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arXiv:2106.12757 · Physical Review Research

Voltage-controlled Hubbard spin transistor

Rozhin Yousefjani, Sougato Bose, Abolfazl Bayat

Published Nov 29, 2021• 8 citations
arXivHTMLPDF

Abstract

Transistors are key elements for enabling computational hardware in both classical and quantum domains. Here we propose a voltage-gated spin transistor using itinerant electrons in the Hubbard model which acts at the level of single electron spins. Going beyond classical spintronics, it enables the controlling of the flow of quantum information between distant spin qubits. The transistor has two modes of operation, open and closed, which are realized by two different charge configurations in the gate of the transistor. In the closed mode, the spin information between source and drain is blocked while in the open mode we have free spin information exchange. The switching between the modes takes place within a fraction of the operation time which allows for several subsequent operations within the coherence time of the transistor. The system shows good resilience against several imperfections and opens up a practical application for quantum dot arrays.

DOI
10.1103/physrevresearch.3.043142

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Transistors are key elements for enabling computational hardware in both classical and quantum domains. Here we propose a voltage-gated spin transistor using itinerant electrons in the Hubbard model which acts at the level of single electron spins. Going beyond classical spintronics, it enables the controlling of the flow of quantum information between distant spin qubits. The transistor has two modes of operation, open and closed, which are realized by two different charge configurations in the gate of the transistor. In the closed mode, the spin information between source and drain is blocked while in the open mode we have free spin information exchange. The switching between the modes takes place within a fraction of the operation time which allows for several subsequent operations within the coherence time of the transistor. The system shows good resilience against several imperfections and opens up a practical application for quantum dot arrays.
Transistors play a vital role in classical computers, and their quantum mechanical counterparts could potentially be as important in quantum computers. Where a classical transistor is operated as a switch that either blocks or allows an electric current, the quantum transistor should operate on quantum information. In terms of a spin model the in-going quantum information is an arbitrary qubit state (spin-1/2 state). In this paper, we derive a model of four qubits with Heisenberg interactions that works as a quantum spin transistor, i.e. a system with perfect state transfer or perfect blockade depending on the state of two gate qubits. When the system is initialized the dynamics complete the gate operation, hence our protocol requires minimal external control. We propose a concrete implementation of the model using state-of-the-art superconducting circuits. Finally, we demonstrate that our proposal operates with high-fidelity under realistic decoherence.
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.
Single-electron transistors (SETs) are attractive candidates for spin qubits. An AlGaAs/GaAs SET consists of a confined two-dimensional droplet of electrons, called an artificial atom or quantum dot, coupled by tunnel barriers to two conducting leads. Controlling the voltages on the lithographic gates that define the quantum dot allows us to confine a single electron in the dot, as well as to adjust the tunnel barriers to the leads. By applying a magnetic field, we can split the spin-up and spin-down states of the electron by an energy |g|μBB; the goal is to utilize coherent superpositions of these spin states to construct a qubit. We will discuss our attempts to observe electron spin resonance (ESR) in this system by applying magnetic fields at microwave frequencies. Observation of ESR would demonstrate that we can manipulate a single spin and allow us to measure the decoherence time T2*.
We propose an implementation of the two-qubit gate in a quantum dot spin qubit system which is immune to charge noise problems. Our proposed implementation, if it could be realized in a physical system, would have the advantage of being robust against uncertainties and fluctuations in the tunnel coupling and barrier gate voltage pulse area. The key idea is to introduce an auxiliary dot and use an analog to the stimulated Raman adiabatic passage pulse sequence in three-level atomic systems, often referred to in the context of electron transport in quantum dot systems as Coherent Tunneling by Adiabatic Passage. Spin-dependent tunneling opens the possibility of performing two-qubit gate operations by this method.
In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.
We consider a single electron in a 1D quantum dot with a static slanting Zeeman field. By combining the spin and orbital degrees of freedom of the electron, an effective quantum two-level (qubit) system is defined. This pseudospin can be coherently manipulated by the voltage applied to the gate electrodes, without the need for an external time-dependent magnetic field or spin-orbit coupling. Single-qubit rotations and the controlled-NOT operation can be realized. We estimated the relaxation (T1) and coherence (T2) times and the (tunable) quality factor. This scheme implies important experimental advantages for single electron spin control.