Superconducting qubits are artificial atoms whose spectra and interactions can be engineered through appropriate circuit design, a versatility that can be exploited for quantum simulation. We theoretically investigate a linear array of capacitively coupled transmons, effectively described by a Bose-Hubbard Hamiltonian with attractive interaction. We revisit the discrete-soliton nature of the lowest-energy band of the spectrum, and identify spatially localized quantum solitons. The solitonic character of these states is revealed through their time evolution, which displays a quantum interference pattern, or quantum walk, highlighting their composite nature. We discuss protocols for preparing spatially localized quantum solitons that are compatible with current state-of-the-art tunable-transmon circuits. Our results demonstrate that superconducting circuits provide a promising and experimentally accessible platform for the investigation of quantum soliton physics.
Superconducting qubits are artificial atoms whose spectra and interactions can be engineered through appropriate circuit design, a versatility that can be exploited for quantum simulation. We theoretically investigate a linear array of capacitively coupled transmons, effectively described by a Bose-Hubbard Hamiltonian with attractive interaction. We revisit the discrete-soliton nature of the lowest-energy band of the spectrum, and identify spatially localized quantum solitons. The solitonic character of these states is revealed through their time evolution, which displays a quantum interference pattern, or quantum walk, highlighting their composite nature. We discuss protocols for preparing spatially localized quantum solitons that are compatible with current state-of-the-art tunable-transmon circuits. Our results demonstrate that superconducting circuits provide a promising and experimentally accessible platform for the investigation of quantum soliton physics.
Superconducting circuits constitute a promising platform for future implementation of quantum processors and simulators. Arrays of capacitively coupled transmon qubits naturally implement the Bose-Hubbard model with attractive on-site interaction. The spectrum of such many-body systems is characterized by low-energy localized states defining the lattice analog of bright solitons. Here, we demonstrate that these bright solitons can be pinned in the system, and we find that a soliton moves while maintaining its shape. Its velocity obeys a scaling law in terms of the combined interaction and number of constituent bosons. In contrast, the source-to-drain transport of photons through the array occurs through extended states that have higher energy compared to the bright soliton. For weak coupling between the source or drain and the array, the populations of the source and drain oscillate in time; for chains of even length, their population remains low at all times, while it can reach half the number of total bosons in odd chains. Implications of our results for actual experimental realizations are discussed.
Nonlinear superconducting circuits are a leading candidate to implement quantum information tasks beyond the reach of classical processors. One such task, quantum simulation, involves using a controllable quantum system to study the dynamics of another. In this thesis, we present a series of experiments using small systems of superconducting circuits to perform various quantum tasks relevant to quantum simulation.In the first experiment, we design and build a circuit comprising three transmon qubits whose dynamics mirror those of interacting bosonic particles on a lattice, described by the Bose-Hubbard Hamiltonian. We verify the predictions of the Bose-Hubbard model for this system spectroscopically and then use time-domain measurements to study the decoherence processes affecting the qubits. Using a Raman process, we engineer artificial decay dynamics in the system which allow us to prepare and stabilize otherwise inaccessible states of the transmon array.The second experimental demonstration concerns topological quantum matter. Certain quantum systems are characterized by quantities known as topological invariants, which are robust to local perturbations. These topological invariants are challenging to measure in naturally-occurring systems. We engineer an artificial system, comprising a transmon qubit coupled to a high-Q cavity, capable of undergoing a protocol known as the quantum walk, which also exhibits topological invariants. By using particular non-classical state of the cavity, we modify the quantum walk protocol to make the topological invariant directly accessible.Finally, we implement a hybrid quantum-classical algorithm—known as the variational quantum eigensolver—in a two-transmon quantum processor. As a proof of principle demonstration, we compute the ground-state and low-lying excited state energies of the hydrogen molecule as a function of nuclear separation. We show that an extension of the basic algorithm, known as the quantum subspace expansion, allows for the mitigation of errors caused by decoherence processes affecting the quantum processor.
