This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.
This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.
There are a number of systems that are currently being considered as candidates for the construction of qubits, quantum logic gates and quantum computers. Some of the systems, notably atoms in magnetic traps and nuclear magnetic resonance (NMR) systems, have had some success in performing the elementary operations that would be required in large-scale quantum computer. However, these systems are not necessarily seen as viable technologies for quantum computing in the longer term. The recent demonstration of macroscopic coherence in a superconducting ring (consisting of a thick superconducting ring containing one or more Josephson weak link devices) has added significant weight to the idea of using superconducting persistent current devices (SQUIDs) in quantum logic systems. In this paper, we consider one aspect of the quantum mechanical SQUID, the nonlinear effect of SQUID on the classical control parameters, and we discuss how it may influence the construction and design of quantum logic gates based on SQUID devices. In particular, we look at problems associated with fixing the classical magnetic flux bias for a quantum mechanical SQUID at, or near, a quantum mechanical transition or resonance.
Superconducting qubits have emerged as a leading platform for realizing quantum computers. Accurate modeling of these devices is essential for predicting performance, improving design, and optimizing control. Many modeling approaches currently rely on lumped circuit approximations or other simplified treatments that can be limited in resolving the interplay between the qubit dynamics and the electromagnetic circuitry, leading to significant experimental deviations from numerical predictions at times. To address many of these limitations, methods that self-consistently solve the Schrödinger equation for qubit dynamics with the classical Maxwell's equations have been developed and shown to accurately predict a wide range of effects related to superconducting qubit control and readout. Despite these successes, these methods have not been able to consider multi-qubit effects that give rise to qubit-qubit entanglement. Here, we address this by rigorously deriving how multi-qubit coupling effects between transmon qubits can be embedded into Maxwell-Schrödinger methods. To support this, we build on earlier first-principles derivations of Maxwell-Schrödinger methods for the specific case of two transmon qubits coupled together through a common electromagnetic system in the dispersive regime. To aid in validating aspects of the Maxwell-Schrödinger framework, we also provide a new interpretation of Maxwell-Schrödinger methods as an efficient simulation strategy to capture the class of non-Markovian open quantum system dynamics. Our results demonstrate that these effects can give rise to strong classical crosstalk that can significantly alter multi-qubit dynamics, which we demonstrate for the cross-resonance gate. These classical crosstalk effects have been noted in cross-resonance experiments, but previous quantum theory and device analysis could not explain their origin.
Mesoscopic electric circuits can exhibit a large number of effects relevant to quantum mechanics, quantum electrodynamics and quantum statistics. The topic presented here can be identified as an analog of conventional cavity quantum electrodynamics, where the quantum objects are multilevel atoms and quantized optical fields (photons), namely, a theoretical subject called “cavity-circuit quantum electrodynamics”, where the atoms are replaced with quantum mesoscopic circuits, will be developed. We will study the quantum characteristics of the interaction between the quantum mesoscopic circuits and the quantized electromagnetic field at microwave frequencies. These issues include quantum entangled eigenstates of two coupled mesoscopic circuits, time evolution of the circuit energy quanta (governed by the time-dependent Schrödinger equation) and entanglement transfer between external photons and mesoscopic circuit energy quanta. Since there is inevitable electromagnetic interaction such as mutual capacitance and inductance coupling between two neighboring circuits, the quantum effects resulting from the aforementioned quantized circuit coupling would unavoidably affect the relevant processes in quantum computing devices and hence they deserve consideration in some issues of quantum information.
A persistent current qubit has two quantum states with opposite currents flowing in a superconducting loop. Their magnetic field couple to nuclear spins. The qubit state is not only perturbed by the spins but it also gets entangled with the spins' state on a very short timescale. However, when the same spins are exposed to a strong but less than critical external magnetic field, then the qubit field is just a small perturbation on top of the external field and the entanglement with each spin is negligible. For a qubit which is more microscopic than certain threshold this partial entanglement results in negligible partial decoherence.
We present a fully quantum-mechanical investigation of synchronisation in two inductively coupled superconducting oscillators modelled as nonlinear rf-SQUID circuits. Unlike semiclassical or hybrid treatments, both SQUID degrees of freedom are evolved as a joint two-body wavefunction by solving the time-dependent Schrödinger equation (TDSE) using a split-operator spectral method. This enables direct access to coherent flux dynamics, entanglement generation, and quantum phase-space structure without introducing dissipation, measurement back-action, or classical approximations. By varying the mutual inductive coupling strength, we identify a transition from effectively desynchronised tunnelling to quasi-periodic phase locking and, at stronger coupling, chaos-assisted synchronised tunnelling. Synchronisation is quantified using three complementary diagnostics: expectation-value locking of the flux variables ϕi(t), von Neumann entanglement entropy S(t), and Husimi phase-space distributions Q(ϕ,p). The results show that coherent quantum synchronisation can emerge solely from Hamiltonian evolution, with entanglement acting as a dynamical correlation channel rather than simply reaching a maximal value. At moderate coupling, bounded entropy oscillations accompany stable phase locking, while stronger coupling produces broadened Husimi structures and irregular but correlated flux dynamics characteristic of chaos-assisted coherence. These findings establish coupled SQUID oscillators as a physically relevant platform for studying Hamiltonian quantum synchronisation, entanglement-mediated phase control, and nonlinear quantum transport. The work also suggests possible routes towards synchronisation-based control in superconducting qubit networks, quantum metrology, and coherent neuromorphic superconducting architectures where dissipation is deliberately minimised.
We study the dynamics of a two-qubit system coupled through time dependent anisotropic XYZ Heisenberg interaction in presence of a time varying non-uniform external magnetic field. Exact results are presented for the time evolution of the system under certain integrability conditions. Furthermore, the corresponding entanglement of the system is studied for different values of the involved parameters. We found that the time evolution and different properties of entanglement such as amplitude, frequency and profile can be finely tuned by the interplay of the characteristics of the time-dependent magnetic field and exchange coupling. Also we show how the discrete symmetries of the system Hamiltonian, which splits its Hilbert space into two distinct subspaces, can be utilized to deduce the dynamics in one of its two distinct subspaces from the other one. Moreover, approximate results for the time evolution are provided utilizing the rotating wave as well as the perturbation approximations for the special case of either static magnetic field or exchange coupling. We compare the range of validity of the two approximation methods and their effectiveness in treating the considered system and determine their critical parameters.