In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin state transfer in long chains of singly occupied quantum dots in a non-adiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems in a systematic way, and use dynamical invariants to design smooth non-adiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we discuss the extensibility of our results to directed shuttling of spin states on two-dimensional lattices of quantum dots with fixed coupling. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin state transfer in long chains of singly occupied quantum dots in a non-adiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems in a systematic way, and use dynamical invariants to design smooth non-adiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we discuss the extensibility of our results to directed shuttling of spin states on two-dimensional lattices of quantum dots with fixed coupling. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
Semiconductor quantum-dot spin qubits are a promising platform for quantum computation, because they are scalable and possess long coherence times. In order to realize this full potential, however, high-fidelity information transfer mechanisms are required for quantum error correction and efficient algorithms. Here, we present evidence of adiabatic quantum-state transfer in a chain of semiconductor quantum-dot electron spins. By adiabatically modifying exchange couplings, we transfer single- and two-spin states between distant electrons in less than 127 ns. We also show that this method can be cascaded for spin-state transfer in long spin chains. Based on simulations, we estimate that the probability to correctly transfer single-spin eigenstates and two-spin singlet states can exceed 0.95 for the experimental parameters studied here. In the future, state and process tomography will be required to verify the transfer of arbitrary single qubit states with a fidelity exceeding the classical bound. Adiabatic quantum-state transfer is robust to noise and pulse-timing errors. This method will be useful for initialization, state distribution, and readout in large spin-qubit arrays for gate-based quantum computing. It also opens up the possibility of universal adiabatic quantum computing in semiconductor quantum-dot spin qubits.
The growing interest in quantum computers has triggered various approaches for the realization of a large-scale quantum processor that can eventually outperform classical high-performance computers. Quantum computers are attracting increasing attention for their potential to enormously accelerate the simulation of quantum systems and the solution of optimization problems, promising an immense impact, particularly in fields such as chemistry, medicine, and cybersecurity. Although it is still a long way to a practical quantum device, the progress over the last decades has shown encouraging results for a so far limited number of quantum bits, or qubits for short, which represent the computational units of the processor. One promising platform for the implementation of qubits is the spin of charge carriers in semiconductor quantum dots. Especially the use of purified silicon as a host material has significantly improved the performance of quantum operations. Advanced fabrication techniques from the established semiconductor industry in principle allow for the manufacturing of a large number of qubits on a small chip, making them specifically competitive from the perspective of scalability. In this thesis, we investigate challenges for electron spin qubits, particularly in the context of scaling to large qubit arrays for quantum computation. We evaluate the performance of quantum gates, present error mitigation strategies, and propose new quantum operations for two particular spin qubit implementations. In a dense array of Loss-DiVincenzo spin qubits on a chip, quantum information can be electrically controlled by microwave pulses. For neighboring qubits, capacitive couplings of nearby electrodes lead to crosstalk that affects the quantum computation. The first examination in this thesis addresses the effect of crosstalk on idling and operating spin qubits due to an interfering microwave drive. After the analysis and characterization of the performance, we suggest mitigation protocols for different constellations of important quantum gates, which can be easily implemented experimentally. We further show how to reduce crosstalk in a two-qubit gate using an asymmetric driving scheme, resulting in an enormous improvement of the gate performance, and may be used to generally overcome the obstacle of crosstalk. An additional source of errors in spin qubit registers originates from the finite residual exchange interaction between neighboring qubits. It arises due to a finite overlap of the electron wave functions and is caused by the limited speed at which the applied voltages can be controlled. We evaluate the fidelity of doing quantum operations under these circumstances with a varying number of neighboring qubits and present robust mitigation schemes with a decent performance also in the presence of noise. Besides crosstalk, another crucial observation in experiments using microwaves is the heating caused by the delivery of high-power radio frequency pulses to the quantum chip and results in a change of the qubit properties. We therefore investigate the impact of phonons on the energy levels in spin qubits to identify a temperature-dependent correction to the qubit state splitting. As microwave pulses are associated with potential errors, exchange-only qubits represent a promising alternative to achieve universal quantum computation only using baseband control. Therefore, we shift our focus towards exchange-only qubits and outline the main error sources in these systems, including residual exchange interactions between spins, charge noise from the applied voltages, and magnetic fluctuations in the material. A consequential complication of this implementation is that the quantum information can leak out of the qubit states. This effect, however, can be reduced in the presence of a finite magnetic field, as we will demonstrate in this thesis. The gate construction for exchange-only qubits usually requires more pulse steps than in the previous qubit type. Nevertheless, if exchange interactions are switched on simultaneously, this can result in faster quantum gates, as we demonstrate in this thesis. Especially the discovery of a quantum operation that introduces relative phases between computational and leakage states can be of interest for the construction of two-qubit gates and will be discussed in an example for a special operation space.
