or, How to make semiconductor-based quantum computers without fabricating quantum dot qubits; Based on talks I gave at the ARO/LPS Quantum Computing Program Review, August 2018, and 4th School and Conference on Spin-Based Quantum Information Processing, September 2018. Comments and feedback welcome
I've been building Powerpoint-based quantum computers with electron spins in silicon for 20 years. Unfortunately, real-life-based quantum dot quantum computers are harder to implement. Materials, fabrication, and control challenges still impede progress. 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 enable small quantum computers. This article may also be useful as a light and light-hearted introduction to quantum dot spin qubits.
Recent achievements in the field of gate defined semiconductor quantum dots reinforce the concept of a spin-based quantum computer consisting of nodes of locally connected qubits which communicate with each other via superconducting circuit resonator photons. In this work we theoretically demonstrate a versatile set of quantum gates between adjacent spin qubits defined in semiconductor quantum dots situated within the same node of such a spin-based quantum computer. The electric dipole acquired by the spin of an electron that moves across a double quantum dot potential in a magnetic field grad…
Superconducting spin qubits, also known as Andreev spin qubits, promise to combine the benefits of superconducting qubits and spin qubits defined in quantum dots. While most approaches to control these qubits rely on controlling the spin degree of freedom via the supercurrent, superconducting spin qubits can also be coupled to each other via the superconductor to implement two-qubit quantum gates. We theoretically investigate the interaction between superconducting spin qubits in the weak tunneling regime and concentrate on the effect of spin-orbit interaction (SOI), which can be large in semi…
As a possible physical realization of a quantum information processor, a system with stacked self-assembled InAs quantum dots buried in GaAs in adjacent to the channel of a spin field-effect transistor has been proposed. In this system, only one of the stacked qubits, i.e. the edge qubit (the qubit closest to the channel), is measurable via "spin-blockade measurement." It is shown that the state tomography of the whole chain of the qubits is still possible even under such a restricted accessibility. The idea is to make use of the entangling dynamics of the qubits. A recipe for the two-qubit sy…
We investigate a hybrid quantum system involving spin qubits, based on the spins of electrons confined in quantum dots, and topological qubits, based on Majorana fermions. In such a system, gated control of the charge on the quantum dots allows transfer of quantum information between the spin and topological qubits, and the topological system can be used to facilitate transfer of spin qubits between spatially separated quantum dots and to initialize entangled spin-qubit pairs. Here, we show that the coupling to the topological system also makes it possible to perform entangling two-qubit gates…
We propose to use the spin-orbit interaction as a means to control electron spins in quantum dots, enabling both single qubit and two qubit operations. Very fast single qubit operations may be achieved by temporarily displacing the electrons. For two qubit operations the coupling mechanism is based on a combination of the spin-orbit coupling and the mutual long-ranged Coulomb interaction. Compared to existing schemes using the exchange coupling, the spin-orbit induced coupling is less sensitive to random electrical fluctuations in the electrodes defining the quantum dots.
Efficient operation sequences to couple and interchange quantum information between quantum dot spin qubits of different kinds are derived using exchange interactions. In the qubit encoding of a single-spin qubit, a singlet-triplet qubit, and an exchange-only (triple-dot) qubit, some of the single-qubit interactions remain on during the entangling operation; this greatly simplifies the operation sequences that construct entangling operations. In the ideal setup, the gate operations use the intra-qubit exchange interactions only once. The limitations of the entangling sequences are discussed, a…
We consider a system of static spin qubits embedded in a one-dimensional spin coherent channel and develop a scheme to readout the state of one and two qubits separately. We use unpolarized flying qubits for this purpose that scatter off from the static qubits due to the Heisenberg exchange interaction. Analysing the transmission coefficient as a function of density matrix elements along with additional unitary gates we reconstruct the state of static qubits.
We present and analyze a hybrid quantum system that interfaces a Majorana-hosted semiconductor nanowire with a single nitrogen-vacancy (NV) center via a magnetized torsional cantilever. We show that, the torsional mode of the mechanical resonator can strongly couple to the Majorana qubit and the spin qubit simultaneously, which allows to interface them for quantum state conversion through a dark state protocol. This work provides a promising interface between the topological qubit and the conventional spin qubit, and can find interesting applications in quantum information and computation.