When quantum particles interact, many-body phenomena that are hard to simulate classically emerge. Quantum analog simulation offers an alternative in which the target system's dynamics is directly realized in controllable quantum hardware. Here, we give a general protocol for simulating the Bose-Hubbard and anyon-Hubbard models using lattices of capacitively coupled flux-tunable transmons. By modulating the transmon frequencies in an alternating pattern, we resonantly drive multiple many-body transitions and can tune the on-site interaction and density-dependent hopping amplitudes for up to three bosons per site, with no additional restriction on the total particle number. By adding phases to the modulation, which renders the transition amplitudes complex-valued, we propose the first simulation protocol for the anyon-Hubbard model with transmons. Numerical simulations of the driven transmon arrays with experimentally realistic parameters reproduce the characteristic dynamics of the target models across a range of interaction strengths and statistical phases, including the interaction-dependent localization and the statistics-dependent asymmetry of the anyonic quantum walk.
Fluxonium superconducting circuits were originally proposed to realize highly coherent qubits. In this work, we explore how these circuits can be used to implement and harness qutrits, by tuning their energy levels and matrix elements via an external flux bias. In particular, we investigate the distinctive features of arrays of fluxonium qutrits, and their potential for the quantum simulation of exotic quantum matter. We identify four different operational regimes, classified according to the plasmon-like versus fluxon-like nature of the qutrit excitations. Highly tunable on-site interactions are complemented by correlated single-particle hopping, pair hopping and non-local interactions, which naturally emerge and have different weights in the four regimes. Dispersive corrections and decoherence are also analyzed. We investigate the rich ground-state phase diagram of qutrit arrays and propose practical dynamical experiments to probe the different regimes. Altogether, fluxonium qutrit arrays emerge as a versatile and experimentally accessible platform to explore strongly correlated bosonic matter beyond the Bose-Hubbard paradigm, and with a potential toward simulating lattice gauge theories and non-Abelian topological states.
In the last two decades, the field of circuit quantum electrodynamics, that studies the interaction between superconducting qubits and 1-dimensional waveguides, has been of great interest. It provides a great potential to build quantum devices, which are important for quantum computing, quantum communication and quantum information. The restriction to one dimension decreases losses and information can be transferred efficiently. Superconducting qubits are artificial atoms that consist of a non-linear Josephson element and work in the microwave regime. These superconducting qubits make on-chip tunable quantum experiments possible.In the appended paper, we investigate the spontaneous emission of an initially excited artificial atom (superconducting transmon qubit) which is capacitively coupled to a semi-infinite transmission line (atom in front of a mirror). We can choose the distance to the mirror arbitrarily so the interaction with the reflected field is delayed if the qubit is far away from the mirror and we have to take time-delay effects into account. We derive equations of motion for the transmon by circuit quantization and solve them semi-classically. In this thesis we give an introduction to circuit quantization, transmission lines and superconducting qubits. Then we discuss the methods and results of the appended paper which are based on the topics introduced.
In a quantum computer, the information carriers, which are bits in ordinary computers, are implemented as devices that exhibit coherent superpositions of physical states and entanglement. Such components, known as quantum bits or qubits, can be realized with various different types of two-state quantum systems. Quantum computers will be built for computational speed, with hoped for applications especially in cryptography and in other tasks where classical computers remain inefficient. Circuit quantum electrodynamics (cQED) is a quantum-computer architecture which employs superconducting electronic components and microwave photon fields as building blocks. Compared to cavity quantum electrodynamics (CQED), where atoms are trapped in physical cavities, cQED is more attractive in that its qubits are tunable and conveniently integrable with the electronics already in use. This architecture has shown some of the most promising qubit designs, despite their coherence times reaching tens of microseconds, are still below the state of the art with spin qubits, which reach milliseconds. Coherence times are historically the most relevant parameters describing the fitness of a qubit, although these days not necessarily the limiting factor. This thesis presents a comprehensive set of theoretical and experimental methods for measuring the characteristic parameters of superconducting qubits. We especially study transmission-line-shunted plasma oscillation qubits, or transmons, and presents experimental results for a single sample. Transmon capacitively couples a superconducting quantum interference device (SQUID) with a coplanar waveguide (CPW) resonator, often with added frequency tunability utilizing an external magnet. The number of superconducting charge carriers tunnelled through a junction in the SQUID are used as qubit degrees of freedom. Readout of the qubit state is carried out by measuring transmission through the CPW. A cryogenic setup is employed with measurement and driving pulses delivered from microwave sources. Steady-state spectroscopy is employed to determine the resonance frequencies of the qubit and the resonator, qubit-resonator coupling constants, and the energy parameters of the qubit. Pulse-modulated measurements are employed to determine the coherence times of the qubit. The related analysis- and simulation programs and scripts are collected togithub.com/patomaki.