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H. W. L. Naus

Publications and source records attributed to H. W. L. Naus.

17 recordsLinked to original sources
arXiv2020

Bell inequality violation on small NISQ computers

Quantum computational experiments exploiting Noisy Intermediate-Scale Quantum (NISQ) devices to demonstrate violation of a Bell inequality are proposed. They consist of running specified quantum algorithms on few-qubit computers. If such a device assures entanglement and performs single-shot measurements, the detection loophole is avoided. Four concise quantum circuits determining the expectation values of the relevant observables are used for a two-qubit system. It is possible to add an ancilla qubit to these circuits and eventually only measure the ancilla to obtain the relevant information. For a four-qubit NISQ computer, two algorithms yielding the same averages, however also guaranteeing a random choice of the observable, are developed. A freedom-of-choice loophole is therefore avoided. Including an additional ancilla reduces the number of measurements by one since in this case only the ancillas need to be measured. Note that these methods, using the NISQ device, are intrinsically quantum mechanical. Locality loopholes cannot be excluded on present NISQ systems. Results of simulations on the QX simulator of Quantum Inspire are presented. The Bell inequality is indeed found to be violated, even if some additional noise is included by means of the depolarizing channel error model. The algorithms have been implemented on the IBM Q Experience as well. The results of these quantum computations support a violation of the Bell inequality by various standard deviations.

quant-ph↗
arXiv2019

NISQ computing for decision making under uncertainty

Noisy Intermediate-Scale Quantum computers are expected to be available this year. It is proposed to exploit such a device for decision making under uncertainty. The probabilistic character of quantum mechanics reflects this uncertainty. Concomitantly, the noise may add to it. The approach is standard in the sense that Bayes decision rule is used to decide on the basis of maximum expected reward. The novelty is to model the various action profiles and the development of `nature' as unitary transformations on a set of qubits. Measurement eventually yields samples of classical binary random variables in which the reward function has to be expressed. In order to achieve sufficiently low variances for reliable decision making more runs of such a quantum algorithm are necessary. Some simple examples have been worked out to elucidate the idea. Here the calculations are still analytically feasible. Presently lacking an operating quantum device, the QX simulator of Quantum Inspire has been used to generate the necessary samples for comparison and demonstration. First obtained results are promising and point at a possible useful application for noisy intermediate-scale quantum computers.

quant-ph↗
arXiv2019

Consequences of unitary evolution of coupled qubit-resonator systems for stabilizing circuits in surface codes

Surface codes based on stabilizer circuits may pave the way for large scale fault-tolerant quantum computation. The surface code uses only single- and two-qubit gates and the error threshold falls close to 1% for a large range of errors. Among the most promising candidates to physically implement such circuits and codes are superconducting qubits coupled by resonators. We investigate a X and Z stabilizing circuit realized by two data qubits, two ancillas and four resonators. The aim is to assess the consequences of unitary evolution of the interacting system, in particular for given stable initial states, on fidelities and error syndrome probabilities. We model the system with a Jaynes-Tavis-Cummings Hamiltonian and construct the low-excitation level evolution operators. The analysis is limited to two stable input states. We assume an ideal system with perfect gates, perfect measurements and no decoherence or leakage. Our analysis shows that the capture probabilities after the execution of a single stabilizer round are not equal to 100%, but vary between 99.2% and 99.99%. This is caused solely by the unitary evolution of the interacting system. Two consecutive rounds of stabilizer measurements result in capture probability values that depend heavily on the duration of the evolution, but vary between 0% and 99%. Also due to the unitary evolution, the final state of the data qubits leaves the the four-dimensional subspace, which results in a state fidelity oscillating between 0 and 1. Even if an error on the qubits is captured, the correcting operation on the qubit will not bring the qubit to the original state. The errors induced by the Hamiltonian evolution of the system cannot be interpreted nor classified as commonly appearing errors. Additional or augmented quantum error correction may be required to compensate these effects of resonator-qubit interaction.

quant-ph↗
arXiv2019

Four electron spin qubits with exchange interaction

Four electron spin qubits in quantum dots are studied by means of an exchange interaction Hamiltonian. The time-independent Schrödinger equation is exactly analytically solved for the symmetric case, that is equal qubit frequencies and equal couplings. The spin system can be used as two data-qubits and two ancillas, thereby realizing a $X$ and $Z$ stabilizing circuit exploited in error correction and surface codes. The unitary evolution of corresponding stable states is calculated and consequences for error syndromes and fidelities are assessed. It is also shown that applying the evolution operator for a prescribed duration and subsequent measurement of the ancillas lead to a `verifiable' two-qubit phase gate.

quant-ph↗
arXiv2018

Semi-analytical RWA formalism to solve Schrödinger equations for multi-qubit systems with resonator couplings

In this study, we develop a semi-analytical framework to solve generalized Jaynes-Tavis-Cummings Hamiltonians describing multi-qudit systems coupled via EM resonators. Besides the multi-level generalization we allow for an arbitrary number of resonators and/or modes, with nonidentical couplings to the qudits. Our method is based on generic excitation-number operators which commute with the respective Hamiltonians in the rotating wave approximation (RWA). The validity of the RWA is assessed explicitly. The formalism enables the study of eigenstates, eigenenergies and corresponding time evolutions of such coupled multi-qudit systems. The technique can be applied in cavity quantum electrodynamics and circuit quantum electrodynamics. It is also applicable to atomic physics, describing the coupling of a single-mode photon to an atom. As an example, we solve the Schrödinger equation for a two-qubit-one-resonator system, in principle to arbitrary high excitations. We also solve the Tavis-Cummings Hamiltonian in the one-excitation subspace for an arbitrary number of identical qubits resonantly coupled to one resonator. As a final example, we calculate of the low-excitation spectrum of a coupled two-transmon system.