Charge, spin and quantum states transfer in solid state devices is an important issue in quantum information. Adiabatic protocols, such as coherent transfer by adiabatic passage have been proposed for direct charge transfer, also denoted as long-range transfer, between the outer dots in a QD array without occupying the intermediate ones. However adiabatic protocols are prone to decoherence. With the aim of achieving direct charge transfer between the outer dots of a QD array with high fidelity, we propose a protocol to speed up the adiabatic transfer, in order to increase the fidelity of the process. Based on adiabaticity shortcuts, by properly engineering the pulses, fast adiabatic-like direct charge transfer between the outer dots can be obtained. We also discuss the impact of transfer fidelity on the operation time in the presence of dephasing. The proposed protocols for accelerating long-range charge and state transfer in a QD array offer a robust mechanism for quantum information transfer, by minimizing the decoherence and relaxation processes.
Abstract A protocol for controlling the localization of an electron with a fixed projection of spin between two quantum dots in a material with spin-orbit (SO) interaction is studied. Due to SO coupling, the manipulation of the electron shuttling between both quantum dots also leads to a mixing between spin projections near to the avoided crossing of levels. We use a transitionless quantum driving approach, neglecting SO interaction, to analytically design simple electric and magnetic pulses able to rapidly drive the electron along an adiabatic Landau–Zener manifold. We show that the same fields in the presence of SO interaction can also give a fast high-fidelity transition between the qubit states. The performance of the proposed protocol is assessed in the presence of SO interactions of typical semiconductor materials. It is shown that it provides a fast and efficient spin-conserving method for controlling the electron position in a double quantum dot.
In silicon quantum computers, a single electron is trapped in a microstructure called a quantum dot, and its spin is used as a qubit. For large-scale integration of qubits, we previously proposed an approach of sharing a control gate in the row or column of a 2-D quantum dot array. In our array, the shuttling of electrons is a useful technique to operate the target qubit independently and avoid crosstalk. However, since the shuttling is also conducted using shared control gates, the movement of qubits is complexly constrained. We, therefore, propose a formal model based on state transition systems to describe those constraints and operation procedures on the array. We also present an approach to generate operation procedures under the constraints. Utilizing this approach, we present a concrete method for our 16 × 8 quantum dot array. By implementing the proposed method as a quantum compiler, we confirmed that it is possible to generate operation procedures in a practical amount of time for arbitrary quantum circuits. We also demonstrated that crosstalk can be avoided by shuttling and that the fidelity in that case is higher than when crosstalk is not avoided.
