arXiv subjects

Samuel Feldman

Publications and source records attributed to Samuel Feldman.

3 recordsLinked to original sources

arXiv2025

Classical analog circuit emulation of quantum Grover search algorithm

We construct a completely analog framework that emulates universal quantum gates and quantum algorithms. It is based on electronic circuits made of operational amplifiers, resistors and capacitors. In these circuits, input and output lines represent the computational basis states (CBSs) and thus $2^n$ lines are required to represent $n$ qubits. An operation of the circuits is based on classical evolution and interference of complex amplitudes associated with each CBS. The framework can emulate entangled states and is free from decoherence, measurements are classical and do not collapse states. Similar to physical quantum computers, emulated quantum algorithms can be constructed as a sequence of the gates belonging to a universal set (phase shift, Hadamard, controlled-NOT), as a unitary matrix and as combinations of the two. Circuits representing the universal gates have been made and tested. We also have made a matrix-based emulator of a 3-qubit Grover search algorithm. We tested it by searching for one and two particular states with one and two iterations and found that its outputs accurately match predicted values. We anticipate that the emulators can work as sub-components of physical quantum computers. On their own, the emulators can be used for operations that require a few qubits or operations that can be split into independent (and perhaps weakly entangled) blocks of qubits.

quant-ph↗

arXiv2024

Quantum phase transition in small-size 1d and 2d Josephson junction arrays: analysis of the experiments within the interacting plasmons picture

Theoretically, Josephson junction (JJ) arrays can exhibit either a superconducting or insulating state, separated by a quantum phase transition (QPT). In this work, we analyzed published data on QPTs in three one-dimensional arrays and two two-dimensional arrays using a recently developed phenomenological model of QPTs. The model is based on the insight that the scaled experimental data depend in a universal way on two characteristic length scales of the system: the microscopic length scale $L_0$ from which the renormalization group flow starts, and the dephasing length, $L_{\varphi}(T)$ as given by the distance travelled by system-specific elementary excitations over the Planckian time. Our analysis reveals that the data for all five arrays (both 1D and 2D) can be quantitatively and self-consistently explained within the framework of interacting superconducting plasmons. In this picture, $L_{\varphi}=v_p\hbar/k_B T$, and $L_0 \approx \Lambda$, where $v_p$ is the speed of the plasmons and $\Lambda$ is the Coulomb screening length of the Cooper pairs. We also observe that, in 1D arrays, the transition is significantly shifted towards the insulating side compared to the predictions of the sine-Gordon model. Finally, we discuss similarities and differences with recent microwave studies of extremely long JJ chains, as well as with the pair-breaking QPT observed in superconducting nanowires and films.

cond-mat.supr-con↗

arXiv2023

Microscopic scales and mechanism of quantum phase transitions in two-dimensional superconducting systems

The superconducting ground state in many two-dimensional materials can be created or destroyed through quantum phase transitions (QPTs) controlled by non-thermal parameters such as carrier density or magnetic field. While various mechanisms for these QPTs have been proposed, it remains unclear which, if any, are applicable to a specific two-dimensional superconducting system. Here, we find that a pair-breaking mechanism which suppresses the Cooper pair density gives a unifying description of magnetic-field-driven QPTs in amorphous MoGe, Pb and TaN films, and the high-temperature superconductor La$_{1.92}$Sr$_{0.08}$CuO$_{4}$. This transition occurs within the superconducting subsystem and is masked by the dominant non-critical contribution of normal electrons. The discovery was enabled by the development of a QPT model that goes beyond the conventional determination of the critical exponents and incorporates into the analysis a microscopic length scale characterizing the transitions. We found that in the materials studied, and MoGe nanowires, this scale corresponds to the size of a Cooper pair. The model has also been successfully applied to QPTs in Josephson junction arrays and various non-superconducting materials. The observation that microscopic scales are encoded in the scaled experimental data of QPTs likely extends beyond equilibrium condensed matter physics and may reveal underlying principles of critical phenomena in a wide variety of systems.

cond-mat.supr-con↗