arXiv subjects

Ossi Niemimäki

Publications and source records attributed to Ossi Niemimäki.

8 recordsLinked to original sources

arXiv2026

Minimizing entanglement entropy for enhanced quantum state preparation

Quantum state preparation is an important subroutine in many quantum algorithms. The goal is to encode classical information directly to the quantum state so that it is possible to leverage quantum algorithms for data processing. However, quantum state preparation of arbitrary states scales exponentially in the number of two-qubit gates, and this makes quantum state preparation a very difficult task on quantum computers, especially on near-term noisy devices. This represents a major challenge in achieving quantum advantage. We present and analyze a novel two-step state preparation method where we first minimize the entanglement entropy of the target quantum state, thus transforming the state to one that is easier to prepare. The state with reduced entanglement entropy is then represented as a matrix product state, resulting in a high accuracy preparation of the target state. Our method is suitable for NISQ devices and we give rigorous lower bounds on the accuracy of the prepared state in terms of the entanglement entropy. We benchmark our method with 2D normal distribution and Ricker wavelet states with 6--20 qubits.

quant-ph↗

arXiv2026

Quantum algorithm for the lattice Boltzmann method with applications on real quantum devices

We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum algorithms for the LBM, while retaining computational efficiency in terms of the gate and qubit complexity. The new algorithm has potential for full end-to-end quantum utility especially for linear problems. We discuss the implementation of examples in linear acoustics, as well as a nonlinear Navier-Stokes problem that was solved on an IBM QPU in a hybrid simulation loop.

quant-ph↗

arXiv2025

Efficient Quantum Lattice Gas Automata

This study presents a novel quantum algorithm for lattice gas automata simulation with a single time step, demonstrating logarithmic complexity in terms of $CX$ gates. The algorithm is composed of three main steps: collision, mapping, and propagation. A computational complexity analysis and a comparison using different error rates and number of shots are provided. Despite the impact of noise, our findings indicate that accurate simulations could be achieved already on current noisy devices. This suggests potential for efficient simulation of classical fluid dynamics using quantum lattice gas automata, conditional on advancements to expand the current method to multiple time steps and state preparation.

quant-ph↗

arXiv2024

Utilizing classical programming principles in the Intel Quantum SDK: implementation of quantum lattice Boltzmann method

We explore the use of classical programming techniques in implementing the quantum lattice Boltzmann method in the Intel Quantum SDK -- a software tool for quantum circuit creation and execution on Intel quantum hardware. As hardware access is limited, we use the state vector simulator provided by the SDK. The novelty of this work lies in leveraging classical techniques for the implementation of quantum algorithms. We emphasize the refinement of algorithm implementation and devise strategies to enhance quantum circuits for better control over problem variables. To this end, we adopt classical principles such as modularization, which allows for systematic and controlled execution of complex algorithms. Furthermore, we discuss how the same implementation could be expanded from state vector simulations to execution on quantum hardware with minor adjustments in these configurations.

quant-ph↗

arXiv2023

Efficient parallelization of quantum basis state shift

Basis state shift is central to many quantum algorithms, most notably the quantum walk. Efficient implementations are of major importance for achieving a quantum speedup for computational applications. We optimize the state shift algorithm by incorporating the shift in different directions in parallel. This provides a significant reduction in the depth of the quantum circuit in comparison to the currently known methods, giving a linear scaling in the number of gates versus working qubits in contrast to the quadratic scaling of the state-of-the-art method based on the quantum Fourier transform. For a one-dimensional array of size $2^n$ for $n > 4$, we derive the total number of $15n + 74$ two-qubit $CX$ gates in the parallel circuit, using a total of $2n-2$ qubits including an ancilla register for the decomposition of multi-controlled gates. We focus on the one-dimensional and periodic shift, but note that the method can be extended to more complex cases.

quant-ph↗

arXiv2020

Current Groups and the Hamiltonian Anomaly

Gauge symmetry invariance is an indispensable aspect of the field-theoretic models in classical and quantum physics. Geometrically this symmetry is often modelled with current groups and current algebras, which are used to capture both the idea of gauge invariance and the algebraic structure of gauge currents related to the symmetry. The Hamiltonian anomaly is a well-known problem in the quantisation of massless fermion fields, originally manifesting as additional terms in current algebra commutators. The appearance of these anomalous terms is a signal of two things: that the gauge invariance of quantised Hamiltonian operators is broken, and that consequently it is not possible to coherently define a vacuum state over the physical configuration space of equivalent gauge connections. In this thesis we explore the geometric and topological origins of the Hamiltonian anomaly, emphasising the usefulness of higher geometric structures. Given this context we also discuss higher versions of the gauge-theoretic current groups. These constructions are partially motivated by the $2$-group models of the abstract string group, and we extend some of these ideas to current groups on the three-sphere $S^3$. The study of the Hamiltonian anomaly utilises a wide variety of tools from such fields as differential geometry, group cohomology, and operator K-theory. We gather together many of these approaches and apply them in the standard case involving the time components of the gauge currents. We then proceed to extend the analysis to the general case with all space-time components. We show how the anomaly terms for these generalised current algebra commutators are derived from the same topological foundations; namely, from the Dixmier-Douady class of the anomalous bundle gerbe. As an example we then compute the full set of anomalous commutators for the three-sphere $S^3$ as the physical space.

math-ph↗

arXiv2018

A 2-group construction from an extension of the 3-loop group $Ω^3G$

We define a 3-loop group $Ω^3G$ as a subgroup of smooth maps from a 3-ball to a Lie group $G$, and then construct a 2-group based on an automorphic action on the Mickelsson-Faddeev extension of $Ω^3G$. In this we follow the strategy of Murray et al., who earlier described a similar construction in one dimension. The three-dimensional situation presented here is further complicated by the fact that the 3-loop group extension is not central.

math.DG↗

arXiv2016

Structure-preserving mesh coupling based on the Buffa-Christiansen complex

The state of the art for mesh coupling at nonconforming interfaces is presented and reviewed. Mesh coupling is frequently applied to the modeling and simulation of motion in electromagnetic actuators and machines. The paper exploits Whitney elements to present the main ideas. Both interpolation- and projection-based methods are considered. In addition to accuracy and efficiency, we emphasize the question whether the schemes preserve the structure of the de Rham complex, which underlies Maxwell's equations. As a new contribution, a structure-preserving projection method is presented, in which Lagrange multiplier spaces are chosen from the Buffa-Christiansen complex. Its performance is compared with a straightforward interpolation based on Whitney and de Rham maps, and with Galerkin projection.

math.NA↗