arXiv subjects

Jan F. Haase

Publications and source records attributed to Jan F. Haase.

15 recordsLinked to original sources

arXiv2024

Simulating 2D lattice gauge theories on a qudit quantum computer

Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in $d$ different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

quant-ph↗

arXiv2023

Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities

Quantum-enhanced computing methods are promising candidates to solve currently intractable problems. We consider here a variational quantum eigensolver (VQE), that delegates costly state preparations and measurements to quantum hardware, while classical optimization techniques guide the quantum hardware to create a desired target state. In this work, we propose a bosonic VQE using superconducting microwave cavities, overcoming the typical restriction of a small Hilbert space when the VQE is qubit based. The considered platform allows for strong nonlinearities between photon modes, which are highly customisable and can be tuned in situ, i.e. during running experiments. Our proposal hence allows for the realization of a wide range of bosonic ansatz states, and is therefore especially useful when simulating models involving degrees of freedom that cannot be simply mapped to qubits, such as gauge theories, that include components which require infinite-dimensional Hilbert spaces. We thus propose to experimentally apply this bosonic VQE to the U(1) Higgs model including a topological term, which in general introduces a sign problem in the model, making it intractable with conventional Monte Carlo methods.

quant-ph↗

arXiv2023

Simulating one-dimensional quantum chromodynamics on a quantum computer: Real-time evolutions of tetra- and pentaquarks

Quantum chromodynamics - the theory of quarks and gluons - has been known for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, that opened a new research field. Crucially, numerous unsolved questions of the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by performing a real-time evolution of tetraquark and pentaquark physics in one-dimensional SU(3) gauge theory on a superconducting quantum computer. Our experiment represents a first quantum computation involving quarks with three colour degrees of freedom, i.e. with the gauge group of QCD.

quant-ph↗

arXiv2023

Adaptive estimation of quantum observables

The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive sampling. Here, we introduce a measurement scheme that adaptively modifies the estimator based on previously obtained data. Our algorithm, which we call AEQuO, continuously monitors both the estimated average and the associated error of the considered observable, and determines the next measurement step based on this information. We allow both for overlap and non-bitwise commutation relations in the subsets of Pauli operators that are simultaneously probed, thereby maximizing the amount of gathered information. AEQuO comes in two variants: a greedy bucket-filling algorithm with good performance for small problem instances, and a machine learning-based algorithm with more favorable scaling for larger instances. The measurement configuration determined by these subroutines is further post-processed in order to lower the error on the estimator. We test our protocol on chemistry Hamiltonians, for which AEQuO provides error estimates that improve on all state-of-the-art methods based on various grouping techniques or randomized measurements, thus greatly lowering the toll of measurements in current and future quantum applications.

quant-ph↗

arXiv2021

3+1D $θ$-Term on the Lattice from the Hamiltonian Perspective

Quantum and tensor network simulations have emerged as prominent sign-problem free approaches to lattice gauge theories. Unlike conventional Markov chain Monte Carlo methods, they are based on the Hamiltonian formulation. In this talk, we fill a gap in the literature and present the first derivation of the Hamiltonian 3+1D $θ$-term -- which is an important sign-problem afflicted term -- for Abelian and non-Abelian lattice gauge theories. Furthermore, we perform exact diagonalization for a 3+1D U(1) lattice gauge theory including the $θ$-term on a unit periodic cube. Our numerical results reveal a novel phase transition at fixed values of $θ$ in the strong-coupling regime. The transition is evidenced by an avoided level crossing in the ground state energy, as well as sudden changes in the plaquette expectation value, the electric energy density, and the topological charge density. Extensions of our work to larger lattices can be readily performed using state-of-the-art tensor network simulations. Moreover, our work provides a concrete starting point for an eventual quantum simulation of the $θ$-dependent phase structure and dynamics of lattice gauge theories in 3+1D. This talk is mainly based on [1]. We expand beyond [1] by including a derivation of the (non-)Abelian fixed-length Higgs term in the Hamiltonian formulation for future studies of (non-)Abelian-Higgs models with a $θ$-term.

hep-lat↗

arXiv2021

Investigating a (3+1)D Topological $θ$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations

Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the (3+1)D topological $θ$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way towards Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory with the $θ$-term via exact diagonalization for a single periodic cube. In the strong coupling regime, our results suggest the occurrence of a phase transition at constant values of $θ$, as indicated by an avoided level-crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density. These results could in principle be cross-checked by the recently developed (3+1)D tensor network methods and quantum simulations, once sufficient resources become available.

hep-lat↗

arXiv2021

Towards simulating 2D effects in lattice gauge theories on a quantum computer

Gauge theories are the most successful theories for describing nature at its fundamental level, but obtaining analytical or numerical solutions often remains a challenge. We propose an experimental quantum simulation scheme to study ground state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology. The proposal builds on a formulation of lattice gauge theories as effective spin models in arXiv:2006.14160, which reduces the number of qubits needed by eliminating redundant degrees of freedom and by using an efficient truncation scheme for the gauge fields. The latter endows our proposal with the perspective to take a well-controlled continuum limit. Our protocols allow in principle scaling up to large lattices and offer the perspective to connect the lattice simulation to low energy observable quantities, e.g. the hadron spectrum, in the continuum theory. By including both dynamical matter and a non-minimal gauge field truncation, we provide the novel opportunity to observe 2D effects on present-day quantum hardware. More specifically, we present two Variational Quantum Eigensolver (VQE) based protocols for the study of magnetic field effects, and for taking an important first step towards computing the running coupling of QED. For both instances, we include variational quantum circuits for qubit-based hardware, which we explicitly apply to trapped ion quantum computers. We simulate the proposed VQE experiments classically to calculate the required measurement budget under realistic conditions. While this feasibility analysis is done for trapped ions, our approach can be easily adapted to other platforms. The techniques presented here, combined with advancements in quantum hardware pave the way for reaching beyond the capabilities of classical simulations by extending our framework to include fermionic potentials or topological terms.

