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arXiv:2104.13571 · IEEE Transactions on Quantum Engineering

Optimal Control of the Operating Regime of a Single-Electron Double Quantum Dot

Vincent Reiher, Yves Bérubé-Lauzière

Published Jan 1, 2023• 4 citations
arXivHTMLPDF

Abstract

The double-quantum-dot device benefits from the advantages of both the spin and charge qubits, while offering ways to mitigate their drawbacks. Careful gate voltage modulation can grant greater spinlike or chargelike dynamics to the device, yielding long coherence times with the former and high electrical susceptibility with the latter for electrically driven spin rotations or coherent interactions with microwave photons. As this architecture is a serious contender for the realization of a versatile physical qubit, improving its control is a critical step toward building a large-scale spin-based universal quantum computer. We show that optimal control pulses generated using the gradient ascent pulse engineering algorithm can yield higher fidelity operating regime transfers than can be achieved using linear methods.

DOI
10.1109/tqe.2023.3324841

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In this thesis we present a spin based QuBit Architecture that implements single-QuBit gates in the QuBit itself and is predicted to have a long coherence time. This architecture has been physically realized in a Ferromagnetic Double Quantum Dot hosted in a Single Wall Carbon Nanotube, and studied through a coupled Microwave cavity. We present a Linear Response Theory model that ties the transmitted amplitude and phase of the microwave signal through the cavity to the microscopic charge susceptibility of the Double Quantum Dot. We fit those two channels of experimental data to a simple 4 level master equation model that allows us to extract the inter-dot tunneling rate, the charge-photons coupling rate and the charge dephasing rate. We also present a numerical algorithm that allows to evolve in time the quantum state of the device also considering the effect of charge noise. This algorithm is used to study the effect of fast Landau-Zener style pulses on the QuBit, giving the ideal shape of the control pulses.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.
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We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.
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