Since the mid-20th century it has been understood that a general-purpose quan- tum computer would be able to efficiently solve problems that will forever be out-of-reach for conventional computers. Since then, many quantum algorithms have been developed with applications in a wide range of domains including cryptography, simulations, machine learning and data analysis. While this has resulted in substantial attention being paid to the development of quantum com- puters, the best architectures to use in their fabrication is not yet clear. Semiconductor quantum dot devices are a particularly promising candidate for use in quantum computing architectures, as it is anticipated that once the funda- mental building blocks are implemented, they might be massively scalable using the existing lithography techniques of the semiconductor industry. So far, how- ever, it is not yet clear how best to implement the high-fidelity gates required for general-purpose quantum computation. In this thesis, we present and characterise novel theoretical proposals for fast, simple and high-fidelity two-qubit gates using magnetic (exchange) coupling for specific semiconductor quantum dot qubits; namely, the singlet-triplet and resonant-exchange qubits. These two-qubit operations are simple enough that it is feasible for them to be implemented in experiments of the near future. Success- ful implementations would significantly extend the experimentally demonstrable frontier of semi-conductor quantum dot devices as relevant to their use in uni- versal quantum computing architectures. We also develop simple parameter estimation schemes by which it is possible to substantially mitigate the dominant sources of error for our proposed gates; namely, low-frequency charge and magnetic noise. We develop the techniques in the context of pseudo-static magnetic field gradient fluctuations in singlet- triplet qubits, and demonstrate that these techniques lead to a several orders of magnitude improvement in single-qubit coherence times. With minimal effort this could be ported to other qubit architectures.
Since the mid-20th century it has been understood that a general-purpose quan- tum computer would be able to efficiently solve problems that will forever be out-of-reach for conventional computers. Since then, many quantum algorithms have been developed with applications in a wide range of domains including cryptography, simulations, machine learning and data analysis. While this has resulted in substantial attention being paid to the development of quantum com- puters, the best architectures to use in their fabrication is not yet clear. Semiconductor quantum dot devices are a particularly promising candidate for use in quantum computing architectures, as it is anticipated that once the funda- mental building blocks are implemented, they might be massively scalable using the existing lithography techniques of the semiconductor industry. So far, how- ever, it is not yet clear how best to implement the high-fidelity gates required for general-purpose quantum computation. In this thesis, we present and characterise novel theoretical proposals for fast, simple and high-fidelity two-qubit gates using magnetic (exchange) coupling for specific semiconductor quantum dot qubits; namely, the singlet-triplet and resonant-exchange qubits. These two-qubit operations are simple enough that it is feasible for them to be implemented in experiments of the near future. Success- ful implementations would significantly extend the experimentally demonstrable frontier of semi-conductor quantum dot devices as relevant to their use in uni- versal quantum computing architectures. We also develop simple parameter estimation schemes by which it is possible to substantially mitigate the dominant sources of error for our proposed gates; namely, low-frequency charge and magnetic noise. We develop the techniques in the context of pseudo-static magnetic field gradient fluctuations in singlet- triplet qubits, and demonstrate that these techniques lead to a several orders of magnitude improvement in single-qubit coherence times. With minimal effort this could be ported to other qubit architectures.
We analyze a simple exchange-based two-qubit gate for singlet-triplet qubits in gate-defined semiconductor quantum dots that can be implemented in a single exchange pulse. Excitations from the logical subspace are suppressed by a magnetic field gradient that causes spin-flip transitions to be non-energy-conserving. We show that the use of adiabatic pulses greatly reduces leakage processes comapred to square pulses. We also characterize the effect of charge noise on the entanglement fidelity of the gate both analytically and in simulations; demonstrating high entanglement fidelities for physically realistic experimental parameters. Specifically we find that it is possible to achieve fidelities and gate times that are comparable to single-qubit states using realistic magnetic field gradients.
