentum. This large angular momentum leads to strong anisotropies, i. e. orientation dependencies, in their mutual interactions. The long-ranged molecular anisotropies are crucial for proposals to use ultracold lanthanide atoms in spin-based quantum computers, the realization of exotic states in correlated matter, and the simulation of orbitronics found in magnetic technologies. Short-ranged interactions and bond formation among these atomic species have thus far not been well characterized. Efficient relativistic computations are required. Here, for the first time we theoretically determine the electronic and ro-vibrational states of heavy homonuclear lanthanide Er2 and Tm2 molecules by applying state-of-the-art relativistic methods. In spite of the complexity of their internal structure, we were able to obtain reliable spin–orbit and correlation-induced splittings between the 91 Er2 and 36 Tm2 electronic potentials dissociating to two ground-state atoms. A tensor analysis allows us to expand the potentials between the atoms in terms of a sum of seven spin–spin tensor operators simplifying future research. The strengths of the tensor operators as functions of atom separation are presented and relationships among the strengths, derived from the dispersive long-range interactions, are explained. Finally, low-lying spectroscopically relevant ro-vibrational energy levels are computed with coupled-channels calculations and analyzed.

Spin-Selective Resonant Tunneling Induced by Rashba Spin-Orbit Interaction in Semiconductor Nanowire

We consider a single electron confined within a quantum wire in a system of two electrostatically-induced QDs defined by nearby gates. The time-varying electric field, of single GHz frequency, perpendicular to the quantum wire, is used to induce the Rashba coupling and enable spin-dependent resonant tunneling of the electron between two adjacent potential wells with fidelity over 99.5%. This effect can be used for the high fidelity all-electrical electron-spin initialization or readout in the spin-based quantum computer. In contrast to other spin initialization methods, our technique can be performed adiabatically without increase in the energy of the electron. Our simulations are supported by a realistic self-consistent time-dependent Poisson-Schroedinger calculations.

Electron Spin Relaxation Mechanisms of Atomic Hydrogen Trapped in Silsesquioxane Cages: The Role of Isotope Substitution

Encapsulated atomic hydrogen in silsesquioxane cages is a promising candidate for applications in emerging technologies like spin-based quantum computing, magnetic field sensing, and atomic clock d...

Hole Spin Qubits in Si FinFETs With Fully Tunable Spin-Orbit Coupling and Sweet Spots for Charge Noise

The strong spin-orbit coupling in hole spin qubits enables fast and electrically tunable gates, but at the same time enhances the susceptibility of the qubit to charge noise. Suppressing this noise is a significant challenge in semiconductor quantum computing. Here, we show theoretically that hole Si FinFETs are not only very compatible with modern CMOS technology, but they present operational sweet spots where the charge noise is completely removed. The presence of these sweet spots is a result of the interplay between the anisotropy of the material and the triangular shape of the FinFET cross-section, and it does not require an extreme fine-tuning of the electrostatics of the device. We present how the sweet spots appear in FinFETs grown along different crystallographic axes and we study in detail how the behaviour of these devices change when the cross-section area and aspect ratio are varied. We identify designs that maximize the qubit performance and could pave the way towards a scalable spin-based quantum computer.

Single-Electron Operation of a Silicon-CMOS 2 × 2 Quantum Dot Array with Integrated Charge Sensing.

The advanced nanoscale integration available in CMOS technology provides a key motivation for its use in spin-based quantum computing applications. Initial demonstrations of quantum dot formation and spin blockade in CMOS foundry-compatible devices are encouraging, but results are yet to match the control of individual electrons demonstrated in university-fabricated multigate designs. We show that quantum dots formed in a CMOS nanowire device can be measured with a remote single electron transistor (SET) formed in an adjacent nanowire, via floating coupling gates. By biasing the SET nanowire with respect to the nanowire hosting the quantum dots, we controllably form ancillary quantum dots under the floating gates, thus enabling control of all quantum dots in a 2 × 2 array, and charge sensing down to the last electron in each dot. We use effective mass theory to investigate the ideal geometrical parameters in order to achieve interdot tunnel rates required for spin-based quantum computation.

An Integrated Silicon MOS Single-Electron Transistor Charge Sensor for Spin-Based Quantum Information Processing

Recent advances demonstrated the feasibility of realizing spin-based quantum computation in Silicon. To make further progress towards a large-scale implementation of spin-based quantum device technologies, a reliable fabrication process with good yield and device uniformity is a crucial requirement. We address this challenge by integrating a prototype spin qubit device in a 300 mm process, using state-of-the-art, CMOS-compatible process steps. We demonstrate well-formed single-electron transistors with a feature size of 50 nm, individual electron controllability and show multi-gate control uniformity from room-down to low-temperature. Dots with charging energies of 1-2 meV and sizes of around 46 nm are estimated, in excellent agreement with design geometry. The noise power spectrum reveals 1/f noise with an amplitude of 2 μeV at 1 Hz. This successful integration enables further exploration of reproducible Silicon-based spin qubit devices and opens paths for systematic investigation of the performance and scalability of future spin-based qubit devices.

Sensitive radiofrequency readout of quantum dots using an ultra-low-noise SQUID amplifier

Fault-tolerant spin-based quantum computers will require fast and accurate qubit read out. This can be achieved using radiofrequency reflectometry given sufficient sensitivity to the change in quantum capacitance associated with the qubit states. Here, we demonstrate a 23-fold improvement in capacitance sensitivity by supplementing a cryogenic semiconductor amplifier with a SQUID preamplifier. The SQUID amplifier operates at a frequency near 200 MHz and achieves a noise temperature below 600 mK when integrated into a reflectometry circuit, which is within a factor 120 of the quantum limit. It enables a record sensitivity to capacitance of 0.07aF/Hz. The setup is used to acquire charge stability diagrams of a gate-defined double quantum dot in a short time with a signal-to-noise ration of about 38 in 1μs of integration time.