Logical qubits are essential for utility scale universal quantum computation and require stable, high-fidelity physical qubits. In this thesis we consider three factors that can affect the performance of phosphorus atom qubits in silicon. Specifically, we determined the number of phosphorus atoms in few-atom qubit registers using the charging energy. We then explored if a new silicon encapsulation recipe could reduce charge noise under realistic qubit operating conditions. Finally, we performed experiments on few qubit devices to identify the dominant causes of qubit decoherence. To attain high-fidelity control requires characterising the underlying atomic structure of qubit registers (≤4P). By combining precise (≤5% error) experimentally measured charging energies with high quality STM images and theoretically modelled charging energies, we show the number of phosphorus atoms present can be determined confidently. Previously, our all-epitaxial nat-Si devices have demonstrated record low charge noise (0.17µeV). In this thesis we consider a new Si-28 growth recipe to assess if introducing an annealed ∼1nm silicon locking layer grown at room temperature can further increase the silicon encapsulation quality, whilst minimising P segregation. We first optimised the geometry of SET charge sensors fabricated in Si-28 to obtain high current contrast (≫1nA). For the locking layer (standard recipe) single electron transistors we found high (low) levels of charge noise at 0V (2.1µeV) that increased with the applied voltage (at 0V (0.29µeV) and 0.5V (0.23µeV)). In addition, we found that the electrical behaviour of the locking layer sensors was highly sensitive to the applied voltage. Since qubits are typically operated at ∼0.5V, further work is needed to assess the viability of this new growth recipe. Finally, we investigated different charge and magnetic noise sources that cause qubit decoherence in a 3P register using a modified Hahn echo experiment. Here, we use resonant drive at the frequencies of different nuclear spin species to identify P-31 in the SET island as causing qubit decoherence. Further, we found that the dominant charge noise source for electron spin qubits was the Stark shift of the g-factor. We also found the spin flip rate of phosphorus nuclei in the spin bath was affected by a change in the mechanical noise coupling into the fridge. For nuclear spin qubits we found the dominant noise source to be the Stark shift of the hyperfine interaction.
Logical qubits are essential for utility scale universal quantum computation and require stable, high-fidelity physical qubits. In this thesis we consider three factors that can affect the performance of phosphorus atom qubits in silicon. Specifically, we determined the number of phosphorus atoms in few-atom qubit registers using the charging energy. We then explored if a new silicon encapsulation recipe could reduce charge noise under realistic qubit operating conditions. Finally, we performed experiments on few qubit devices to identify the dominant causes of qubit decoherence. To attain high-fidelity control requires characterising the underlying atomic structure of qubit registers (≤4P). By combining precise (≤5% error) experimentally measured charging energies with high quality STM images and theoretically modelled charging energies, we show the number of phosphorus atoms present can be determined confidently. Previously, our all-epitaxial nat-Si devices have demonstrated record low charge noise (0.17µeV). In this thesis we consider a new Si-28 growth recipe to assess if introducing an annealed ∼1nm silicon locking layer grown at room temperature can further increase the silicon encapsulation quality, whilst minimising P segregation. We first optimised the geometry of SET charge sensors fabricated in Si-28 to obtain high current contrast (≫1nA). For the locking layer (standard recipe) single electron transistors we found high (low) levels of charge noise at 0V (2.1µeV) that increased with the applied voltage (at 0V (0.29µeV) and 0.5V (0.23µeV)). In addition, we found that the electrical behaviour of the locking layer sensors was highly sensitive to the applied voltage. Since qubits are typically operated at ∼0.5V, further work is needed to assess the viability of this new growth recipe. Finally, we investigated different charge and magnetic noise sources that cause qubit decoherence in a 3P register using a modified Hahn echo experiment. Here, we use resonant drive at the frequencies of different nuclear spin species to identify P-31 in the SET island as causing qubit decoherence. Further, we found that the dominant charge noise source for electron spin qubits was the Stark shift of the g-factor. We also found the spin flip rate of phosphorus nuclei in the spin bath was affected by a change in the mechanical noise coupling into the fridge. For nuclear spin qubits we found the dominant noise source to be the Stark shift of the hyperfine interaction.
Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.