We elaborate on a number of issues concerning our recent proposal for spin-qubit manipulation in nanowires using the spin-orbit coupling. We discuss the experimental status and describe in further detail the scheme for single-qubit rotations. We present a derivation of the effective two-qubit coupling which can be extended to higher orders in the Coulomb interaction. The analytic expression for the coupling strength is shown to agree with numerics.
We review progress on the use of electron spins to store and process quantum information, with particular focus on the ability of the electron spin to interact with multiple quantum degrees of freedom. We examine the benefits of hybrid quantum bits (qubits) in the solid state that are based on coupling electron spins to nuclear spin, electron charge, optical photons, and superconducting qubits. These benefits include the coherent storage of qubits for times exceeding seconds, fast qubit manipulation, single qubit measurement, and scalable methods for entangling spatially separated matter-based…
A comparison of gate fidelities between different spin qubit types defined in quantum dots and a donor under different control errors is reported. We studied five qubit types, namely the quantum dot spin qubit, the double quantum dot singlet-triplet qubit, the double quantum dot hybrid qubit, the donor qubit and the quantum dot spin-donor qubit. For each one, we derived analytical time sequences that realize single qubit rotations along the principal axis of the Bloch sphere. We estimated the effects of control errors on the gate fidelity by using a Gaussian noise model. Then we compared the g…
We propose entangling operations based on the energy curvature couplings of encoded spin qubits to a superconducting cavity, exploring the non-linear qubit response to a gate voltage variation. For a 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 even when the qubits and the cavity are far detuned. No dipole moment is necessary: the qubit transverse $σ_x$-coupling to the resonator is zero at the full sweet spot of the encoded spin qubit of interest (a triple quantum dot three-electron…
We study the influence of a thermal environment on a non-adiabatic spin-flip driving protocol of spin-orbit qubits. The driving protocol operates by moving the qubit, trapped in a harmonic potential, along a nanowire in the presence of a time-dependent spin-orbit interaction. We consider the harmonic degrees of freedom to be weakly coupled to a thermal bath. We find an analytical expression for the Floquet states and derive the Lindblad equation for a strongly non-adiabatically driven qubit. The Lindblad equation corrects the dynamics of an isolated qubit with Lamb shift terms and a dissipativ…
Monolayer transition metal dichalcogenides (TMDs) offer a novel two-dimensional platform for semiconductor devices. One such application, whereby the added low dimensional crystal physics (i.e. optical spin selection rules) may prove TMDs a competitive candidate, are quantum dots as qubits. The band structure of TMD monolayers offers a number of different degrees of freedom and combinations thereof as potential qubit bases, primarily electron spin, valley isospin and the combination of the two due to the strong spin orbit coupling known as a Kramers qubit. Pure spin qubits in monolayer MoX$_2$…
A semiconductor nanowire quantum dot with strong spin-orbit coupling (SOC) can be used to achieve a spin-orbit qubit. In contrast to a spin qubit, the spin-orbit qubit can respond to an external ac electric field, an effect called electric-dipole spin resonance. Here we develop a theory that can apply in the strong SOC regime. We find that there is an optimal SOC strength η_{opt}=\sqrt{2}/2, where the Rabi frequency induced by the ac electric field becomes maximal. Also, we show that both the level spacing and the Rabi frequency of the spin-orbit qubit have periodic responses to the direction …
Recent advances in silicon nanofabrication have allowed the manipulation of spin qubits that are extremely isolated from noise sources, being therefore the semiconductor equivalent of single atoms in vacuum. We investigate the possibility of directly coupling an electron spin qubit to a superconducting resonator magnetic vacuum field. By using resonators modified to increase the vacuum magnetic field at the qubit location, and isotopically purified 28Si substrates, it is possible to achieve coupling rates faster than the single spin dephasing. This opens up new avenues for circuit-quantum elec…
A key challenge in quantum computation is the implementation of fast and local qubit control while simultaneously maintaining coherence. Qubits based on hole spins offer, through their strong spin-orbit interaction, a way to implement fast quantum gates. Strikingly, for hole spins in one-dimensional germanium and silicon devices, the spin-orbit interaction has been predicted to be exceptionally strong yet highly tunable with gate voltages. Such electrical control would make it possible to switch on demand between qubit idling and manipulation modes. Here, we demonstrate ultrafast and universal…