A key ingredient for fault-tolerant quantum computers are sufficiently accurate logic gates on single and multiple qubits in the presence of decohering noise. In this thesis, we theoretically develop and experimentally demonstrate such high-fidelity quantum gates for semiconductor-based quantum computing. Specifically, we consider a qubit encoded in the singlet and one triplet state of two electron spins in GaAs. While its potential for optical coupling makes GaAs an attractive material, highly auto-correlated magnetic field noise from fluctuating nuclear spins leads to considerably lower coherence times than for Si-based devices, where nuclear spins can be removed by isotopic purification. In addition to noise, the control methods used in earlier experiments are based on unrealistic approximations. For these reasons, fidelities well above 99 %, as required by current quantum error correction (QEC) schemes, have not been obtained before this thesis. To tackle these issues, we extend the filter function formalism to describe quantum gates and processes in the presence of experimentally relevant non-Markovian noise. Since this formalism can consider all relevant noise sources in a computationally efficient manner, it can be used to find optimal control pulses by numerical optimization, leading to predicted single-qubit gate fidelities of 99.9 %. Furthermore, we deal with the considerable control challenges associated with this qubit type by experimental calibration of the optimized control pulses. To this end, we extend our previous experimental gate set calibration (GSC) routine to remove systematic gate errors on an arbitrary number of qubits. We apply the numerically optimized single-qubit control pulses to our GaAs sample and experimentally calibrate them with GSC. This procedure yields an average gate fidelity of 99.50 ± 0.04 % and a low leakage rate of 0.13 ± 0.03 % out of the computational subspace, characterized by randomized benchmarking. We also optimize realistic two-qubit control pulses, considering current control hardware as well as interqubit Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we show that two-qubit gate fidelities of 99.90 % can be reached in GaAs, while 99.99 % can be achieved in Si. These results demonstrate that high-fidelity gates can be realized even in the presence of nuclear spins as in GaAs.
Hybrid systems comprising superconducting and semiconducting materials are promising architectures for quantum computing. Superconductors induce long-range interactions between the spin degrees of freedom of semiconducting quantum dots. These interactions are widely anisotropic when the semiconductor material has strong spin-orbit interactions. We show that this anisotropy is tunable and enables fast and high-fidelity two-qubit gates between singlet-triplet (ST) spin qubits. Our design is immune to leakage of the quantum information into noncomputational states and removes always-on interactions between the qubits, thus resolving key open challenges for these architectures. Our ST qubits do not require additional technologically demanding components nor fine-tuning of parameters. They operate at low magnetic fields of a few millitesla and are fully compatible with superconductors. By suppressing systematic errors in realistic devices, we estimate infidelities below ${10}^{\ensuremath{-}3}$, which could pave the way toward large-scale hybrid superconducting-semiconducting quantum processors.
There is a huge, worldwide effort to build a quantum computer due to its potential to perform chemical and materials simulations and to break current cryptography schemes. While there has been incredible progress in recent years, each potential platform still faces meaningful obstacles. The singlet-triplet qubit in gallium arsenide, which is based on electric spin, boasts several advantages, including fast single-gate times and readout, long lifetimes, and a clear path to large-scale integration using current semiconductor manufacturing techniques. However, it also suffers from electric and magnetic field noise that limits coherence time and weak two-qubit interactions, which have prevented the construction of multi-qubit systems so far. In this thesis, I will discuss my research measuring and working to improve noise and entangling gates in singlet-triplet qubits and will examine the viability of the singlet-triplet qubit as the building block for a quantum computer. \nBy measuring the dynamics of the electric and magnetic field noise that the singlet-triplet experiences, we can develop an understanding of their origins and how to reduce their impact. The singlet-triplet can be operated rapidly enough to use it as a sensor and directly measure the fluctuating magnetic field arising from the nuclear spins in the semiconductor heterostructure surrounding it. We use Hamiltonian parameter estimation, a technique that maximizes the rate at which we learn information, given the strange properties of quantum measurement, to measure magnetic noise to within 15 μT at a rate of 2 kHz, and we use these measurements to provide real-time feedback to system controls, increasing the coherence time by a factor of 30. Charge noise has much larger high-frequency components than magnetic noise, and thus requires use of dynamical decoupling methods borrowed from NMR to measure it. We measure its power spectrum up to 1 MHz and find that it has a 1/f spectrum. We perform these measurements for several different devices and have begun to determine how our growth and fabrication processes affect dephasing. \nPlacing a high-impedance resonator between two singlet-triplet qubits to mediate their interaction shows promise as way to create long-distance entanglement and to increase the speed of the entangling gate. We analyze this gate theoretically, finding that we expect the fidelity to be over 95%, with a straightforward path to increasing it to above 99% with improved resonator parameters. However, because the singlet-triplet qubit is extremely sensitive to changes in its electrostatic environment, which can be affected both by the resonator’s fabrication process and the presence of the proximal resonator gate, implementing this gate experimentally is challenging. We have developed processes for fabricating narrow, thin, NbN resonators directly adjacent to the double quantum dots that compose singlet-triplet qubits. These processes yield quantum dots that can be tuned into low-noise, stable singlet-triplet qubits, and superconducting resonators with impedances over 1 kOhm.
Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. owever, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations.\n\n\n\nThe focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*.\n\n\n\nWe probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency- dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled.\n\n\n\nThis work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor.
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.