Related papers: Circuit Quantisation from First Principles
We extend a recently developed projective circuit quantisation approach to incorporate superconducting Higgs modes associated to gap dynamics. This approach starts from a microscopic fermionic Hamiltonian for mesoscopic superconductors, and…
The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an…
As superconducting circuits emerge as a leading platform for scalable quantum information processing, building comprehensive bridges from the foundational principles of macroscopic quantum phenomena to the architecture of modern quantum…
The quantised Josephson junction equation that underpins the behaviour of charge qubits and other tunnel devices is usually derived through cannonical quantisation of the classical macroscopic Josephson relations. However, this approach may…
Building on the established methods for superconducting circuit quantization, we present a new theoretical framework for approximate numerical simulation of Josephson quantum circuits. Simulations based on this framework provide access to a…
Recent advances in quantum information processing with superconducting qubits have fueled a growing demand for scaling and miniaturizing circuit layouts. Despite significant progress, predicting the Hamiltonian of complex circuits remains a…
The quantization of superconducting transmission-line resonators is usually introduced phenomenologically by modeling the resonator as an effective LC circuit and imposing canonical commutation relations on macroscopic variables such as…
We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. Starting from the microscopic description of the latter in terms of two tunneling BCS models in…
Superconducting circuits have become a leading quantum technology for testing fundamentals of quantum mechanics and for the implementation of advanced quantum information protocols. In this chapter, we revise the basic concepts of circuit…
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…
The development of new superconducting circuits and the improvement of existing ones rely on the accurate modeling of spectral properties which are key to achieving the needed advances in qubit performance. Systematic circuit analysis at…
When first proposed in 1957, the BCS theory for superconductivity, which explained the quasi-totality of its thermodynamic and transport properties, was greeted with great circumspection, before it became the play ground of particle…
We use two truly canonical approaches to describe superconductivity in ultrasmall metallic grains: (a) a variational fixed-N projected BCS-like theory and (b) an exact solution of the model Hamiltonian developed by Richardson in context…
We derive a mesoscopic theory of the Josephson junction from non-relativistic scalar electrodynamics. Our theory reproduces the Josephson relations with the canonical current phase relation acquiring a weak second harmonic term, and it…
Recently, a new theory of superconductivity has been put forward that attributes the origin of superconductivity to the appearance of a non-trivial Berry connection from many-electron wave functions. This theory reproduces the major results…
Quantum simulators are attractive as a means to study many-body quantum systems that are not amenable to classical numerical treatment. A versatile framework for quantum simulation is offered by superconducting circuits. In this…
We apply polymer quantization, a quantization technique sometimes used in high energy physics, to several superconducting circuits including: transmons, transmission line resonators, and LC circuits. In the case of transmon qubits and…
In the design and investigation of superconducting qubits and related devices, a lumped element circuit model is the standard theoretical approach. However, many important physical questions lie beyond its scope, e.g. the behavior of…