The recent realization of a coherent interface between a single electron in a silicon quantum dot and a single photon trapped in a superconducting cavity opens the way for implementing photon-mediated two-qubit entangling gates. In order to couple a spin to the cavity electric field some type of spin-charge hybridization is needed, which impacts spin control and coherence. In this work we propose a cavity-mediated two-qubit gate and calculate cavity-mediated entangling gate fidelities in the dispersive regime, accounting for errors due to the spin-charge hybridization, as well as photon- and p…
A spin qubit in semiconductor quantum dots holds promise for quantum information processing for scalability and long coherence time. An important semiconductor qubit system is a double quantum dot trapping two electrons or holes, whose spin states encode either a singlet-triplet qubit or two single-spin qubits coupled by exchange interaction. In this article, we report progress on spin dephasing of two exchange-coupled spins in a double quantum dot. We first discuss the schemes of two-qubit gates and qubit encodings in gate-defined quantum dots or donor atoms based on the exchange interaction.…
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and inter-cluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decohe…
Scaling up spin qubit systems requires high-fidelity single-qubit and two-qubit gates. Gate fidelities exceeding $98\%$ were already demonstrated in silicon based single and double quantum dots, whereas for the realization of larger qubit arrays crosstalk effects on neighboring qubits must be taken into account. We analyze qubit fidelities impacted by crosstalk when performing single-qubit and two-qubit operations on neighbor qubits with a simple Heisenberg model. Furthermore we propose conditions for driving fields to robustly synchronize Rabi oscillations and avoid crosstalk effects. In our …
One of the challenges when scaling up semiconductor-based quantum processors consists in the presence of crosstalk errors caused by control operations on neighboring qubits. In previous work, crosstalk in spin qubit arrays has been investigated for non-driven single qubits near individually driven quantum gates and for two simultaneously driven single-qubit gates. Nevertheless, simultaneous gates are not restricted to single-qubit operations but also include frequently used two-qubit gates such as the CNOT gate. We analyse the impact of crosstalk drives on qubit operations, such as the CNOT an…
Electron spins in semiconductors are promising qubits because their long coherence times enable nearly 10^9 coherent quantum gate operations. However, developing a scalable high-fidelity two-qubit gate remains challenging. Here, we demonstrate an entangling gate between two double-quantum-dot spin qubits in GaAs by using a magnetic field gradient between the two dots in each qubit to suppress decoherence due to charge noise. When the magnetic gradient dominates the voltage-controlled exchange interaction between electrons, qubit coherence times increase by an order of magnitude. Using randomiz…
Two level quantum mechanical systems like spin 1/2 particles lend themselves as a natural qubit implementation. However, encoding a single qubit in several spins reduces the resources necessary for qubit control and can protect from decoherence channels. While several varieties of such encoded spin qubits have been implemented, accurate control remains challenging, and leakage out of the subspace of valid qubit states is a potential issue. Here, we realize high-fidelity single qubit operations for a qubit encoded in two electron spins in GaAs quantum dots by iterative tuning of the all-electri…
The valley degree of freedom in the electronic band structure of silicon, graphene, and other materials is often considered to be an obstacle for quantum computing (QC) based on electron spins in quantum dots. Here we show that control over the valley state opens new possibilities for quantum information processing. Combining qubits encoded in the singlet-triplet subspace of spin and valley states allows for universal QC using a universal two-qubit gate directly provided by the exchange interaction. We show how spin and valley qubits can be separated in order to allow for single-qubit rotation…
We study a pair of capacitively coupled singlet-triplet spin qubits. We characterize the two-qubit decoherence through two complementary measures, the decay time of coupled-qubit oscillations and the fidelity of entangled state preparation. We provide a quantitative map of their dependence on charge noise and field noise, and we highlight the magnetic field gradient across each singlet-triplet qubit as an effective tool to suppress decoherence due to charge noise.
