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- PostEncoding of Qubit States in Resonators With Cat Codes(2019) Winther, Johan; Chalmers tekniska högskola / Institutionen för mikroteknologi och nanovetenskap; Chalmers University of Technology / Department of Microtechnology and NanoscienceQuantum computing has gained a lot of interest in recent years and commercial products are just now entering the market. However one of the main challenges in realising a quantum computer is noise and one key technology to remedy this is quantum error correction (QEC). One way of performing QEC exploits the storage of the quantum information of a qubit in a resonator as cat codes. To do this one needs to apply encoding pulses to the coupled qubit-resonator system in order to perform a state transfer from the qubit to the resonator. These pulses need to be numerically obtained by simulation. This thesis studies the potential of using a gradient-based optimization method, the so called Krotov's method, to numerically optimize encoding pulses for encoding arbitrary qubit states in cat codes. The Python package Krotov, a package for quantum optimal control using the method, is first used to perform state evolution from |0> to |1> and |0> to |2> of an anharmonic resonator in order to familiarise with the package and optimal control in general. It is shown that, assuming a maximum drive amplitude and no dissipation, the method can realise a |0> to |1> evolution with fidelity F > 0.99999 and a total pulse length of only 10.75 ns. For the |0> to |2> evolution a total pulse length of 30 ns is needed to reach the same fidelity. Finally, the Krotov is used to optimize pulses for transferring qubit states into the resonator as cat codes. The transfer of six states were simultaneously optimized in order to approximate a unitary which transfers an arbitrary qubit state into the resonator as a cat code. Using mostly experimentally realistic parameters, it is shown that the method can optimize pulses which realise the encoding of arbitrary qubit states to cat codes with a fidelity of at least F > 0.998900. Although plenty of challenges still remain to prove this can be done in experiments, the results points to the Krotov package as a viable tool for encoding pulse optimization.
- PostOn improving the expressive power of chemical computation(2015) Bergh, Erik; Chalmers tekniska högskola / Institutionen för mikroteknologi och nanovetenskap; Chalmers University of Technology / Department of Microtechnology and NanoscienceTraditional CMOS computers are Turing complete information processing systems. They can compute any function that can be described algorithmically. In the past, the computing speed of such systems has been constantly improved. However, for various technological reasons this trends is expected to stop, and alternative ways of computing are under investigation. The computational power of chemical systems has been investigated for quite some time. However, it is not clear what the computing capacity of such systems is. It has been studied how to construct a Turing complete chemical computer in the well-mixed chemical reactor setup. Liekens and Fernando (“Turing complete catalytic computers”, in: Advances in Artificial life, Springer, 2007, pp. 1202-1211) have suggested a systematic way to investigate the chemical completeness issue. Their main finding was that chemical computers are Turing complete in principle. However, spontaneous errors in computation can occur. The frequency of these errors defines the fail rate. In this study, the aim is to understand how the effects of diffusion (e.g. speed of mixing) and the dimensionality of the system influence the fail rate. This is done by performing Monte Carlo simulations. The main conclusions are: The effects of diffusion are indeed extremely important. Finite mixing (low diffusion constant) leads to higher fail rates. It is possible to improve the accuracy of the computer (lower the fail rate) by optimizing the reaction system that implements the chemical computer.