Session D17: Focus Entanglement in Quantum Dot Arrays

Conditional teleportation of quantum dot spin states

Among the different experimental platforms for quantum information processing, individual electron spins in semiconductor quantum dots stand out for their long coherence times and potential for scalable fabrication. The past years have witnessed substantial progress in the capabilities of spin qubits. However, coupling between distant electron spins, which is required for quantum error correction, presents a challenge, and this goal remains the focus of intense research. Quantum teleportation is a canonical method to transmit qubit states, but it has not previously been implemented in quantum-dot spin qubits. Here, we present a conditional quantum teleportation protocol for electron spin qubits in semiconductor quantum dots. We demonstrate this method, which relies on a recently-developed technique to distribute entangled states of spin qubits, through conditional teleportation of spin eigenstates, entanglement swapping, and gate teleportation. This method is a promising addition to the quantum-dot spin-qubit toolbox, and it will alleviate many of the challenges associated with long-distance coupling between spins and open the door to scalable spin-based quantum information processing.   

Rydberg blockade entangling gates in silicon

Spin qubits of donors in silicon show some of the longest coherence times recorded and promise seemless integration of quantum computing into current semiconductor fabrication. However, current entangling gate implementations rely on knowledge of the exact value of the exchange interaction between donors, which decays as a highly oscillating exponential, making high fidelity entangling gates in multi-qubit fabricated devices a challenge. In this work, we show how this constraint can be released by using Rydberg blockade entangling gates between orbital excited states of donors, which are robust against variations in the interaction strength. We obtain these results by calculating induced dipole interactions of shallow and singly ionised deep donors using the finite element method and by simulating the entangling gate pulse sequence in the presence of decoherence with a Markovian Lindblad Master equation. Our study paves the way for near-term large scale quantum computations with donors in silicon by lowering the precision requirements on single donor placement.   

Entanglement of encoded spin-qubits via curvature couplings to a superconducting cavity

We propose entangling operation and preparation procedures based on curvature couplings of encoded spin qubits to a superconducting cavity, exploring the non-linear qubit response to a voltage variation. For two-qubit (n-qubit) entangling gate we explore acquired geometric phases via a time-modulated longitudinal σ_z-coupling, offering gate times of 10s of ns. No dipole moment is necessary: the qubit transverse σ_x-coupling to the resonator is zero at full sweet spot. This approach allows always-on, exchange-only qubits, for example, to stay on their ``sweet spots'' during gate operations, minimizing the charge noise and eliminating an always-on static longitudinal qubit-qubit coupling. We calculate gate errors due to the diffusion noise and damping of the resonator, the qubit charge dephasing, and a static spin-dependent resonator frequency shift (via a ``dispersive-like'' curvature coupling). Using spin-echo-like error suppression at optimal regimes, gate infidelities 10^-2-10^-3 can be achieved. For entangling preparation, one uses designated resonators to perform joint n-qubit quantum measurements with entangling times of 10s of ns, exploring both longitudinal and dispersive-like curvature couplings. The proposed schemes seem suitable for remote spin-to-spin entanglement.
  

Far-detuned two-qubit operation of the quantum-dot hybrid qubit coupled to a microwave resonator

The quantum-dot hybrid qubit has a natural spin-charge hybridization that provides an electric dipole that can be used to perform EDSR or to couple the qubit to cavity photons. This electric-dipole moment is maximized in the charge-like regime, at small detuning, and it is reduced by going to the far-detuned regime. In this latter regime, the qubit behaves as a spin qubit, with good coherence properties, yet with a small dipolar moment.

In this work, we explore this far-detuned regime. The control parameters of the quantum-dot hybrid qubit can be adjusted to form a sweet spot in the far-detuned regime, increasing the qubit coherence times enough to allow operation with a small dipolar moment. At this sweet spot, the qubit can be strongly coupled to a superconducting resonator, allowing two-qubit gates to be performed. We find that the optimal operation of two-qubit gates, in terms of gate speed and experimental feasibility, is obtained by exploiting sideband transitions, achieving a 99% two-qubit gate fidelity in the best case.   

Coherent transport of spin by adiabatic passage in quantum dot arrays

The coherent transport of spin in arrays of quantum dots is important for distributing quantum information, or realizing more efficient spin-readout, across the array. A natural strategy to achieve charge transport in quantum dot arrays is known as coherent transport by adiabatic passage (CTAP). The simplicity of this method motivates the search for spin-based analogs of CTAP (spin-CTAP) that may allow robust spin transport. We develop the theoretical framework of spin-CTAP using the Heisenberg exchange interaction in a linear array of quantum dots. Applying an AC exchange modulation according to CTAP pulse sequences allows adiabatic spin-transfer across arbitrarily large arrays of dots. By choosing a staggered static exchange profile, we can ensure that only certain spin configurations realize the transfer protocol across the array, while other states are blocked from spin-CTAP. We show how to use this feature to generate arbitrarily large Greenberger-Horne-Zeilinger (GHZ) states in the system. Our transfer and entanglement generation protocols are immediately applicable to current experiments in quantum dot arrays.   

Robust two-qubit entangling gates using shaped pulses in silicon double quantum dots

Addressibility of spin qubits in a silicon double quantum dot setup in the (1,1) charge configuration relies on the difference between Zeeman splittings of electrons. When the difference is not sufficiently large, rotating wave approximation breaks down. We consider a device working in this regime, with always-on exchange coupling, and describe how a CZ gate and arbitrary one-qubit gates which are robust against charge noise can be implemented by smoothly pulsing the microwave source, while eliminating the crosstalk stroboscopically. We find that the correction required to compensate the most significant errors due to rotating-wave approximation, which is analogous to Bloch-Siegert shift in two-level systems, can be implemented by using virtual local gates.   