The coherent control of spin qubits forms the basis of many applications in quantum information processing and nanoscale sensing, imaging and spectroscopy. Such control is conventionally achieved by direct driving of the qubit transition with a resonant global field, typically at microwave frequencies. Here we introduce an approach that relies on the resonant driving of nearby environment spins, whose localised magnetic field in turn drives the qubit when the environmental spin Rabi frequency matches the qubit resonance. This concept of environmentally mediated resonance (EMR) is explored expe…
Spin qubits in semiconductor quantum dots represent a prominent family of solid-state qubits in the effort to build a quantum computer. They are formed when electrons or holes are confined in a static potential well in a semiconductor, giving them a quantized energy spectrum. The simplest spin qubit is a single electron spin located in a quantum dot, but many additional varieties have been developed, some containing multiple spins in multiple quantum dots, each of which has different benefits and drawbacks. While these spins act as simple quantum systems in many ways, they also experience comp…
The three-qubit Toffoli gate plays an important role in quantum error correction and complex quantum algorithms such as Shor's factoring algorithm, motivating the search for efficient implementations of this gate. Here we introduce a Toffoli gate suitable for exchange-coupled electron spin qubits in silicon quantum dot arrays. Our protocol is a natural extension of a previously demonstrated resonantly driven CNOT gate for silicon spin qubits. It is based on a single exchange pulse combined with a resonant microwave drive, with an operation time on the order of 100 ns and fidelity exceeding 99%…
We propose a spin-orbit qubit in a nanowire quantum dot on the surface of a multiferroic insulator with a cycloidal spiral magnetic order. The spiral exchange field from the multiferroic insulator causes an inhomogeneous Zeeman-like interaction on the electron spin in the quantum dot, producing a spin-orbit qubit. The absence of an external magnetic field benefits the integration of such spin-orbit qubit into high-quality superconducting resonators. By exploiting the Rashba spin-orbit coupling in the quantum dot via a gate voltage, one can obtain an effective spin-photon coupling with an effic…
Nuclear spin qubits have the longest coherence times in the solid state, but their quantum read-out and initialization is a great challenge. We present a theory for the interaction of an electric current with the nuclear spins of donor impurities in semiconductors. The theory yields a sensitivity criterion for quantum detection of nuclear spin states using electrically detected magnetic resonance, as well as an all electrical method for fast nuclear spin qubit initialization.
In this theoretical manuscript I propose a scheme for entangling a single electron semiconductor spin qubit with a single electron semiconductor charge qubit in a triangular triple quantum dot configuration. Two out of three quantum dots are used to define a single electron semiconductor charge qubit. Furthermore, the spin qubit is embedded in the Zeeman sub-levels of the third quantum dot. Combining single qubit gates with entangling CNOT gates allows one to construct a SWAP gate, and therefore to use the semiconductor spin qubit as a long-lived memory for the semiconductor charge qubit.
Capacitively coupled semiconductor spin qubits hold promise as the building blocks of a scalable quantum computing architecture with long-range coupling between distant qubits. However, the two-qubit gate fidelities achieved in experiments to date have been severely limited by decoherence originating from charge noise and hyperfine interactions with nuclear spins, and are currently unacceptably low for any conceivable multi-qubit gate operations. Here, we present control protocols that implement two-qubit entangling gates while substantially suppressing errors due to both types of noise. These…
The realization of spin-based logical gates crucially depends on magnetically-coupled spin qubits. Thus, understanding decoherence when spin qubits are in close proximity will become a roadblock to overcome. Herein, we provide a general first-principles model that straightforwardly evaluates the spin bath effect on the qubit phase memory time $T_m$ . The method is applied to a ground-spin $J=8$ magnetic molecule 1 displaying atomic clock transitions, which remarkably increase $T_m$ at unusually high spin concentrations. Besides reproducing experimental $T_m$ values calculated by recent models …
In this perspective piece, I benchmark gallium arsenide, silicon, and germanium as material platforms for gate-defined quantum dot spin qubits. I focus on materials stacks, quantum dot architectures, bandstructure properties and qualifiers for disorder from electrical transport. This brief note is far from being exhaustive and should be considered a first introduction to the materials challenges and opportunities towards a larger spin qubit quantum processor.
