The analysis conducted by Rymarz and DiVincenzo (Phys. Rev. X 13, 021017 (2023)) regarding quantization of superconducting circuits is insufficient to justify their general conclusions,most importantly the need to discard Kirchhoff’s laws to effect variable reductions. Amongst a variety of reasons, one source of several disagreements with experimental and theoretical results is the long-standing dispute between extended vs compact variables in the presence of Josephson junctions.
We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of a redundant configuration-space description. The algorithm is basedon an original, explicit, and constructive implementation of the symplectic diagonalization of positive semidefinite Hamiltonian matrices, a particular instance of Williamson’s theorem. With it, we derive canonically quantized discrete-variable descriptions of passive causal systems. We exemplify the algorithm with representative {\it singular} electrical networks, a nonreciprocal extension for the black-box quantization method, as well as an archetypal Landau quantization problem.
We present an exact full symmetry analysis of the 0-π superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofolddegeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus providing us with a strong candidate for robust qubit engineering.
We develop a systematic procedure to quantize canonically Hamiltonians of light-matter models of transmission lines point-wise coupled through linear lossless ideal circulators in acircuit QED set-up. This is achieved through a description in terms of both flux and charge fields. This apparent redundancy allows the derivation of the relevant Hamiltonian. By making use of the electromagnetic duality symmetry proper to the case at hand we provide unambiguous identification of the physical degrees of freedom, separating out the nondynamical parts. Furthermore, this doubled description is amenable to a treatment of other pointwise contacts that is regular and presents no spurious divergences, as we show explicitly in the example of a circulator connected to a Josephson junction through a transmission line. This theory enhances the quantum engineering toolbox to design complex networks with nonreciprocal elements.
Non-reciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that it couples, and they can be used to create chiral informationprocessing networks. We study how to systematically include ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general non-reciprocal networks on the quantum regime. We apply it to useful and pedagogical examples of circuits containing Josephson junctions and non-reciprocal ideal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on non-reciprocal devices characterized by impedance and/or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and non-reciprocal devices.
Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit modelsthat contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analog quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation withneuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instanceof a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms.
Quantum field theories (QFTs) are among the deepest descriptions of nature. In this sense, different computing approaches have been developed, as Feynman diagrams or lattice gauge theories.In general, the numerical simulations of QFTs are computationally hard, with the processing time growing exponentially with the system size. Nevertheless, a quantum simulator could provide an efficient way to emulate these theories in polynomial time. Here, we propose the quantum simulation of fermionic field modes interacting via a continuum of bosonic modes with superconducting circuits, which are among the most advanced quantum technologies in terms of quantum control and scalability. An important feature of superconducting devices is that, unlike other quantum platforms, they offer naturally a strong coupling of qubits to a continuum of bosonic modes. Therefore, this system is a specially suited platform to realize quantum simulations of scattering processes involving interacting fermionic and bosonic quantum field theories, where access to the continuum of modes is required.