Large superconducting quantum circuits have a number of important applications in quantum computing. Accurately predicting the performance of these devices from first principles is challenging, as it requires solving the many-body Schrödinger equation. This work introduces a new, general ab-initio method for analyzing large quantum circuits based on lattice field theory, a tool commonly applied in nuclear and particle physics. This method is competitive with state-of-the-art techniques such as tensor networks, but avoids introducing systematic errors due to truncation of the infinite-dimensional Hilbert space associated with superconducting phases. The approach is applied to fluxonium, a specific many-component superconducting qubit with favorable qualities for quantum computation. A systematic study of the influence of impedance on fluxonium is conducted that parallels previous experimental studies, and ground capacitance effects are explored. The qubit frequency and charge noise dephasing rate are extracted from statistical analyses of charge noise, where thousands of instantiations of charge disorder in the Josephson junction array of a fixed fluxonium qubit are explicitly averaged over at the microscopic level. This is difficult to achieve with any other existing method.
Large superconducting quantum circuits have a number of important applications in quantum computing. Accurately predicting the performance of these devices from first principles is challenging, as it requires solving the many-body Schrödinger equation. This work introduces a new, general ab-initio method for analyzing large quantum circuits based on lattice field theory, a tool commonly applied in nuclear and particle physics. This method is competitive with state-of-the-art techniques such as tensor networks, but avoids introducing systematic errors due to truncation of the infinite-dimensional Hilbert space associated with superconducting phases. The approach is applied to fluxonium, a specific many-component superconducting qubit with favorable qualities for quantum computation. A systematic study of the influence of impedance on fluxonium is conducted that parallels previous experimental studies, and ground capacitance effects are explored. The qubit frequency and charge noise dephasing rate are extracted from statistical analyses of charge noise, where thousands of instantiations of charge disorder in the Josephson junction array of a fixed fluxonium qubit are explicitly averaged over at the microscopic level. This is difficult to achieve with any other existing method.
Abstract We use a tensor network method to compute the low-energy excitations of a large-scale fluxonium qubit up to a desired accuracy. We employ this numerical technique to estimate the pure-dephasing coherence time of the fluxonium qubit due to charge noise and coherent quantum phase slips from first principles, finding an agreement with previously obtained experimental results. By developing an accurate single-mode theory that captures the details of the fluxonium device, we benchmark the results obtained with the tensor network for circuits spanning a Hilbert space as large as 15180. Our algorithm is directly applicable to the wide variety of circuit-QED systems and may be a useful tool for scaling up superconducting quantum technologies.
Fluxonium qubits, designed to mitigate charge noise and enhance anharmonicity, are among the most promising superconducting platforms for quantum computing. To understand and exploit their quantum properties and design novel fluxonium-based architectures with improved functionalities, these systems require an accurate Hamiltonian formulation to capture their energy level structure and quantum dynamics. This work presents a systematic method for constructing the Hamiltonian for multi-loop circuits that partitions the system into a set of uncoupled harmonic oscillators and a coupled anharmonic part originating from the Josephson circuit elements, allowing clear identification of independent modes and isolating the nonlinearity in the Josephson terms. While demonstrated for fluxonium-type multi-loop circuits, this method can be generalized to other superconducting qubit architectures within the broader context of circuit QED, making it a versatile tool for exploring different circuit configurations. Our systematic and flexible modeling approach forms the theoretical basis for the qubit measurement and control experiments validating multi-loop fluxonium architectures.
Quantum computing provides significantly more efficient methods than classical computers for doing rigorous calculations such as encryption, search algorithms, and physical simulations. This is accomplished through the use of qubits which exist in a superposition of multiple states at once allowing for both complex and fast calculations. Environmental fluctuations interfere with these states and resulting in decoherence and dephasing and the break down of the algorithm. One type of qubit is the fluxonium: a superconducting artificial atom derived from the Cooper pair box. The purpose of this project was to analyze the effect of charge noise on the fluxonium qubit which, in the past, has never systematically been done before. Charge noise enters the qubit in the form of 1/f noise resulting in interference with the Cooper pairs, two loosely bound electrons, hopping between the superconducting island and reservoir. A program was developed to simulate the qubit's state over time by solving a stochastic differential Schrodinger equation numerically. The program simulated the noise by using its 1/f power spectrum. Looking into the both its wavefunction and density matrix, its dephasing and decoherence rates were determined for different inductive, capacitive, and Josephson energies. Results will be presented.