A measurement-based quantum feedback protocol is developed for spin state initialization in a gate-defined double quantum dot spin qubit coupled to a superconducting resonator. The protocol improves qubit state initialization as it is able to robustly prepare the spin in shorter time and reach a higher fidelity, which can be pre-set. Being able to pre-set the fidelity aimed at is a highly desired feature enabling qubit initialization to be more deterministic. The protocol developed herein is also effective at high temperatures, which is critical for the current efforts towards scaling up the n…
We propose a quadrupolar exchange-only spin (QUEX) qubit that is highly robust against charge noise and nuclear spin dephasing, the dominant decoherence mechanisms in quantum dots. The qubit consists of four electrons trapped in three quantum dots, and operates in a decoherence-free subspace to mitigate dephasing due to nuclear spins. To reduce sensitivity to charge noise, the qubit can be completely operated at an extended charge noise sweet spot that is first-order insensitive to electrical fluctuations. Due to on-site exchange mediated by the Coulomb interaction, the qubit energy splitting …
We develop the theory of single-electron silicon spin qubit relaxation in the presence of a magnetic field gradient. Such field gradients are routinely generated by on-chip micromagnets to allow for electrically controlled quantum gates on spin qubits. We build on a valley-dependent envelope function theory that enables the analysis of the electron wave function in a silicon quantum dot with an arbitrary roughness at the interface. We assume the presence of single-layer atomic steps at a Si/SiGe interface and study how the presence of a gradient field modifies the spin-mixing mechanisms. We sh…
Spins associated to single defects in solids provide promising qubits for quantum information processing and quantum networks. Recent experiments have demonstrated long coherence times, high-fidelity operations and long-range entanglement. However, control has so far been limited to a few qubits, with entangled states of three spins demonstrated. Realizing larger multi-qubit registers is challenging due to the need for quantum gates that avoid crosstalk and protect the coherence of the complete register. In this paper, we present novel decoherence-protected gates that combine dynamical decoupl…
We consider the spin echo dynamics of a nitrogen-vacancy center qubit based the $S\!= \! 1$ ground state spin manifold, caused by a dynamically polarized nuclear environment. We show that the echo signal acquires then a nontrivially time-dependent phase shift. This effect should be observable for polarization $\approx \! 0.5$ of nuclei within $\sim \! 1$ nm from the qubit, and for the NV center initialized in a superposition of $m\! = \! 0$ and either $m\! =\! 1$ or $m\! =\! -1$ states. This phase shift is much smaller when the NV center is prepared in a superposition of $m\! = \! 1$ and $m\! …
We study relaxation of a moving spin qubit caused by phonon noise. As we vary the speed of the qubit, we observe several interesting features in spin relaxation and the associated phonon emission, induced by Doppler effect. In particular, in the supersonic regime, the phonons emitted by the relaxing qubit is concentrated along certain directions, similar to the shock waves produced in classical Cherenkov effect. As the speed of the moving qubit increases from the subsonic regime to the supersonic regime, the qubit experiences a peak in the spin relaxation rate near the speed of sound, which we…
We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit. These results constitute a first proof of concept of spin-ensemb…
A macroscopic spintronic qubit based on spin superfluidity and spin Hall phenomena is proposed. This magnetic quantum information processing device realizes the spin-supercurrent analog of the superconducting phase qubit and allows for full electrical control and readout. We also show that an array of interacting magnetic phase qubits can realize a quantum annealer. These devices can be built through standard solid-state fabrication technology, allowing for scalability. However, the upper bound for the operational temperature can, in principle, be higher than the superconducting counterpart, a…
Defect centers in diamond are exceptional solid-state quantum systems that can have exceedingly long electron and nuclear spin coherence times. So far, single-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a nitrogen-vacancy (NV) center electron spin, and entanglement between nearby nitrogen nuclear spins have been demonstrated. Here, we develop a scheme to implement a universal two-qubit gate between two distant nitrogen nuclear spins. Virtual excitation of an NV center that is embedded in an optical cavity can scatter a laser photon into the cavity mode; we show that this p…
Spin qubits in silicon and germanium quantum dots are promising platforms for quantum computing, but entangling spin qubits over micrometer distances remains a critical challenge. Current prototypical architectures maximize transversal interactions between qubits and microwave resonators, where the spin state is flipped by nearly resonant photons. However, these interactions cause back-action on the qubit, that yield unavoidable residual qubit-qubit couplings and significantly affect the gate fidelity. Strikingly, residual couplings vanish when spin-photon interactions are longitudinal and pho…
