Solomon Freer, Stephanie Simmons, Arne Laucht, Juha T. Muhonen, Juan Pablo Dehollain, Rachpon Kalra, Fahd A. Mohiyaddin, Fay E. Hudson, Kohei M. Itoh, Jeffrey Colin McCallum, David N. Jamieson, Andrew S. Dzurak, Andrea Morello
Abstract Long coherence times and fast gate operations are desirable but often conflicting requirements for physical qubits. This conflict can be resolved by resorting to fast qubits for operations, and by storing their state in a ‘quantum memory’ while idle. The 31 P donor in silicon comes naturally equipped with a fast qubit (the electron spin) and a long-lived qubit (the 31 P nuclear spin), coexisting in a bound state at cryogenic temperatures. Here, we demonstrate storage and retrieval of quantum information from a single donor electron spin to its host phosphorus nucleus in isotopically enriched 28 Si. The fidelity of the memory process is characterised via both state and process tomography. We report an overall process fidelity F p ≈ 81 %, and memory storage times up to 80 ms. These values are limited by a transient shift of the electron spin resonance frequency following high-power radiofrequency pulses.
Abstract Long coherence times and fast gate operations are desirable but often conflicting requirements for physical qubits. This conflict can be resolved by resorting to fast qubits for operations, and by storing their state in a ‘quantum memory’ while idle. The 31 P donor in silicon comes naturally equipped with a fast qubit (the electron spin) and a long-lived qubit (the 31 P nuclear spin), coexisting in a bound state at cryogenic temperatures. Here, we demonstrate storage and retrieval of quantum information from a single donor electron spin to its host phosphorus nucleus in isotopically enriched 28 Si. The fidelity of the memory process is characterised via both state and process tomography. We report an overall process fidelity F p ≈ 81 %, and memory storage times up to 80 ms. These values are limited by a transient shift of the electron spin resonance frequency following high-power radiofrequency pulses.
Conventional computing faces a huge technical challenge as traditional transistors will soon reach their size limitations. This will halt progress in reaching faster processing speeds and to overcome this problem, require an entirely new approach. Quantum computing (QC) is a natural solution offering a route to miniaturisation by, for example, storing information in electron or nuclear spin states, whilst harnessing the power of quantum physics to perform certain calculations exponentially faster than its classical counterpart. However, QCs face many difficulties, such as, protecting the quantum-bit (qubit) from the environment and its irreversible loss through the process of decoherence.Hybrid systems provide a route to harnessing the benefits of multiple degrees of freedom through the coherent transfer of quantum information between them. In this thesis I show coherent qubit transfer between electron and nuclear spin states in a 15N@C60 molecular system (comprising a nitrogen atom encapsulated in a carbon cage) and a solid state system, using phosphorous donors in silicon (Si:P). The propagation uses a series of resonant mi- crowave and radiofrequency pulses and is shown with a two-way fidelity of around 90% for an arbitrary qubit state. The transfer allows quantum information to be held in the nuclear spin for up to 3 orders of magnitude longer than in the electron spin, producing a 15N@C60 and Si:P ‘quantum memory’ of up to 130 ms and 1.75 s, respectively. I show electron and nuclear spin relaxation (T1), in both systems, is dominated by a two-phonon process resonant with an excited state, with a constant electron/nuclear T1 ratio. The thesis further investigates the decoherence and relaxation properties of metal atoms encapsulated in a carbon cage, termed metallofullerenes, discovering that exceptionally long electron spin decoherence times are possible, such that these can be considered a viable QC candidate.
Quantum memories capable of storing and retrieving coherent information for extended times at room temperature would enable a host of new technologies. Electron and nuclear spin qubits using shallow neutral donors in semiconductors have been studied extensively but are limited to low temperatures (≲10 kelvin); however, the nuclear spins of ionized donors have the potential for high-temperature operation. We used optical methods and dynamical decoupling to realize this potential for an ensemble of phosphorous-31 donors in isotopically purified silicon-28 and observed a room-temperature coherence time of over 39 minutes. We further showed that a coherent spin superposition can be cycled from 4.2 kelvin to room temperature and back, and we report a cryogenic coherence time of 3 hours in the same system.
Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual (31)P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized (31)P nucleus of a single P donor in isotopically purified (28)Si. We find average gate fidelities of 99.95% for the electron and 99.99% for the nuclear spin. These values are above certain error correction thresholds and demonstrate the potential of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware and not the intrinsic behaviour of the qubit.
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.
A high degree of controllability and long coherence time make the nuclear spin of a phosphorus donor in isotopically purified silicon a promising candidate for a quantum bit. However, long-distance two-qubit coupling and fast, robust gates remain outstanding challenges for these systems. Here, following recent proposals for long-distance coupling via dipole-dipole interactions, we present a simple method to implement fast, high-fidelity arbitrary single- and two-qubit gates in the absence of charge noise. Moreover, we provide a method to make the single-qubit gates robust to moderate levels of charge noise to well within an error bound of ${10}^{\ensuremath{-}3}$.