arXiv subjects

Matthias Werner

Publications and source records attributed to Matthias Werner.

8 recordsLinked to original sources

arXiv2026

Polynomial equivalence of the global transverse-field Ising model and the gate model of quantum computation

The transverse-field Ising model has attracted a lot of attention in recent years, especially in the quantum simulation and quantum computation literature. This interest is driven by many platforms for analog quantum computation, which implement the transverse-field Ising model for solving optimization problems, such as quantum annealing. However, it has remained an open question whether the Ising model with a global transverse field is equivalent to the gate model of quantum computation. Here we answer this question affirmatively for the case of a non-monotonic time-dependent transverse field. Building on a recent result by Cesa and Pichler on global control of Rydberg atoms, we provide a construction that allows simulating arbitrary quantum circuits using the Ising model with global transverse field with polynomial overhead in time, qubit number, and energy scale. Although the polynomial overheads we establish here are large relative to what is feasible on real-world quantum hardware, our result motivates the development of more sophisticated methods for simulating quantum circuits using the Ising model with a global transverse field. Additionally, under the assumption that quantum computing is strictly more powerful than classical computing, our result serves as a no-go theorem for efficient classical simulation of the transverse-field Ising model with a time-dependent global transverse field. Therefore, our finding is relevant for multiple communities, from analog quantum simulation and quantum optimization on various platforms to complexity and control theory.

quant-ph↗

arXiv2026

Leveraging Landau-Zener-St\"uckelberg interference for accelerating diabatic quantum annealing

Diabatic quantum annealing with variationally optimized schedules can exhibit exponential speedups over conventional adiabatic quantum annealing, as was demonstrated numerically for a frustrated Ising ring model by C{\^o}t{\'e} et al. Here we identify Landau-Zener-St{\"u}ckelberg interference as the underlying mechanism for this speedup, and based on this insight we propose a variational schedule ansatz with far fewer parameters. This simplified ansatz allows us to show analytically that the classical optimization of the schedule parameters can be done in polynomial time and discuss conditions when we expect this type of mechanism to provide speedups over adiabatic annealing. Furthermore, we provide an analytical argument that coherence is an essential resource for this mechanism, which we verify numerically. We perform extensive numerical tests of the proposed ansatz and observe substantial improvements over adiabatic annealing and competitive performance in particularly challenging problem instances, including a well-studied MAXCUT instance commonly used for benchmarking. Our work shows that explicitly leveraging physical mechanisms can lead to more effective designs of variational annealing algorithms.

quant-ph↗

arXiv2025

A quantum state transfer protocol with Ising Hamiltonians

Quantum state transfer is a fundamental requirement for scalable quantum computation, where fast and reliable communication between distant subsystems is essential. In this work, we present a protocol for quantum state transfer in linear Ising chains. Starting from a perfect state transfer scheme via a Heisenberg Hamiltonian with inhomogeneous couplings, we adapt it for architectures implementing the transverse-field Ising model by encoding the information in domain walls. The resulting linear Ising chain makes quantum transport experiments accessible to many platforms for analog quantum simulation. We test the protocol for 1-, 2-, and 3- spin states, obtaining high transfer fidelities of up to 0.99 and study the accuracy dependence on the domain wall approximation. These results are the first step in paving the way for an experimental implementation of the protocol.

quant-ph↗

arXiv2024

Quantum annealing eigensolver as a NISQ era tool for probing strong correlation effects in quantum chemistry

The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is arguably the most popular noisy intermediate-scale quantum (NISQ) era approach to quantum chemistry. We consider the underexplored quantum annealing eigensolver (QAE) algorithm as a worthy alternative. We use a combination of numerical calculations for a system where strong correlation effects dominate, and conclusions drawn from our preliminary scaling analysis for QAE and VQE to make the case for QAE as a NISQ era contender to VQE for quantum chemistry. For the former, we pick the representative example of computing avoided crossings in the H4 molecule in a rectangular geometry, and demonstrate that we obtain results to within about 1.2% of the full configuration interaction value on the D-Wave Advantage system 4.1 hardware. We carry out analyses on the effect of the number of shots, anneal time, and the choice of Lagrange multiplier on our obtained results. Following our numerical results, we carry out a detailed yet preliminary analysis of the scaling behaviours of both the QAE and the VQE algorithms. We analyze the non-recurring and recurring costs involved in both the algorithms and arrive at their net scaling behaviours.