Abstract : As classical computers begin to reach their fundamental performance limits, quantum computers will be an invaluable tool for the advance of science and technology. The trillion dollar silicon electronics industry sets the perfect stage for the evolution of quantum computation, yet it has so far proved to be a tough challenge to implement all the elements needed to build a scalable quantum computer in silicon. This thesis presents the first experimental demonstration of the full operation of single-spin qubits in Si. Our qubits consist of the electron and nuclear spins of a single phosphorus atom, implanted in a Si substrate, and controlled by a gated nanostructure. We describe an experimental setup tailored to minimise electron temperature and perform realtime data acquisition, analysis and instrument control. We present modeling, simulation and characterisation of a novel nanoscale coplanar antenna for spin control, designed to work at frequencies up to 50 GHz. These tools have allowed us to demonstrate the first ever single-atom spin-qubits in natural silicon, leading the way to demonstrating record qubit performances in isotopically purified 28Si: an electron spin qubit with measurement and control fidelities 97% and coherence times of 0.5 seconds; and a nuclear spin qubit with fidelities 99.99% and a record single-spin coherence of 30 s. We have performed noise spectroscopy in our system and concluded that decoherence is currently limited by magnetic noise originating from our broadband antenna.
Abstract : Artificial two-level quantum systems are widely investigated as the fundamental building blocks of future quantum computers. These quantum bits (qubits) can be realized in many solid state systems, including Josephson junction based devices, nitrogen vacancy centers in diamond, and electron spins in semiconductor quantum dots. Among these systems, Si is very promising since it can be isotopically purified to eliminate random fluctuating hyperfine fields from lattice nuclei, leading to ultra-long quantum coherence times. However, lower heterostructure quality, higher electron effective mass and valley degeneracy present many challenges in realizing high quality qubits in Si. This thesis demonstrates consistent realization of robust single-electron silicon qubits with high yield. With optimized device designs and DC/RF measurement techniques developed at Petta lab in Princeton University, we have achieved versatile quantum control of a single electron, as well as sensitive read-out of its quantum state. By applying microwave radiation to the gate electrodes, we can probe the energy level structure of the system with 1 mu-eV resolution. We apply bursts of microwave radiation to extract the qubit lifetime, T1 . By experimentally tuning the qubit, we demonstrate a four order of magnitude variation of T1 with gate voltage. We show that our experimental results are consistent with a theory that takes into account phonon-mediated charge relaxation.
Abstract Phosphorus atoms in silicon are an outstanding platform for quantum computing as their nuclear spins exhibit coherence time over seconds [1, 2]. By placing multiple phosphorus atoms within a radius of a few nanometers, they couple via the hyperfine interaction to a single, shared electron. Such a nuclear spin register enables multi-qubit control above the fault-tolerant threshold [3] and the execution of small-scale quantum algorithms [4]. To achieve quantum error correction, fast and efficient interconnects have to be implemented between spin registers while maintaining high fidelity across all qubit metrics. Here, we demonstrate such integration with a fully controlled 11-qubit atom processor composed of two multi-nuclear spin registers which are linked via electron exchange interaction. Through the development of scalable calibration and control protocols, we achieve coherent coupling between nuclear spins using a combination of single- and multi-qubit gates with all fidelities ranging from 99.5% to 99.99%. We verify the efficient all-to-all connectivity by preparing both local and non-local Bell states with a record state fidelity beyond 99% and extend entanglement through the generation of Greenberger-Horne-Zeilinger (GHZ) states over all data qubits. By establishing high-fidelity operation across interconnected nuclear-spin registers, we ealise a key milestone towards fault-tolerant quantum computation with atom processors.
We report a nanofabrication, control and measurement scheme for charge-based silicon quantum computing which utilises a new technique of controlled single ion implantation. Each qubit consists of two phosphorus dopant atoms ~50 nm apart, one of which is singly ionized. The lowest two energy states of the remaining electron form the logical states. Surface electrodes control the qubit using voltage pulses and dual single electron transistors operating near the quantum limit provide fast readout with spurious signal rejection. A low energy (keV) ion beam is used to implant the phosphorus atoms in high-purity Si. Single atom control during the implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure, while positional accuracy is provided by a nanomachined resist mask. We describe a construction process for implanted single atom and atom cluster devices with all components registered to better than 20 nm, together with electrical characterisation of the readout circuitry. We also discuss universal one- and two-qubit gate operations for this architecture, providing a possible path towards quantum computing in silicon.
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.