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The rise of electron spin qubit architectures for quantum computing processors has led to a strong interest in designing and integrating ferromagnets to induce stray magnetic fields for electron dipole spin resonance (EDSR). The integration of nanomagnets imposes however strict layout and processing constraints, challenging the arrangement of different gating layers and the control of neighboring qubit frequencies. This work reports a successful integration of nano-sized cobalt control gates into a multi-gate FD-SOI nanowire with nanometer-scale dot-to-magnet pitch, simultaneously exploiting electrical and ferromagnetic properties of the gate stack at nanoscale. The electrical characterization of the multi-gate nanowire exhibits full field effect functionality of all ferromagnetic gates from room temperature to 10 mK, proving quantum dot formation when ferromagnets are operated as barrier gates. The front-end-of-line (FEOL) compatible gate-first integration of cobalt is examined by energy dispersive X-ray spectroscopy and high/low frequency capacitance characterization, confirming the quality of interfaces and control over material diffusion. Insights into the magnetic properties of thin films and patterned control-gates are provided by vibrating sample magnetometry and electron holography measurements. Micromagnetic simulations anticipate that this structure fulfills the requirements for EDSR driving for magnetic fields higher than 1 T, where a homogeneous magnetization along the hard magnetic axis of the Co gates is expected. The FDSOI architecture showcased in this study provides a scalable alternative to micromagnets deposited in the back-end-of-line (BEOL) and middle-of-line (MOL) processes, while bringing technological insights for the FEOL-compatible integration of Co nanostructures in spin qubit devices., Comment: 15 pages, 7 figures

The inhomogeneous magnetic stray field of micromagnets has been extensively used to manipulate electron spin qubits. By means of micromagnetic simulations and scanning superconducting quantum interference device microscopy, we show that the polycrystallinity of the magnet and non-uniform magnetization significantly impact the stray field and corresponding qubit properties. We find that the random orientation of the crystal axis in polycrystalline Co magnets alters the qubit frequencies by up to 0.5 GHz, compromising single qubit addressability and single gate fidelities. We map the stray field of Fe micromagnets with an applied magnetic field of up to 500 mT (mimicking conditions when operating qubits), finding field gradients above 1 mT/nm. The measured gradients and the lower magnetocrystalline anisotropy of Fe demonstrate the advantage of using Fe instead of Co for magnets in spin qubit devices. These properties of Fe also enabled us to design a 2D arrangement of nanomagnets for driving spin qubits distributed on a 2D lattice.

Building a practical quantum processor involves integrating millions of physical qubits along with the necessary components for individual qubit manipulation and readout. Arrays of gated silicon spins offer a promising route toward achieving this goal. Optimized radio frequency resonators with high internal quality factor are based on superconducting inductors and enable fast spin readout. All-electrical spin control and gate-dispersive readout remove the need for additional device components and simplify scaling. However, superconducting high-Q tank circuits are susceptible to crosstalk induced ringup from electrical qubit control pulses, which causes fluctuations of the quantum dot potential and is suspected to degrade qubit performance. Here, we report on the coherent and all-electrical control of a hole spin qubit at 1.5K, integrated into a silicon fin field-effect transistor and connected to a niobium nitride nanowire inductor gate-sensor. Our experiments show that qubit control pulses with their broad range of higher harmonics ring up the tank when the control pulse spectrum overlaps with the tank resonance. This can cause a reduction of the readout visibility if the tank ringing amplitude exceeds the excited state splitting of the quantum dot, lifting Pauli spin blockade and thus leading to state preparation and measurement errors. We demonstrate how to circumvent these effects by engineering control pulses around the tank resonances. Importantly, we find that the ringup does not limit the spin coherence time, indicating that efficient high-Q resonators in gate-sensing are compatible with all-electrical spin control., Comment: 12 pages, 4 main and 5 supplementary figures, upcoming presentation at Silicon Quantum Electronics Workshop 2024

In gate-based dispersive sensing, the response of a resonator attached to a quantum dot gate is detected by a reflected radio-frequency signal. This enables fast readout of spin qubits and tune up of arrays of quantum dots, but comes at the expense of increased susceptibility to crosstalk, as the resonator can amplify spurious signals and induce fluctuations in the quantum dot potential. We attach tank circuits with superconducting NbN inductors and internal quality factors $Q_{\mathrm{i}}$>1000 to the interdot barrier gate of silicon double quantum dot devices. Measuring the interdot transition in transport, we quantify radio-frequency crosstalk that results in a ring-up of the resonator when neighbouring plunger gates are driven with frequency components matching the resonator frequency. This effect complicates qubit operation and scales with the loaded quality factor of the resonator, the mutual capacitance between device gate electrodes, and with the inverse of the parasitic capacitance to ground. Setting qubit frequencies below the resonator frequency is expected to substantially suppress this type of crosstalk., Comment: 7 pages, 4 figures, supplementary information