physics.chem-ph↗

arXiv2024

Quantum simulation of one-dimensional fermionic systems with Ising Hamiltonians

In recent years, analog quantum simulators have reached unprecedented quality, both in qubit numbers and coherence times. Most of these simulators natively implement Ising-type Hamiltonians, which limits the class of models that can be simulated efficiently. We propose a method to overcome this limitation and simulate the time-evolution of a large class of spinless fermionic systems in 1D using simple Ising-type Hamiltonians with local transverse fields. Our method is based on domain wall encoding, which is implemented via strong (anti-)ferromagnetic couplings $|J|$. We show that in the limit of strong $|J|$, the domain walls behave like spinless fermions in 1D. The Ising Hamiltonians are one-dimensional chains with nearest-neighbor and, optionally, next-nearest-neighbor interactions. As a proof-of-concept, we perform numerical simulations of various 1D-fermionic systems using domain wall evolution and accurately reproduce the systems' properties, such as topological edge states, Anderson localization, quantum chaotic time evolution and time-reversal symmetry breaking via Floquet-engineering. Our approach makes the simulation of a large class of fermionic many-body systems feasible on analogue quantum hardware that natively implements Ising-type Hamiltonians with transverse fields.

quant-ph↗

arXiv2023

Bounding first-order quantum phase transitions in adiabatic quantum computing

In the context of adiabatic quantum computation (AQC), it has been argued that first-order quantum phase transitions (QPTs) due to localisation phenomena cause AQC to fail by exponentially decreasing the minimal spectral gap of the Hamiltonian along the annealing path as a function of the qubit number. The vanishing of the spectral gap is often linked to the localisation of the ground state in a local minimum, requiring the system to tunnel into the global minimum at a later stage of the annealing. Recent methods have been proposed to avoid this phenomenon by carefully designing the involved Hamiltonians. However, it remains a challenge to formulate a comprehensive theory of the effect of the various parameters and the conditions under which QPTs make the AQC algorithm fail. Equipped with concepts from graph theory, in this work we link graph quantities associated to the Hamiltonians along the annealing path with the occurrence of QPTs. These links allow us to derive bounds on the location of the minimal spectral gap along the annealing path, augmenting the toolbox for the analysis of strategies to improve the runtime of AQC algorithms.

quant-ph↗

arXiv2021

Informed Equation Learning

Distilling data into compact and interpretable analytic equations is one of the goals of science. Instead, contemporary supervised machine learning methods mostly produce unstructured and dense maps from input to output. Particularly in deep learning, this property is owed to the generic nature of simple standard link functions. To learn equations rather than maps, standard non-linearities can be replaced with structured building blocks of atomic functions. However, without strong priors on sparsity and structure, representational complexity and numerical conditioning limit this direct approach. To scale to realistic settings in science and engineering, we propose an informed equation learning system. It provides a way to incorporate expert knowledge about what are permitted or prohibited equation components, as well as a domain-dependent structured sparsity prior. Our system then utilizes a robust method to learn equations with atomic functions exhibiting singularities, as e.g. logarithm and division. We demonstrate several artificial and real-world experiments from the engineering domain, in which our system learns interpretable models of high predictive power.

cs.LG↗

arXiv2017

gearshifft - The FFT Benchmark Suite for Heterogeneous Platforms

Fast Fourier Transforms (FFTs) are exploited in a wide variety of fields ranging from computer science to natural sciences and engineering. With the rising data production bandwidths of modern FFT applications, judging best which algorithmic tool to apply, can be vital to any scientific endeavor. As tailored FFT implementations exist for an ever increasing variety of high performance computer hardware, choosing the best performing FFT implementation has strong implications for future hardware purchase decisions, for resources FFTs consume and for possibly decisive financial and time savings ahead of the competition. This paper therefor presents gearshifft, which is an open-source and vendor agnostic benchmark suite to process a wide variety of problem sizes and types with state-of-the-art FFT implementations (fftw, clfft and cufft). gearshifft provides a reproducible, unbiased and fair comparison on a wide variety of hardware to explore which FFT variant is best for a given problem size.

cs.PF↗