Single spin quantum dot qubits in silicon are a promising candidate for a scalable quantum processor due to their long coherence times, compact size, and ease of integration into existing fabrication technologies. Realizing a large quantum processor composed of thousands or more logical qubits requires the integration of conventional transistor circuitry \nand wiring interconnects to control each individual dot in the processor. The high density of control wiring required for these processors presents many engineering challenges. In this thesis, we propose a surface code quantum processor for silicon quantum dot qubits based on a node/network architecture. Local nodes consisting of just seven quantum dots are \nspatially separated on the order of microns to facilitate space for the necessary high density wiring. Entanglement is distributed between individual nodes via shuttling of entangled electron pairs throughout the network. X or Z stabilizer operations, necessary for operating the surface code, are realized by distributing three electron spin singlet pairs across four local nodes followed by local gate operations and ancilla measurements. Simulations of electron shuttling indicate that adiabatic transport is possible on timescales that do not bottleneck the processor speed. Phase rotation of the shuttled spin, induced by the Stark shift, can lower the overall shuttling fi delity; however, the error can be mitigated by proper electrostatic tuning of the stationary electron's g-factor. Using realistic noise models, we estimate error thresholds with respect to single and two-qubit gate fidelities as well as \nsinglet dephasing errors during shuttling. Electron shuttling is a key resource of the proposed network architecture. We continue the shuttling simulations by presenting an algorithm for finding constant-adiabatic shuttling control pulses, which enables a more rigorous study of how different conditions impact the shuttling speed and fidelity. These constant adiabatic pulses are used to optimize the physical device geometry to maximize charge shuttling speeds up to 300 nm/ns in the single-valley case. We then switch to an effective Hamiltonian representation where spin and valley degrees of freedom are accounted for during shuttling. Using realistic device and material parameters, shuttle speeds in the range 10-100 nm/ns with high spin entanglement \n fidelities are obtained when the tunneling energy exceeds the Zeeman energy. High fidelity shuttling also requires the inter-dot valley phase difference to be below a threshold determined by the ratio of tunneling and Zeeman energies, so that spin-valley-orbit mixing is weak. In this regime, we find that the primary source of infi delity is a coherent spin rotation that is correctable, in principle, using single spin rotations. Two-qubit gates in the network architecture are mediated by the exchange interaction, \nan interaction that stems from the Coulomb interaction but manifests as a rotation between the |0,1> and |1,0> two qubit states. Realizing fault tolerant two-qubit gates has proven difficult in silicon quantum dots due to charge noise which perturbs the electron orbitals states, causing decoherence. Quantitatively accurate modelling of exchange in general quantum dot networks is important towards realizing fault tolerant gates. Traditional modelling methods, such as a full con figuration interaction approach, are cumbersome due to significant computational overhead required when accounting for the electron-electron interactions in the calculation. We present a modi ed linear combination of harmonic orbitals con figuration interaction (LCHO-CI) approach which signifi cantly reduces the computational time for obtaining quantitatively accurate estimations of exchange. The method works by approximating the single electron orbitals of the quantum dot network using an orthogonal basis of harmonic orbitals. This choice of orthogonal basis allows a precalculated library of matrix elements to be used in evaluating the Coulomb interactions, which speeds up the LCHO-CI calculation. The modi ed LCHO-CI approach is then used to study how the physical device geometry impacts the charge noise sensitivity of a double quantum dot system. We fi nd that, in general, geometries which increase the dot charging energy and decrease the gate lever arms improve the system's sensitivity to charge noise. We conclude this thesis by pivoting away from theoretical studies of silicon quantum dots and towards experimental studies of electron transport in dopant-free GaAs heterostructures. In modulation doped GaAs heterostructures, a doping layer is used to induce a two-dimensional electron gas (2DEG) at the heterojunction. Dopant-free GaAs lack the doping layer which makes fabrication more difficult as local electron reservoirs must be used to bring carriers and induce a 2DEG. The lack of the doping layer offers several advantages over modulation doped heterostructures, such as gate-ability of the 2DEG and ability to make ambipolar devices (both n- and p-type ohmic contacts). Realizing n- and p-type ohmic contacts requires etching a recess pit and depositing the ohmic material at an angle in order to preventing screening of the top gate when inducing a 2DEG or two-dimensional hole gas (2DHG). Magnetotransport experiments are used to characterize an induced 2DEG and 2DHG in a Hall bar fabricated on a 310 nm deep single heterojunction. The carrier mobility and density can be tuned using the top gate, and we achieve peak mobility values of 4.5E6 cm2/Vs and 0.65E6 cm2/Vs for the 2DEG and 2DHG respectively. We then move to a one-dimensional system and study electron transport through a quantum point contact. Conductance quantization is observed, and subband spectroscopy \nmeasurements indicate a 1D subband spacing of 4.5 meV. Finally, we study dynamically driven electron transport in a zero-dimensional system using a tunable-barrier quantum dot acting as a single electron pump. Single electron pumping is observed up to T = 5 K, and fi ts to the electron cascade model suggests pumping errors of 1.87 ppm when operated at a driving frequency of f = 500 MHz.