quant-ph↗
arXiv1999

Covariance of Light-Front Models: Pair Current

We compute the "+" component of the electromagnetic current of a composite spin-one two-fermion system for vanishing momentum transfer component $q^+=q^0+q^3$. In particular, we extract the nonvanishing pair production amplitude on the light-front. It is a consequence of the longitudinal zero momentum mode, contributing to the light-front current in the Breit-frame. The covariance of the current is violated, if such pair terms are not included in its matrix elements. We illustrate our discussion with some numerical examples.

hep-ph↗
arXiv1998

Non-Perturbative Hamiltonian Approaches To Strong Interaction Physics

The theory of the strong interactions, Quantum Chromodynamics (QCD), has been addressed by a variety of non-perturbative techniques over the decades since its introduction. We have investigated Hamiltonian formulations with different quantization methods and approximation schemes. In one method, we utilize light-front coordinates to investigate the role of bosonic zero modes in leading to confinement. In another method we are able to obtain spectra for the mesons and baryons using constituent quark masses but no phenomenological confinement. We survey our principal accomplishments to date and indicate our future directions.

hep-th↗
arXiv1997

Ward-Takahashi Identidy on the Ligth-Front

The Ward-Takahashi identity, reflecting local gauge invariance, is perturbatively verified for a boson model in light front field theory. A careful integration over the light front energy, corresponding to exactly taking into account pair terms, which are the contributions of the zero longitudinal momentum mode, is crucial to obtain this result. Furthermore, the one-loop boson form factors are calculated for arbitrary off-shell momenta.

hep-ph↗
arXiv1997

Pion Eletromagnetic Current in the Ligth-Cone Formalism

The electromagnetic form factor of the pion is calculated in a pseudoscalar field theoretical model which constituent quarks. We extract the form factor using the "+" component of the electromagnetic current in the light-cone formalism. For comparison, we also compute the form factor in the covariant framework and we obtain perfect agreement. It is shown that the pair terms do not contribute in this pseudoscalar model. This explains why a naive light-cone calculation, i.e., omitting pair terms from the onset, also yields the same results.

hep-ph↗
arXiv1997

Construction of gauge invariant effective nucleonic theories: functional approach

Starting from relativistic quantum field theories, describing interacting nucleons and pions coupled to the dynamical electromagnetic field, the pion degrees of freedom are eliminated by means of functional integration. Apart from taking into account some operators perturbatively in $e$, e.g. the vacuum polarization, this procedure is exact, giving effective theories for nucleons and photons. The subsequent nonrelativistic reduction yields the corresponding nonrelativistic quantum field theory. The latter is unique, irrespective of the precize form of the original nucleon-pion interaction. Nucleonic potentials and electromagnetic interactions are mutually consistent. Local gauge invariance is satisfied at any stage of the formal developments.

nucl-th↗
arXiv1997

QCD near the Light Cone

Starting from the QCD Lagrangian, we present the QCD Hamiltonian for near light cone coordinates. We study the dynamics of the gluonic zero modes of this Hamiltonian. The strong coupling solutions serve as a basis for the complete problem. We discuss the importance of zero modes for the confinement mechanism.

hep-th↗
arXiv1996

Local gauge invariance implies Siegert's hypothesis

The nonrelativistic Ward-Takahashi identity, a consequence of local gauge invariance in quantum mechanics, shows the necessity of exchange current contributions in case of nonlocal and/or isospin-dependent potentials. It also implies Siegert's hypothesis: in the nonrelativistic limit, two-body charge densities identically vanish. Neither current conservation, which follows from global gauge invariance, nor the constraints of (lowest order) relativity are sufficient to arrive at this result. Furthermore, a low-energy theorem for exchange contributions is established.

nucl-th↗
arXiv1996

Quantum Electrodynamics in the Light-Front Weyl Gauge

We examine QED(3+1) quantised in the `front form' with finite `volume' regularisation, namely in Discretised Light-Cone Quantisation. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge $A^-=0$. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply `quantum mechanical gauge fixing' to implement Gauß' law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely displacements. On the light-cone the symmetry manifests itself quite differently.

hep-th↗
arXiv1995

The electron-nucleon cross section in $(e,e'p)$ reactions

We examine commonly used approaches to deal with the scattering of electrons from a bound nucleon. Several prescriptions are shown to be related by gauge transformations. Nevertheless, due to current non-conservation, they yield different results. These differences reflect the size of the uncertainty that persists in the interpretation of $(e,e'p)$ experiments.

nucl-th↗
arXiv1995

Effective Hamiltonian for Scalar Theories in the Gaussian Approximation

We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in principle, be treated perturbatively. In this scheme we analyze the $O(1)$ and $O(2)$ scalar models. For the $O(2)$--theory we first explicitly calculate the massless Goldstone excitation and then show that the one-loop corrections of the effective Hamiltonian do not generate a mass.

hep-ph↗
arXiv1995

Analysis of the Low-Energy Theorem for γp \to p π^0

The derivation of the `classical' low-energy theorem (LET) for γp \rightarrow pπ^0 is re-examined and compared to chiral perturbation theory. Both results are correct and are not contradictory; they differ because different expansions of the same quantity are involved. Possible modifications of the extended partially conserved axial-vector current relation, one of the starting points in the derivation of the LET, are discussed. An alternate, more transparent form of the LET is presented.

nucl-th↗