arXiv subjects

N. J. S. Loft

Publications and source records attributed to N. J. S. Loft.

9 recordsLinked to original sources

arXiv2023

The superconducting circuit companion -- an introduction with worked examples

This tutorial aims at giving an introductory treatment of the circuit analysis of superconducting qubits, i.e., two-level systems in superconducting circuits. It also touches upon couplings between such qubits and how microwave driving and these couplings can be used for single- and two-qubit gates, as well as how to include noise when calculating the dynamics of the system. We also discuss higher-dimensional superconducting qudits. The tutorial is intended for new researchers with limited or no experience with the field but should be accessible to anyone with a bachelor's degree in physics. The tutorial introduces the basic methods used in quantum circuit analysis, starting from a circuit diagram and ending with a quantized Hamiltonian, that may be truncated to the lowest levels. We provide examples of all the basic techniques throughout the discussion, while in the last part of the tutorial we discuss several of the most commonly used circuits for quantum-information applications. This includes both worked examples of single qubits and examples of how to analyze the coupling methods that allow multiqubit operations. In several detailed appendices, we provide the interested reader with an introduction to more advanced techniques for handling larger circuit designs.

quant-ph↗

arXiv2022

Application of the Diamond Gate in Quantum Fourier Transformations and Quantum Machine Learning

As we are approaching actual application of quantum technology, it is essential to exploit the current quantum resources in the best possible way. With this in mind, it might not be beneficial to use the usual standard gate sets, inspired from classical logic gates, when compiling quantum algorithms when other less standardized gates currently perform better. We, therefore, consider a promising native gate, which occurs naturally in superconducting circuits, known as the diamond gate. We show how the diamond gate can be decomposed into standard gates and, using single-qubit gates, can work as a controlled-not-swap (CNS) gate. We then show how this CNS gate can create a controlled phase gate. Controlled phase gates are the backbone of the quantum Fourier transform algorithm, and we, therefore, show how to use the diamond gate to perform this algorithm. We also show how to use the diamond gate in quantum machine learning; namely, we use it to approximate non-linear functions and classify two-dimensional data.

quant-ph↗

arXiv2020

Reducing the amount of single-qubit rotations in VQE and related algorithms

With the advent of hybrid quantum classical algorithms using parameterized quantum circuits the question of how to optimize these algorithms and circuits emerges. In this paper we show that the number of single-qubit rotations in parameterized quantum circuits can be decreased without compromising the relative expressibility or entangling capability of the circuit. We also show that the performance of a variational quantum eigensolver is unaffected by a similar decrease in single-qubit rotations. We compare relative expressibility and entangling capability across different number of qubits in parameterized quantum circuits. High-dimensional qudits as a platform for hybrid quantum classical algorithms is a rarity in the literature. Therefore we consider quantum frequency comb photonics as a platform for such algorithms and show that we can obtain an relative expressibility and entangling capability comparable to the best regular parameterized quantum circuits.

quant-ph↗

arXiv2019

Realization of efficient quantum gates with a superconducting qubit-qutrit circuit

Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possible, to reduce the amount of required control and operation time and thus improve the quantum state coherence. Here we propose a superconducting circuit for implementing a tunable system consisting of a qutrit coupled to two qubits. This system can efficiently accomplish various quantum information tasks, including generation of entanglement of the two qubits and conditional three-qubit quantum gates, such as the Toffoli and Fredkin gates. Furthermore, the system realizes a conditional geometric gate which may be used for holonomic (non-adiabatic) quantum computing. The efficiency, robustness and universality of the presented circuit makes it a promising candidate to serve as a building block for larger networks capable of performing involved quantum computational tasks.

quant-ph↗

arXiv2018

Quantum spin transistors in superconducting circuits

Transistors play a vital role in classical computers, and their quantum mechanical counterparts could potentially be as important in quantum computers. Where a classical transistor is operated as a switch that either blocks or allows an electric current, the quantum transistor should operate on quantum information. In terms of a spin model the in-going quantum information is an arbitrary qubit state (spin-1/2 state). In this paper, we derive a model of four qubits with Heisenberg interactions that works as a quantum spin transistor, i.e. a system with perfect state transfer or perfect blockade depending on the state of two gate qubits. When the system is initialized the dynamics complete the gate operation, hence our protocol requires minimal external control. We propose a concrete implementation of the model using state-of-the-art superconducting circuits. Finally, we demonstrate that our proposal operates with high-fidelity under realistic decoherence.

quant-ph↗

arXiv2016

CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension

We consider a one-dimensional system of particles with strong zero-range interactions. This system can be mapped onto a spin chain of the Heisenberg type with exchange coefficients that depend on the external trap. In this paper, we present an algorithm that can be used to compute these exchange coefficients. We introduce an open source code CONAN (Coefficients of One-dimensional N-Atom Networks) which is based on this algorithm. CONAN works with arbitrary external potentials and we have tested its reliability for system sizes up to around 35 particles. As illustrative examples, we consider a harmonic trap and a box trap with a superimposed asymmetric tilted potential. For these examples, the computation time typically scales with the number of particles as $O(N^{3.5 \pm 0.4})$. Computation times are around 10 seconds for $N=10$ particles and less than 10 minutes for $N=20$ particles.

cond-mat.quant-gas↗

arXiv2016

Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity

We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles for general interaction strengths and up to 30 particles in the strongly interacting case. We also calculate the contact coefficient in the strongly interacting regime. The different theoretical predictions are compared to recent experimental results with few-atom systems. Firstly, we find that the local density approximation suffers from great ambiguity in the few-atom regime, yet it works surprisingly well for some models. Secondly, we find that the strong interaction theories quickly break down when the number of particles increase or the interaction strength decreases.

cond-mat.quant-gas↗

arXiv2016

Tunable self-assembled spin chains of strongly interacting cold atoms

We have developed an efficient computational method to treat long, one-dimensional systems of strongly-interacting atoms forming self-assembled spin chains. Such systems can be used to realize many spin chain model Hamiltonians tunable by the external confining potential. As a concrete demonstration, we consider quantum state transfer in a Heisenberg spin chain and we show how to determine the confining potential in order to obtain nearly-perfect state transfer.

quant-ph↗

arXiv2015

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in the strongly and weakly interacting limits can be accurately described using wave function factorized in hyperspherical coordinates. Inspired by this result we propose an interpolation ansatz for the wave function for arbitrary repulsive zero-range interactions. By comparison to numerical calculations, we show that this interpolation scheme yields an extremely good approximation to the numerically exact solution both in terms of the energies and also in the spin-resolved densities. As an outlook, we discuss the case of mass imbalanced systems in the strongly interacting limit. Here we find spectra that demonstrate that the triply degenerate spectrum at infinite coupling strength of the equal mass case is in some sense a singular case as this degeneracy will be broken down to a doubly degenerate or non-degenerate ground state by any small mass imbalance.

cond-mat.quant-gas↗