quant-ph↗

arXiv2021

SU(2) hadrons on a quantum computer

We realize, for the first time, a non-Abelian gauge theory with both gauge and matter fields on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Quantum computers are able to create important new opportunities for ongoing essential research on gauge theories by providing simulations that are unattainable on classical computers. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a resource-efficient approach that not only allows the implementation of a full SU(2) gauge theory on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.

quant-ph↗

arXiv2021

Parallel selective nuclear spin addressing for fast high-fidelity quantum gates

Due to their long coherence times, nuclear spins have gained considerable attention as physical qubits. Two-qubit gates between nuclear spins of distinct resonance frequencies can be mediated by electron spins, usually employing a sequence of electron-nuclear gates. Here we present a different approach inspired by, but not limited to, NV centers in diamond and discuss possible applications. To this end we generalize external electron spin control sequences for nuclear spin initialization and hyperpolarization to achieve the simultaneous control of distinct nuclear spins via an electron spin. This approach results in efficient entangling gates that, compared to standard techniques, reduce the gate time by more than 50% when the gate time is limited by off-resonant coupling to other spins, and by up to 22% when the gate time is limited by small electron-nuclear coupling.

quant-ph↗

arXiv2021

A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use $2+1$ dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

quant-ph↗

arXiv2019

Non-monotonic population and coherence evolution in Markovian open-system dynamics

We consider a simple microscopic model where the open-system dynamics of a qubit, despite being Markovian, shows features which are typically associated to the presence of memory effects. Namely, a non monotonic behavior both in the population and in the coherence evolution arises due to the presence of non-secular contributions, which break the phase covariance of the Lindbladian (semigroup) dynamics. We also show by an explicit construction how such a non-monotonic behaviour can be reproduced by a phase covariant evolution, but only at the price of inserting some state-dependent memory effects.

quant-ph↗

arXiv2018

Precision Limits in Quantum Metrology with Open Quantum Systems

The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcome when using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment. We adopt a complementary approach, where we first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system's dissipative time evolution. We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.

quant-ph↗

arXiv2018

Controllable Non-Markovianity for a Spin Qubit in Diamond

We present a flexible scheme to realize non-artificial non-Markovian dynamics of an electronic spin qubit, using a nitrogen-vacancy center in diamond where the inherent nitrogen spin serves as a regulator of the dynamics. By changing the population of the nitrogen spin, we show that we can smoothly tune the non-Markovianity of the electron spin's dynamic. Furthermore, we examine the decoherence dynamics induced by the spin bath to exclude other sources of non-Markovianity. The amount of collected measurement data is kept at a minimum by employing Bayesian data analysis. This allows for a precise quantification of the parameters involved in the description of the dynamics and a prediction of so far unobserved data points.

quant-ph↗

arXiv2018

Fundamental limits to frequency estimation: A comprehensive microscopic perspective

We consider a scenario in which qubit-like probes are used to sense an external field that linearly affects their energy splitting. Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide a systematic study of the attainable precision under the impact of noise originating from independent bosonic baths. We invoke an explicit microscopic derivation of the probe dynamics using the spin-boson model with weak coupling of arbitrary geometry and clarify how the secular approximation leads to a phase-covariant dynamics, where the noise terms commute with the field Hamiltonian, while the inclusion of non-secular terms breaks the phase-covariance. Moreover, unless one restricts to a particular (i.e., Ohmic) spectral density of the bath modes, the noise terms may contain relevant information about the frequency to be estimated. Thus, by considering general evolutions of a single probe, we study regimes in which these two effects have a non-negligible impact on the achievable precision. We then consider baths of Ohmic spectral density yet fully accounting for the lack of phase-covariance, in order to characterize the ultimate attainable scaling of precision when $N$ probes are used in parallel. Crucially, we show that beyond the semigroup (Lindbladian) regime the Zeno limit imposing the $1/N^{3/2}$ scaling of the mean squared error, derived assuming phase-covariance, generalises to any dynamics of the probes, unless the latter are coupled to the baths in the direction perfectly transversal to the encoding---when a novel scaling of $1/N^{7/4}$ arises. As our microscopic approach covers all classes of dissipative dynamics, from semigroup to non-Markovian ones (potentially non-phase-covariant), it provides an exhaustive picture, in which all the different asymptotic scalings of precision naturally emerge.

quant-ph↗

arXiv2016

Positioning Nuclear Spins in Interacting Clusters for Quantum Technologies and Bio-imaging

We propose a method to measure the hyperfine vectors between a nitrogen-vacancy (NV) center and an environment of interacting nuclear spins. Our protocol enables the generation of tunable electron-nuclear coupling Hamiltonians while suppressing unwanted inter-nuclear interactions. In this manner, each nucleus can be addressed and controlled individually thereby permitting the reconstruction of the individual hyperfine vectors. With this ability the 3D-structure of spin ensembles and spins in bio-molecules can be identified without the necessity of varying the direction of applied magnetic fields. We demonstrate examples including the complete reconstruction of an interacting spin cluster in diamond and 3D imaging of all the nuclear spins in a bio-molecule.

quant-ph↗