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.
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.
Quantum computers are a promising new technology that enables the use of quantum algorithms to solve certain problems faster than classical computers. An especially auspicious method for realizing such a device is using a superconducting circuit as the foundational computational unit of the quantum computer, the qubit. These serve as two-level systems allowing for the storage and manipulation of quantum information. For large-scale adoption, precise control of qubits via rapid driving pulses is essential in order to carry out desired operations known as quantum gates. In superconducting qubits, this is often achieved with an external electromagnetic field coupled to the qubit capacitively or inductively. In this case, to achieve faster pulses, the power of the driving field must be increased. This, however, leads to increased heating of the qubit, which in turn can lead to decoherence and the loss of quantum information. One proposed solution is the use of off-resonance driving of the qubit, which enables faster pulses with lower driving power when compared to resonance drive. It also allows for drive line attenuation at the qubit frequency, suppressing decay of the qubit’s energy into the drive line. Another challenge in the operation of the qubit is preventing excitation outside the two states used for computation, known as the computational subspace. In this thesis, we look at optimizing the drive pulse shape as a remedy to this problem in the context of resonance drive, as well as two off-resonant driving methods: subharmonic drive and two-frequency drive. In particular, we make use of the Derivative Removal by Adiabatic Gate (DRAG) method with different pulse shapes in order to attenuate the transition between the first and second excited states of the qubit. The results are obtained with numerical simulation for the transmon, which is a common superconducting qubit. The results show strong suppression of leakage outside the computational subspace using the DRAG method in resonance and two-frequency drive, while in subharmonic drive, no major advantage is gained. We find that in all cases, the edge profiles of driving pulses have major effects on the excitation of unwanted transitions, suggesting that pulse shape optimization is a viable method for improving quantum gate fidelity in all three driving regimes.
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.
Quantum computers store and manipulate information in individual quantized energy levels. These devices, not yet realized in their full potential, have the ability to perform certain computational tasks more efficiently than any classical computer. One possible way to implement a quantum computer is to use superconducting circuits controlled by single-mode electromagnetic fields. These circuits constitute the physical quantum bits, or qubits, that are used to store quantum information. A complete, fault-tolerant quantum computer potentially consists of at least millions of physical qubits which are grouped to form fault-tolerant logical qubits. Controlling each physical qubit individually requires a great amount of energy, and hence a future challenge is to reduce the energy consumption in qubit control while maintaining the high precision. In this thesis, we derive a fundamental upper bound for the gate fidelity of a single-qubit not gate implemented with a single resonant driving pulse. It is shown that the upper bound approaches unity inversely proportionally to the increasing mean photon number of the pulse. Furthermore, we find that the upper bound is achieved with an optimal superposition of squeezed states. The typically employed coherent state produces twice as high gate error as the corresponding optimal state. In addition, we present and numerically study a correction protocol that allows using the same drive state for multiple qubit operations. This sustained state is refreshed by sequentially coupling ancillary qubits to it, effectively resetting it and removing entanglement with the previously operated qubits. Thus our protocol allows using the same drive state to implement not gates for different qubits indefinitely, and hence provides a possible route to energy-efficient large-scale quantum computing.
Superconducting circuits are one of the most promising and rapidly developing platforms for implementing quantum bits and their control operations for the purpose of large-scale quantum computing. A quantum algorithm is run by executing a series of precise operations on the quantum bits, or qubits. The most important of these operations are the quantum gates along with the measurement and initialization of the states of the qubits and auxiliary components.
In this dissertation, we develop techniques to enhance each of these three operations. The work employs systems of coupled qubits and resonators in the framework of circuit quantum electrodynamics.