On-chip micromagnets enable electrically controlled quantum gates on electron spin qubits. Extending the concept to a large number of qubits is challenging in terms of providing large enough driving gradients and individual addressability. Here we present a design aimed at driving spin qubits arranged in a linear chain and strongly confined in directions lateral to the chain. Nanomagnets are placed laterally to one side of the qubit chain, one nanomagnet per two qubits. The individual magnets are "U"-shaped, such that the magnetic shape anisotropy orients the magnetization alternately towards and against the qubit chain even if an external magnetic field is applied along the qubit chain. The longitudinal and transversal stray field components serve as addressability and driving fields. Using micromagnetic simulations we calculate driving and dephasing rates and the corresponding qubit quality factor. The concept is validated with spin-polarized scanning electron microscopy of Fe nanomagnets fabricated on silicon substrates, finding excellent agreement with micromagnetic simulations. Several features required for a scalable spin qubit design are met in our approach: strong driving and weak dephasing gradients, reduced crosstalk and operation at low external magnetic field., Comment: 6 pages, 4 figures

The utility of classical neural networks as universal approximators suggests that their quantum analogues could play an important role in quantum generalizations of machine-learning methods. Inspired by the proposal in [Torrontegui and Garc\'ia-Ripoll 2019 EPL 125 30004], we demonstrate a superconducting qubit implementation of an adiabatic controlled gate, which generalizes the action of a classical perceptron as the basic building block of a quantum neural network. We show full control over the steepness of the perceptron activation function, the input weight and the bias by tuning the adiabatic gate length, the coupling between the qubits and the frequency of the applied drive, respectively. In its general form, the gate realizes a multi-qubit entangling operation in a single step, whose decomposition into single- and two-qubit gates would require a number of gates that is exponential in the number of qubits. Its demonstrated direct implementation as perceptron in quantum hardware may therefore lead to more powerful quantum neural networks when combined with suitable additional standard gates.

Spatiotemporal spin dynamics under spin-orbit interaction is investigated in a (001) GaAs two-dimensional electron gas using magneto-optical Kerr rotation microscopy. Spin polarized electrons are diffused away from the excited position, resulting in spin precession because of the diffusion-induced spin-orbit field. Near the cancellation between spin-orbit field and external magnetic field, the induced spin precession frequency depends nonlinearly on the diffusion velocity, which is unexpected from the conventional linear relation between the spin-orbit field and the electron velocity.This behavior originates from an enhancement of the spin relaxation anisotropy by the electron velocity perpendicular to the diffused direction. We demonstrate that the spin relaxation anisotropy, which has been regarded as a material constant, can be controlled via diffusive electron motion., Comment: 5 pages, 5 figures

A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of the target Hamiltonian. Such an adiabatic quantum simulation is demonstrated by directly implementing a controllable and smoothly varying Hamiltonian in the rotating frame of two superconducting qubits, including longitudinal and transverse fields and iSWAP-type two-qubit interactions. The evolution of each eigenstate is tracked using time-resolved state tomography. The energy gaps between instantaneous eigenstates are chosen such that depending on the energy transition rate either diabatic or adiabatic passages are observed in the measured energies and correlators. Errors in the obtained energy values induced by finite $T_1$ and $T_2$ times of the qubits are mitigated by extrapolation to short protocol times., Comment: 5 pages, 4 figures

For the variational quantum eigensolver we propose to generate trial wavefunctions from a small amount of selected Pauli terms of the problem Hamiltonian. Two different approaches, one inspired by the quantum approximate optimization algorithm and the other by imaginary-time evolution, are proposed and studied in detail. Using numerical calculations, we study the efficiency of these trial wavefunctions for finding the ground-state energy of three molecules: H2, LiH and H2O. We find that only a small number of Pauli terms are needed to reach chemical accuracy, leading to short-depth quantum circuits with a small number of variational parameters. For the LiH molecule, the quantum circuit consists of 36 two-qubit gates, 45 one-qubit gates, and four variational parameters, with a favorable scaling for larger molecules.

A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Complementing the theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95% we are able to compute the eigenstates within an accuracy of 50 mHartree on average, a limit set by the coherence time of the tunable coupler.

For spin-based quantum computation in semiconductors, dephasing of electron spins by a fluctuating background of nuclear spins is a main obstacle. Here we show that this nuclear background can be precisely controlled in generic quantum dots by periodically exciting electron spins. We demonstrate this universal phenomenon in many-electron GaAs/AlGaAs quantum dot ensembles using optical pump-probe spectroscopy. A feedback mechanism between the saturable electron spin polarization and the nuclear system focuses the electron spin precession frequency into discrete spin modes. Employing such control of nuclear spin polarization, the electron spin lifetime within individual dots can surpass the limit of nuclear background fluctuations, thus substantially enhancing the spin coherence time. This opens the door to achieve long electron spin coherence times also in lithographically-defined many-electron systems that can be controlled in shape, size and position.

