39 research outputs found
Analog simulator of integro-differential equations with classical memristors
An analog computer makes use of continuously changeable quantities of a
system, such as its electrical, mechanical, or hydraulic properties, to solve a
given problem. While these devices are usually computationally more powerful
than their digital counterparts, they suffer from analog noise which does not
allow for error control. We will focus on analog computers based on active
electrical networks comprised of resistors, capacitors, and operational
amplifiers which are capable of simulating any linear ordinary differential
equation. However, the class of nonlinear dynamics they can solve is limited.
In this work, by adding memristors to the electrical network, we show that the
analog computer can simulate a large variety of linear and nonlinear
integro-differential equations by carefully choosing the conductance and the
dynamics of the memristor state variable. To the best of our knowledge, this is
the first time that circuits based on memristors are proposed for simulations.
We study the performance of these analog computers by simulating
integro-differential models related to fluid dynamics, nonlinear Volterra
equations for population growth, and quantum models describing non-Markovian
memory effects, among others. Finally, we perform stability tests by
considering imperfect analog components, obtaining robust solutions with up to
relative error for relevant timescales
Embedded Quantum Correlations in thermalized quantum Rabi systems
We study the quantum correlations embedded in open quantum Rabi systems.
Specifically, we study how the quantum correlation depends on the coupling
strength, number of qubits, and reservoir temperatures. We numerically
calculate the quantum correlations of up to three qubits interacting with a
single field mode. We find that the embedded quantum correlations exhibit a
maximum for a given coupling strength, which depends inversely on the number of
subsystems and the reservoir temperature. We explore how this feature affects
the performance of a many-qubit Otto heat engine, finding numerical evidence of
a direct correspondence between the minimum of the extractable work and the
maximum of the embedded quantum correlations in the qubit-cavity bi-partition.
Furthermore, as we increase the number of qubits, the maximum extractable work
is reached at smaller values of the coupling strength. This work could help
design more sophisticated quantum heat engines that rely on many-body systems
with embedded correlations as working substances.Comment: 12 pages and 12 figure
Tripartite entanglement in quantum memristors
We study the entanglement and memristive properties of three coupled quantum
memristors. We consider quantum memristors based on superconducting asymmetric
SQUID architectures which are coupled via inductors. The three quantum
memristors are arranged in two different geometries: linear and triangular
coupling configurations. We obtain a variety of correlation measures, including
bipartite entanglement and tripartite negativity. We find that, for identical
quantum memristors, entanglement and memristivity follow the same behavior for
the triangular case and the opposite one in the linear case. Finally, we study
the multipartite correlations with the tripartite negativity and entanglement
monogamy relations, showing that our system has genuine tripartite
entanglement. Our results show that quantum correlations in multipartite
memristive systems have a non-trivial role and can be used to design quantum
memristor arrays for quantum neural networks and neuromorphic quantum computing
architectures.Comment: 9 pages, 6 figure
Microwave Quantum Memristors
We propose a design of a superconducting quantum memristive device in the
microwave regime, that is, a microwave quantum memristor. It comprises two
linked resonators, where the primary one is coupled to a superconducting
quantum interference device (SQUID), allowing the adjustment of the resonator
properties with an external magnetic flux. The auxiliary resonator is operated
through weak measurements, providing feedback to the primary resonator via the
SQUID and establishing stable memristive behavior via the external magnetic
flux. The device operates with a classical input signal in one cavity while
reading the response in the other, serving as a fundamental building block for
arrays of microwave quantum memristors. In this sense, we observe that a
bipartite setup can retain its memristive behavior while gaining entanglement
and quantum correlations. Our findings open the door to the experimental
implementation of memristive superconducting quantum devices and arrays of
microwave quantum memristors on the path to neuromorphic quantum computing.Comment: 9+6 pages, 10 figure
One-Photon Solutions to the Multiqubit Multimode Quantum Rabi Model for Fast W -State Generation
General solutions to the quantum Rabi model involve subspaces with an unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for an arbitrary number of qubits and photon modes. Such solutions exist for arbitrary single qubit-photon coupling strength with constant eigenenergy, while still being qubit-photon entangled states. Taking advantage of their peculiarities and the reach of the ultrastrong coupling regime, we propose an adiabatic scheme for the fast and deterministic generation of a two-qubit Bell state and arbitrary single-photon multimode W states with nonadiabatic error less than 1%. Finally, we propose a superconducting circuit design to catch and release the W states, and shows the experimental feasibility of the multimode multiqubit quantum Rabi model.PGC2018-095113-B-I00, PID2019-104002GB-C21 and PID2019-104002GB-C22 (MCIU/AEI/FEDER, UE
One-photon Solutions to Multiqubit Multimode quantum Rabi model
General solutions to the quantum Rabi model involve subspaces with unbounded
number of photons. However, for the multiqubit multimode case, we find special
solutions with at most one photon for arbitrary number of qubits and photon
modes. Unlike the Juddian solution, ours exists for arbitrary single
qubit-photon coupling strength with constant eigenenergy. This corresponds to a
horizontal line in the spectrum, while still being a qubit-photon entangled
state. As a possible application, we propose an adiabatic scheme for the fast
generation of arbitrary single-photon multimode W states with nonadiabatic
error less than 1%. Finally, we propose a superconducting circuit design,
showing the experimental feasibility of the multimode multiqubit Rabi model.Comment: 6 pages, 5 figures plus Supplemental Material