Democratizing Spin Qubits

I’ve been building Powerpoint-based quantum computers with electron spins in silicon for 19 years. Unfortunately, real-life-based quantum dot quantum computers are harder to implement. Fabrication, control, and materials challenges abound. The way to accelerate discovery is to make and measure more qubits. Here, I discuss separating the qubit realization and testing circuitry from the materials science and on-chip fabrication that will ultimately be necessary. This approach should allow us, in the shorter term, to characterize wafers non-invasively for their qubit-relevant properties, to make small qubit systems on various different materials with little extra cost, and even to test spin-qubit to superconducting cavity entanglement protocols where the best possible cavity quality is preserved. Such a testbed can advance the materials science of semiconductor quantum information devices and even enable small quantum computers.   

Fabrication and Measurement of Arrays of Few-Donor Quantum Dots

NIST is using atomically precise fabrication to develop electronic devices for use in quantum information processing and quantum materials research. We are using hydrogen-based scanning probe lithography (STM) to enable deterministic placement of individual dopant atoms with atomically aligned contacts and gates to fabricate single and few atom transistors, as well as coupled few donor/quantum dot devices for spin and charge readout.

Here, we extend the STM-patterning method to fabricate coupled arrays of few atom clusters having multiple donors per dot, including a functional 3×3 quantum dot array device. Using the Si(100)2x1 surface reconstruction lattices as a natural atomic ruler, we designed the separation between a dot and its nearest neighbor dots or source/drain leads to span the regime from weakly coupled to strongly coupled ~ 5 to 8 nm separation. Low-temperature transport measurements are used to investigate the electron levels and energy spectra formed in individual dots versus energy spectra across the array of dots that result from the hybridization of quantum states. Combining electrical measurement results with simulations, we analyze the tunnel and capacitance couplings within this device to explore the rich physics in dot-arrays.   

Realizing Discrete Time Crystals in Quantum Dot Spin Arrays with Magnetic Field Gradients

A discrete time crystal is a non-equilibrium phase of matter that arises from a combination of interactions, disorder, and periodic driving. Previous work showed that it is possible to realize this phase in quantum dot spin arrays with nearest-neighbor exchange interactions if the number of pulses per period is substantially increased. Here, we show that the same result can be achieved using a magnetic field gradient instead of additional pulses, significantly reducing the demands on experimental capabilities. Numerical simulations of the return probability and mutual information confirm the time crystalline structure, which survives over a broad range of parameters and perturbations. In addition, we derive a stroboscopic effective Hamiltonian that provides further insight into the nature of this phase and the quantum state preservation properties it features.   

Exploring Many-body Localization in Quantum Dot Systems

Recent experimental progress in the design and control of quantum dot arrays has opened new possibilities for studying one-dimensional spin chains within a highly tunable platform. We theoretically investigate the realization of many-body localized phases in a quantum dot system, the latter naturally yielding the nearest-neighbor Heisenberg model subject to a magnetic field gradient. We demonstrate how strong gradients take the Heisenberg model into an effective Ising Hamiltonian, and calculate various experimental and theoretical signatures of many-body localization in these systems. These include the quantum Fisher information and energy absorption, which are shown to agree with other metrics recently discussed in the literature. Our results indicate that gate-defined quantum dots provide a promising platform on which to explore many-body localization and related phenomena such as discrete time crystal phases in a controlled setting.   

Fine-tuning electron entanglement in two-dimensional artificial atoms

The spatial correlation of few electrons confined in semiconductor quantum dots is of great interest for realizing solid state quantum computing devices. Tunability of inter-electron interaction in quantum dots through geometrical manipulations, and external fields facilitates an enhanced level of control of their electronic properties. To this end, there have been several proposals to define deterministic teleportation protocols for quantum information processing using these artificial atoms. However, for all application purposes it is important to fabricate devices operating at resonant entanglement values. Here, we develop an action integral formalism in coordinate space for solving few-particle wavefunctions in arbitrary confinements. We obtain the spatial entanglement values for a wide range of two-dimensional quantum dots with varying potentials. Spectroscopy of two-electron entanglement reveals several novel phenomena such as entanglement resonances due to anti-crossings of excited states, and electron cluster formation. We further investigate the dependence of entanglement on external electric and magnetic fields and discuss the fine-tuning of electron correlation for useful quantum processes.   

Operating four singlet-triplet qubits in a two-dimensional array of GaAs dots

Building small-scale spin-based quantum processors requires the ability to perform simultaneous, fast measurements in single- and two-dimensional qubit arrays, as well as overcome challenges like gate crosstalk, tuning in large parameter spaces, and pulse calibration. Here we present the simultaneous coherent manipulation and readout of a two-by-two singlet-triplet qubit array in GaAs, with a large multielectron dot coupler at the center. Using four independent charge-sensors read out via a frequency-multiplexed RF-reflectometry setup, we show coherent exchange oscillations, concurrently monitor the Overhauser field at the four sites of the array, and interlace different pulse operations. Finally, we establish a coherent exchange coupling between one qubit and the central multi-electron dot coupler, suggesting its use as a mechanism to provide on-demand connectivity within the array.