Superconducting circuits are one of the leading candidates for scalable quantum computation, owing to their long coherence time and compatibility with fabrication techniques. Despite their experimental success, the conventional theoretical framework for superconducting circuit quantisation relies on a semiclassical procedure that requantises the phenomenological Ginzburg-Landau order parameter, introducing the postulated canonical relations and leaving the microscopic origins of circuit parameters hidden. In the present thesis, we develop a rigorous and first-principles approach for the quantisation of superconducting circuits, directly grounded in Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity, and extend this framework to investigate the dynamics of the superconducting Higgs amplitude mode. The central methodological contribution of this work is a projective approach, in which the full many-body electronic Hamiltonian of a superconducting system is projected onto a carefully constructed low-energy BCS Hilbert space, HBCS, spanned by phase parameterised BCS ground states. We systematically characterise the kinematic properties of this subspace, quantify the orthogonality and completeness of the phase basis via the BCS overlap and the projection error, and show that the effective dimensionality of the space is scaled as the square root of the number of single electronic modes. This approach does not impose a spontaneously broken symmetry so that it consistently describes quantised circuits that support superpositions of phases, and the canonical commutation relations between phase and number are derived from the underlying fermionic commutation properties, rather than imposed. This establishes the fully quantum mechanical foundation upon which the standard circuit quantisation approach implicitly rests. The projective formalism is subsequently applied to derive the effective Hamiltonian for superconducting circuit elements. For point-like elements, \eg, capacitive islands and Josephson junctions, projection of the fermionic Hamiltonian onto HBCS yields analytical expressions for the charging energy and the Josephson energy in terms of microscopic material parameters. The resulting Hamiltonian reproduces the standard Cooper-pair-box and transmon Hamiltonians, but now on an unambiguous microscopic footing. We further extend the approach to spatially distributed elements. Inductance is derived from the constitutive response to spatially varying phase torsion in a superconducting wire, yielding the lumped-element inductive energy from first principles. This analysis also identifies the emergent low-energy Hilbert space of the inductor. Combining the results, a complete microscopic derivation of the standard superconducting inductance-capacitance-junction (LCJ) circuit Hamiltonian is recovered. The final part of this thesis extends the projective methodology to the superconducting Higgs mode associated to the amplitude dynamics of the superconducting order parameter. A general BCS space parameterised by phase and gap amplitude is constructed, onto which we project the microscopic Hamiltonian. This yields a generalised eigenvalue problem governing the dynamics of the gap amplitude. The Higgs mode of a superconducting island is thereby shown to behave as a quantum harmonic oscillator. We derive the analytical expressions for the superconducting Higgs mass, spring constant, and oscillation frequency of the gap dynamics. While our results reveal a logarithmic correction to the Higgs frequency reported in previous literature, we numerically validate these results, and compute quantum anharmonic corrections to the Higgs frequency for higher excitations. This thesis proposes a novel, formal and quantitative circuit quantisation theory for superconducting circuits, based on which we explore the Higgs amplitude mode dynamics. The approach is capable of resolving the fundamental question about the compactness of superconducting phase and is extendable to cover quasiparticle contributions. This microscopic circuit theory equips us with a new tool to understand superconducting devices at a level of microscopic detail inaccessible to the standard semiclassical framework, paving the way for a principled treatment of quasiparticle losses and the exploration of exotic superconducting circuit elements.
The fluxonium qubit has arisen as one of the most promising candidate devices for implementing quantum information in superconducting devices, since it is both insensitive to charge noise (like flux qubits) and insensitive to flux noise (like charge qubits). Here, we investigate the stability of the quantum information to quasiparticle tunneling through a Josephson junction. Microscopically, this dephasing is due to the dependence of the quasiparticle transmission probability on the qubit state. We argue that on a phenomenological level the dephasing mechanism can be understood as originating from heat currents, which are flowing in the device due to possible effective temperature gradients, and their sensitivity to the qubit state. The emerging dephasing time is found to be insensitive to the number of junctions with which the superinductance of the fluxonium qubit is realized. Furthermore, we find that the dephasing time increases quadratically with the shunt-inductance of the circuit which highlights the stability of the device to this dephasing mechanism.