Firstly, we derive a theoretical lower bound for the error of a single-qubit gate implemented with a linear oscillator mode and show how to reach this bound. Secondly, we experimentally demonstrate a technique for measuring the state of a qubit by simultaneously driving the qubit and the accompanying readout resonator. Compared to our method, the standard technique involving only the resonator drive yields up to 100% larger error. Moreover, we experimentally and theoretically develop quantum devices and protocols that may be used to initialize or reset auxiliary quantum circuits such as resonators. By coupling a quantum circuit to a strongly dissipative environment through a coupler, the decay rate of the circuit may be tuned on demand by several orders of magnitude. Finally, we propose a general method to analytically solve the dynamics of a complex, open bosonic system that may be used to describe, for example, the experimental systems of this dissertation.
The experimental techniques developed in this dissertation may potentially be utilized in future implementations of a quantum computer, and the proposed theoretical protocols pave the way for future experiments aiming to improve qubit control and heat management in large-scale quantum processors.; Suprajohtavat kvanttipiirit ovat yksi lupaavimmista ja nopeimmin kehittyvista alustoista, joilla voi mahdollisesti toteuttaa suuren kokoluokan kvanttilaskentaa. Kvanttilaskennassa keskeisessa asemassa ovat kvanttibitit eli kubitit seka niilla tehtavat tarkat operaatiot, joista kvanttialgoritmit muodostuvat. Operaatioista tarkeimmat ovat loogiset kvanttiportit seka kubittien ja muiden tarvittavien komponenttien tilojen mittaus ja alustus.Tassa vaitoskirjassa kehitetaan tapoja naiden kolmen operaation parantamiseksi. Tyossa kasitellaan kvanttielektrodynamiikkaan perustuvia, kubittien ja resonaattorien muodostamia kytkettyja systeemeja.
Ensimmaiseksi johdamme teoreettisen alarajan lineaarisella varahtelymoodilla toteutetulle yhden kubitin kvanttiportin virheelle seka naytamme, miten alaraja on mahdollista saavuttaa. Toiseksi toteutamme kokeellisesti menetelman, jolla voi mitata kubitin tilan ajamalla kubittia ja siihen kytkettya lukuresonaattoria samanaikaisesti. Yleisesti kaytetty mittaustapa, jossa ajetaan ainoastaan resonaattoria, tuottaa jopa 100% suuremman virheen kuin toteuttamamme menetelma.…
The ability to perform fast and accurate rotations between the computational basis states of quantum bits is one of the most fundamental requirements for building a quantum computer. Because physical qubits generally contain more than two levels, faster gates often result in a higher leakage rate outside of the computational space. In this Letter, we enhance the state-of-the-art single qubit gate by introducing active leakage cancellation. This is accomplished via a second drive tone near the leakage transition such that we cancel the leakage caused by the main drive. Furthermore, we describe a measurement sequence that can be used to calibrate the parameters of this leakage cancellation drive. Finally, we apply the technique to superconducting transmon qubits and achieve leakage suppression by up to a factor of 20 when compared to pulses shaped with the standard derivative removal by adiabatic gate technique. This results in a coherence-limited gate infidelity of 7.5×10^{-5} with leakage below 10^{-5} level, for a 10 ns π/2 gate and 196 MHz qubit anharmonicity.
Quantum processors with native multi-qubit gates may offer very efficient implementations of near-term quantum algorithms on noisy hardware. Here, we introduce the multiunimon, a superconducting multimode circuit that encodes multiple qubits and enables native multi-qubit gates in a device consisting of a single Josephson junction embedded in a coplanar waveguide structure. Closely related to the unimon qubit, it inherits properties such as high anharmonicity, full protection against low-frequency charge noise, and partial protection against flux noise. By designing such a three-qubit device with Josephson-to-inductive energy ratio above unity and using a leakage-aware encoding scheme for the computational states, we simulate all twelve different controlled-controlled-NOT gates with a mean fidelity of 99.5% with simple sine-squared pulses of comparable length to single-qubit gates. The performance is limited by incoherent errors dominated by dielectric loss. With improvements in noise protection, design, and pulse shaping, the simulations suggest that fidelities approaching 99.99% are within reach. Our results demonstrate the potential of the multiunimon as a highly connected multi-qubit unit for larger superconducting quantum processors.