Meet the Unimon, the New Qubit on the BlockIn initial tests, a simplified version of a popular superconducting qubit achieves high computation accuracies, making it attractive for future quantum computers.
Quantum computers utilize qubits to store and process quantum information. In superconducting quantum computers, qubits are implemented as quantum superconducting resonant circuits. The circuits are operated only at the two energy states, which form the computational basis for the qubit. To suppress leakage to uncomputational states, superconducting qubits are designed to be anharmonic oscillators, which is achieved using one or more Josephson junctions, a nonlinear superconducting element. One of the main challenges in developing quantum computers is minimizing the decoherence caused by environmental noise. Decoherence is characterized by two coherence times, T1 for depolarization processes and T2 for dephasing. This thesis reviews and investigates the decoherence properties of superconducting qubits. The main goal of the thesis is to analyze the tradeoff between anharmonicity and dephasing in a qubit unimon. Recently developed unimon incorporates a single Josephson junction shunted by a linear inductor and a capacitor. Unimon is tunable by external magnetic flux, and at the half flux quantum bias, the Josephson energy is partially canceled by the inductive energy, allowing unimon to have relatively high anharmonicity while remaining fully protected against low-frequency charge noise. In addition, at the sweet spot with respect to the magnetic flux, unimon becomes immune to first-order perturbations in the flux. The sweet spot, however, is relatively narrow, making unimon susceptible to dephasing through the quadratic coupling to the flux noise. In the first chapter of this thesis, we present a comprehensive look into the basic theory of superconducting qubits, starting with two-state quantum systems, followed by superconductivity and superconducting circuit elements, and finally combining these two by introducing circuit quantum electrodynamics (cQED), a framework for building superconducting qubits. We follow with a theoretical discussion of decoherence in two-state quantum systems, described by the Bloch-Redfield formalism. We continue the discussion by estimating decoherence using perturbation theory, with special care put into the dephasing due to the low-frequency 1/f noise. Finally, we review the theoretical model of unimon, which is used in the numerical analysis. As a main result of this thesis, we suggest a design parameter regime for unimon, which gives the best ratio between anharmonicity and T2.
Inductively shunted superconducting qubits, such as the unimon qubit, combine high anharmonicity with protection from low-frequency charge noise, positioning them as promising candidates for the implementation of fault-tolerant superconducting quantum computers. In this work, we develop accurate closed-form approximations for the frequency and anharmonicity of the unimon qubit that are also applicable to any single-mode superconducting qubits with a single-well potential profile, such as the quarton qubit or the kinemon qubit. We use these results to theoretically explore the single-qubit gate fidelity and coherence times across the parameter space of qubits with a single-well potential. We find that the gate fidelity can be optimized by tuning the Hamiltonian to (1) a high qubit mode impedance of 1 – 2 k Ω , (2) a low qubit frequency of 1 GHz, (3) and a perfect cancellation of the linear inductance and the Josephson inductance attained at a flux bias of half flux quantum. According to our theoretical analysis, the proposed qubit parameters have the potential to enhance the single-qubit gate fidelity of the unimon beyond 99.99%, even without significant improvements to the dielectric quality factor or the flux noise density measured for the first unimon qubits. Furthermore, we compare unimon, transmon, and fluxonium qubits in terms of their energy spectra and qubit coherence subject to dielectric loss and 1 / f flux noise in order to highlight the advantages and limitations of each qubit type.
A quantum computer is a new kind of computer which utilizes quantum phenomena in computing. This machine has the potential to solve specific tasks faster than the most powerful supercomputers and therefore has potential real-life applications across various sectors of society. One promising approach to realize a quantum computer is to store information in superconducting qubits, which are artificial two-level quantum systems made from superconducting electrical circuits. Extremely precise control of these qubits is essential but also challenging due to the excitations out of the two lowest energy states of the quantum system that constitute the computational subspace. In this thesis, we propose a new way to control a superconducting multimode qubit using the unimon qubit as an example. By coupling differently to the different modes of the multimode qubit circuit, we cancel the transition from the first excited state to the second excited state, which is typically the main transition causing a leakage out of the computational subspace. We present a theoretical description of this model by utilizing methods of circuit quantum electrodynamics to compute the energy spectrum and the transition matrix elements of the qubit. By using these results, we simulate the dynamics of the driven unimon qubit undergoing as a single-qubit gate. The result of the simulation shows that this method decreases the leakage relative to the conventional method of driving a qubit, where only one external drive is applied. However, by improving the conventional method with a more advanced pulse optimization method, the leakage becomes smaller than in the standard case of two drive fields. In addition, we find that the practical implementation of our method may be sensitive to variations in the qubit parameters. Therefore, the practical implementation of the method needs further research in the future. By cancelling one energy-level transition of the qubit, we find that other transitions in modes of similar frequency were strongly suppressed. Therefore, this method might be potentially utilized in other qubit operations than the quantum gates, such as in the qubit resetting process, where driving to higher frequency modes of the unimon is preferred.