Superconducting quantum computing is a solid state quantum computing technology based on Josephson junction circuits. It becomes one of the most promising candidates for realizing practical quantum computer/simulator, because of its scalability, easy to coupling and control, compatibility to semiconductor technologies, etc. As the complicated electromagnetic environment in solid state metal and insulator, superconducting quantum bits (qubits) suffered from shot coherence time since its early development. In this review, we described some recently developed superconducting qubit structures, including Transmon/Xmon, Fluxonium and C-shunt flux qubit. Although these new qubit structures have very different circuit parameters and energy scales, they all find their way to effectively suppress environmental noises. As a result, their coherence time were improved significantly. Transmon, a transmission-line shunted plasma oscillation qubit, was now among the most popular structures for building a multi-qubit superconducting quantum circuit. It introduced a relatively large shunt capacitor to remarkably reduce the charge dispersion. Although the non-linearity is also decreased, by operating in a properly chosen EJ/Ec, transmon can greatly reduce the charge noise while only sacrificing a small amount of non-linearity. Xmon can be considered as a modified version of transmon. It is designed and optimized for multi-qubit operation and measurement with separate X/Y and Z control lines for each qubit, and a readout bus (a transmission line or a low-Q bandpass filter) for simultaneous readout of all the qubits. Fluxonium provide another solution for suppressing the charge noise in Cooper-pair box (CPB). It introduces a large shunt inductance to filter low-frequency offset charge in the small capacitor of the phase-slip junction (the small junction). To keep the qubit operating in the charge region, the shunt inductor should be large enough to keep the impedance larger than the superconducting impedance quantum RQ~1 kΩ. As a result, the inductance can only be provided by a large series of Josephson junctions. Fluxonium keeps the advantage of high anharmonicity of CPB. In addition, it introduces another degree of freedom: external flux Φext. Quasiparticles (electrons or holes) tunneling at the small junction add coherently to produce a ″1+cosφ″ term. As a result, when Φext= Φ0/2, dissipation caused by quasiparticle tunneling is suppressed and the energy relaxation time (T1) increases drastically. C-shunt flux qubit (CSFQ) decreases α and EJ to suppress flux noise in the qubit. While the charge noise becomes the dominant noise source, a large shunt capacitor is added to suppress the charge noise, similar to that in a transmon qubit. It is worth to notice that in CSFQ, the α decreases to below but near 1/2. As a result, the double-well potential no longer exists. The energy structure become similar to transmon, with the anharmonicity be opposite. CSFQ can get a much improved coherence time, while its anharmonicity can be larger than that of transmon. Those new superconducting qubit structures provide different solutions to improve the coherence time. Although it looks much different in circuit models and parameters, they have ideas in common, and may act as guides to other novel designs with longer coherence time. We can summarize as below. (1) The qubit circuit should be free of small superconducting islands. Charge fluctuation in small islands is a major source of decoherence. As a result, increase the area of the islands, that is, increase the capacitance becomes a straight forward way to suppress the charge noise. In Fluxonium, the small junction is connected with a large series of large junctions that there is also no small islands in the whole loop. (2) Remove superconducting loops in the qubit circuit, or minimize the loop size and loop current to suppress flux noise. (3) Bias the phase difference of the small junction to π, where dissipation caused by quasiparticle tunneling can be suppressed coherently. (4) Decrease the coupling bandwidth of qubit to the environment. In a circuit-QED readout scheme, a high-Q readout resonator that dispersively coupled to the qubit protects the qubit from exposed to the electromagnetic environment of the readout circuit. A ″Purcell filter″ can also be added to suppress such decoherence further. In conclusion, we overviewed some qubit engineering techniques or ideas to improve the coherence time, which is a very important figure for building practical quantum computer/simulator. We hope that someone can combine and optimize these ideas, while interact with developments in materials and micro-fabrication technologies, to develop novel new generation superconducting qubit structures in the near future.