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 sublevels of the third quantum dot. Combining single-qubit gates with entangling controlled-not 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.
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 sublevels of the third quantum dot. Combining single-qubit gates with entangling controlled-not 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.
This thesis addresses the concept of quantum computing with semiconductor quantum dots. The basic unit of a quantum computer is a quantum mechanical two-level system, the so-called quantum bit (qubit). The qubit can be defined as the spin of an electron confined in a quantum dot or as a two-dimensional subspace of the Hilbert space for several spins. Some semiconductors have several minima in their conduction band, socalled valleys. A two-dimensional valley degree of freedom can also be considered as a qubit. In this thesis, quantum registers storing spin as well as valley qubits are described theoretically. Virtual hopping yields an exchange interaction between neighboring quantum dots, which reduces the energy of antisymmetric spin-valley states according to the Pauli principle. Considering the spin and the valley degrees of freedom of two electrons in neighboring quantum dots as qubits, the exchange interaction is a four-qubit interaction. In this thesis, it will be shown that it is, nevertheless, possible to generate a universal two-qubit gate for spin qubits or for valley qubits by combining the exchange interaction and individual single-qubit gates. The exchange interaction in this two-electron double quantum dot directly provides a universal two-qubit gate for one spin and one valley qubit as well. For this, the qubits are defined as suitable subspaces, spanned by the singlet and one triplet state of the spin and the valley states, respectively, Using those gates, arbitrary quantum operations can be performed for single-spin and single-valley qubits in the same quantum register, where in one double quantum dot the quantum states are restricted to the singlet-triplet subspace. While in this register single-spin and single-valley rotations are required, these gates are dispensable in a quantum register storing spin and valley singlet-triplet qubits. The single-qubit operations, in this case, can be provided by the exchange interaction and a gradient in the energy splitting of spin and valley states when the spin qubit is stored in a double quantum dot with spin degrees of freedom only and when the spin states in the double quantum dot which stores the valley qubit are polarized. For providing the two-qubit gate, the spin and the valley qubits need to be stored in the same double quantum dot. The crucial task for this register is to interchange the spin of a spin-only and a spin-valley quantum dot in order to switch between the single-qubit and the two-qubit operation mode. This interchanging of the spin can be achieved by a valley-depending virtual hopping between the quantum dots. Furthermore, echo sequences for a so-called exchange-only qubit are considered. An exchange-only qubit is defined as a subspace in a system of three electron spins in a triple quantum dot. An inhomogeneous magnetic field, which may be caused by nuclear spins in the semiconductor, can lead to decoherence and leakage, i.e., the state might leave the qubit subspace. Suppressing this effect by an echo sequence which consists of pulses interchanging neighboring spin states, so-called SWAP gates, was proposed. Controllability over these quantum operations is provided via the exchange interaction. In this thesis, the performance of different such sequences is investigated. The analysis shows that optimization strategies developed for single spin echoes can be adapted for the three spin system. The echo sequences can be different in their order of applied SWAP gates interchanging the spins in the first and second dots or in the second and third dots. The noise suppression performance depends slightly on this order of SWAP gates. For two spins in a double quantum dot a scheme for quantum state tomography is presented. The corresponding measurement operators are constructed from a set of mutually unbiased bases of the four-dimensional two-qubit Hilbert space. These measurements are represented by short sequences of no more than three elementary quantum gates and projective measurements by the well-established spin-to-charge conversion.
In quantum computing based on semiconductor quantum dots, adding dots (or just electrons) allows a wider search for an optimal qubit-encoding scheme that is both controllable and coherent. This work reports experiments to realize a hybrid charge-spin qubit in a linear triple quantum dot with asymmetric tunnel couplings, in a multielectron charge configuration. This qubit's energy splitting can be tuned conveniently over a wide range, and the authors attain qualitative understanding of the observations in terms of a three-electron system. This should stimulate further exploration of quantum coherent dynamics in the few-electron regime for semiconductor quantum processors.
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.
Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.
Implementations of quantum information processing systems based on optically controlled electron spins in semiconductor quantum dots are particulary appealing due to several features. These features include inherent ultrafast gate operation times, reasonably long decoherence times, small optical control power and a natural ability to link to optical fiber communication networks. We will discuss the current state of the art in the experimental implementations of the main elements of semiconductor spin qubits: qubit initialization, single-qubit gates, two-qubit gates, entanglement distribution, projective measurement, quantum memory and indistinguishable single-photon generation.
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.