We propose a quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by a polychromatic magnetic flux modulation of a tunable bus element. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multi-qubit Hamiltonian which features independently tunable $XX$ and $YY$-type interactions as well as local bias fields over a large parameter range. We demonstrate the adiabatic simulation of the ground state of a hydrogen molecule using two superconducting qubits and one tunable bus element. The time required to reach chemical accuracy lies in the few microsecond range and therefore could be implemented on currently available superconducting circuits. Further applications of this technique may also be found in the simulation of interacting spin systems., Comment: 11 pages, 6 figures

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward 'translation' of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.

We investigate a non-adiabatic holonomic operation that enables us to entangle two fixed-frequency superconducting transmon qubits attached to a common bus resonator. Two coherent microwave tones are applied simultaneously to the two qubits and drive transitions between the first excited resonator state and the second excited state of each qubit. The cyclic evolution within this effective 3-level $\Lambda$-system gives rise to a holonomic operation entangling the two qubits. Two-qubit states with 95\% fidelity, limited mainly by charge-noise of the current device, are created within $213~\rm{ns}$. This scheme is a step toward implementing a SWAP-type gate directly in an all-microwave controlled hardware platform. By extending the available set of two-qubit operations in the fixed-frequency qubit architecture, the proposed scheme may find applications in near-term quantum applications using variational algorithms to efficiently create problem-specific trial states.

Improving coherence times of quantum bits is a fundamental challenge in the field of quantum computing. With long-lived qubits it becomes, however, inefficient to wait until the qubits have relaxed to their ground state after completion of an experiment. Moreover, for error-correction schemes it is import to rapidly re-initialize ancilla parity-check qubits. We present a simple pulsed qubit reset protocol based on a two-pulse sequence. A first pulse transfers the excited state population to a higher excited qubit state and a second pulse into a lossy environment provided by a low-Q transmission line resonator, which is also used for qubit readout. We show that the remaining excited state population can be suppressed to $2.2\pm0.8\%$ and utilize the pulsed reset protocol to carry out experiments at enhanced rates.

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits., Comment: Contribution to the special issue of Quantum Science & Technology on "What would you do with 1000 qubits"

A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two and more quantum bits in arrays of coupled qubits. Gates based on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we study theoretically and experimentally a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic expressions for exchange-interaction gates swapping excitations between the qubits (iSWAP) and for two-photon gates creating and annihilating simultaneous two-qubit excitations (bSWAP). We find that the bSWAP gate is generally slower than the more commonly used iSWAP gate, but features favorable scalability properties with less severe frequency crowding effects, which typically degrade the fidelity in multi-qubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation., Comment: 10 pages, 5 figures

The theory of spin drift and diffusion in two-dimensional electron gases is developed in terms of a random walk model incorporating Rashba, linear and cubic Dresselhaus, and intersubband spin-orbit couplings. The additional subband degree of freedom introduces new characteristics to the persistent spin helix (PSH) dynamics. As has been described before, for negligible intersubband scattering rates, the sum of the magnetization of independent subbands leads to a checkerboard pattern of crossed PSHs with long spin lifetime. For strong intersubband scattering we model the fast subband dynamics as a new random variable, yielding a dynamics set by averaged spin-orbit couplings of both subbands. In this case the crossed PSH becomes isotropic, rendering circular (Bessel) patterns with short spin lifetime. Additionally, a finite drift velocity breaks the symmetry between parallel and transverse directions, distorting and dragging the patterns. We find that the maximum spin lifetime shifts away from the PSH regime with increasing drift velocity. We present approximate analytical solutions for these cases and define their domain of validity. Effects of magnetic fields and initial package broadening are also discussed., Comment: 14 pages, 6 figures

Spin-orbit coupling is a manifestation of special relativity. In the reference frame of a moving electron, electric fields transform into magnetic fields, which interact with the electron spin and lift the degeneracy of spin-up and spin-down states. In solid-state systems, the resulting spin-orbit fields are referred to as Dresselhaus or Rashba fields, depending on whether the electric fields originate from bulk or structure inversion asymmetry, respectively. Yet, it remains a challenge to determine the absolute value of both contributions in a single sample. Here we show that both fields can be measured by optically monitoring the angular dependence of the electrons' spin precession on their direction of movement with respect to the crystal lattice. Furthermore, we demonstrate spin resonance induced by the spin-orbit fields. We apply our method to GaAs/InGaAs quantum-well electrons, but it can be used universally to characterise spin-orbit interactions in semiconductors, facilitating the design of spintronic devices.