In recent years there was a huge experimental progress towards the development of prototypes of algorithmic quantum processors. These quantum machines are not free from imperfectionsand various technological and scientific problems remain to be solved in the following years. Until that moment computational schemes different from the digital approach can be used in order to perform calculations using state-of-the-art quantum hardware. A prospective idea is to combine positive aspects of both digital and analog computation. Particularly, it is possible to use qubit-qubit interaction embedded in architecture in order to replace those parts of algorithms which are responsible for the quantum entanglement. In this paper, we provide an example of such an approach based on unwanted couplings between fixed-frequency superconducting qubits (crosstalks). These couplings are normally considered as a source of errors in standard digital quantum computation, but we argue that they can be utilized instead of two-qubit gates in some quantum algorithms thus avoiding an accumulation of errors associated with these gates. We illustrate our ideas with quantum processors of IBM Quantum Experience, which are used by us for simulating the dynamics of spin clusters through the Trotterized evolution. We demonstrate a significant improvement in the quality of results compared to the conventional digital approach with the same processor. We also show that crosstalks result in a highly non-markovian dynamics of qubits. This fact must be taken into account while developing error-correction strategies with qubits of this type.
We consider dynamics of a disordered ensemble of qubits interacting with single mode photon field, which is described by exactly solvable inhomogeneous Dicke model. In particular, weconcentrate on the crossover from few-qubit systems to the system of many qubits and analyze how collective behavior of coupled qubits-cavity system emerges despite of the broadening. We show that quantum interference effects survive in the mesoscopic regime — dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxation of these states is slowed down due to the formation of collective dark states weakly coupled to light. Dark states also significantly influence dynamics of excitations of photon subsystem by absorbing them into the qubit subsystem and releasing quasiperiodically in time. We argue that predicted phenomena can be useful in quantum technologies based on superconducting qubits. For instance, they provide tools to deeply probe both collective and quantum properties of such artificial macroscopic systems.
We consider a superconducting qubit coupled to the nonstationary transmission line cavity with modulated frequency taking into account energy dissipation. Previously, it was demonstratedthat in the case of a single nonadiabatical modulation of a cavity frequency there are two channels of a two-level system excitation which are due to the absorption of Casimir photons and due to the counter-rotating wave processes responsible for the dynamical Lamb effect. We show that the periodical modulation of the resonator frequency can increase dramatically the excitation probability. Remarkably, counter-rotating wave processes, which are generally believed to be negligible, under such a modulation start to play an important role even in the resonant regime. Our predictions can be used to control qubit-resonator quantum states as well as to study experimentally different channels of a parametric qubit excitation.
Superconducting circuits provide a new platform to study nonstationary cavity QED phenomena. An example of such a phenomenon is a dynamical Lamb effect which is a parametric excitationof an atom due to the nonadiabatic modulation of its Lamb shift. This effect has been initially introduced for a natural atom in a varying cavity, while we suggested its realization in a superconducting qubit-cavity system with dynamically tunable coupling. In the present paper, we study the interplay between the dynamical Lamb effect and the energy dissipation, which is unavoidable in realistic systems. We find that despite of naive expectations this interplay can lead to unexpected dynamical regimes. One of the most striking results is that photon generation from vacuum can be strongly enhanced due to the qubit relaxation, which opens a new channel for such a process. We also show that dissipation in the cavity can increase the qubit excited state population. Our results can be used for the experimental observation and investigation of the dynamical Lamb effect and accompanying quantum effects.
We suggest that a transmission line cavity coupled with a superconducting qubit can be used for the experimental investigation of the dynamical Lamb effect, which can be viewed as anatom excitation due to the nonadiabatic modulation of atomic level Lamb shift. The qubit (artificial macroscopic atom) and resonator can be integrated in a tunable way. By varying nonadiabatically the coupling strength, it is possible to parametrically excite the qubit. This approach allows one to get rid of Casimir photons and thus to isolate the mechanism of the qubit excitation due to the dynamical Lamb effect from another mechanism due to the Casimir photons absorbtion. We evaluate a qubit excitation probability within the Jaynes-Cummings model using the perturbation theory and also numerically. We argue that the most efficient method to increase an excitation probability is a periodic driving of a qubit-resonator coupling constant. We also study a statistics of photon states and show that a significant squeezing can be obtained by using a suggested approach.