We investigate the behavior of qubits consisting of three electron spins in double and triple quantum dots subject to external electric fields. Our model includes two independent bias parameters, $\ensuremath{\varepsilon}$ and ${\ensuremath{\varepsilon}}_{M}$, which both couple to external electromagnetic fields and can be controlled by gate voltages applied to the quantum dot structures. By varying these parameters, one can switch the qubit type by shifting the energies in the single quantum dots, thus changing the electron occupancy in each dot. Starting from the asymmetric resonant exchange qubit with a (2,0,1) and (1,0,2) charge admixture, one can smoothly cross over to the resonant exchange qubit with a detuned (1,1,1) charge configuration, and to the exchange-only qubit with the same charge configuration but equal energy levels down to the hybrid qubits with (1,2,0) and (0,2,1) charge configurations. Here,
(l,m,n) describes a configuration with
l electrons in the left dot,
m electrons in the center dot, and
n electrons in the right dot. We first focus on random electromagnetic field fluctuations, i.e., ``charge noise,'' at each quantum dot resulting in dephasing of the qubit, and we provide a complete map of the resulting dephasing time as a function of the bias parameters. We pay special attention to the so-called sweet spots and double sweet spots of the system, which are least susceptible to noise. In the second part, we investigate the coupling of the qubit system to the coherent quantized electromagnetic field in a superconducting strip-line cavity, and we also provide a complete map of the coupling strength as a function of the bias parameters. We analyze the asymmetric qubit-cavity coupling via $\ensuremath{\varepsilon}$ and the symmetric coupling via ${\ensuremath{\varepsilon}}_{M}$.
We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor of six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise.
We propose a quadrupolar exchange-only spin 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. Because of on-site exchange mediated by the Coulomb interaction, the qubit energy splitting is electrically controllable and can amount to several GHz even in the "off" configuration, making it compatible with conventional microwave cavities.
Initialization, two-spin coherent manipulation, and readout of a three-spin qubit are demonstrated using a few-electron triple quantum dot. The three-spin qubit is designed to allow all operations for full qubit control to be tuned via nearest-neighbor exchange interaction. Fast readout of charge states takes advantage of multiplexed reflectometry. Decoherence measured in a two-spin subspace is found to be consistent with predictions based on gate voltage noise with a uniform power spectrum. The theory of the exchange-only qubit is developed and it is shown that initialization of only two spins suffices for operation. Requirements for full multiqubit control using only exchange and electrostatic interactions are outlined.
The energy landscape of a single electron in a triple quantum dot can be tuned such that the energy separation between ground and excited states becomes a flat function of the relevant gate voltages.These so-called sweet spots are beneficial for charge coherence since the decoherence effects caused by small fluctuations of gate voltages or surrounding charge fluctuators are minimized.We propose a new operation point for a triple quantum dot charge qubit, a so-called CQ 3 -qubit, having a third-order sweet spot.We show strong coupling of the qubit to single photons in a frequency tunable high-impedance SQUID-array resonator.In the dispersive regime, we investigate the qubit linewidth in the vicinity of the proposed operating point.In contrast to the expectation for a higher-order sweet spot, we there find a local maximum of the linewidth.We find that this is due to a non-negligible contribution of noise on the quadrupolar detuning axis not being in a sweet spot at the proposed operating point.While the original motivation to realize a low-decoherence charge qubit was not fulfilled, our analysis provides insights into charge decoherence mechanisms relevant also for other qubits.
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.