arXiv subjects

Martin Plesch

Publications and source records attributed to Martin Plesch.

At least 19 recordsLinked to original sources

arXiv2026

Classical Regularization in Variational Quantum Eigensolvers

While quantum computers are a very promising tool for the far future, in their current state of the art they remain limited both in size and quality. This has given rise to hybrid quantum-classical algorithms, where the quantum device performs only a small but vital part of the overall computation. Among these, variational quantum algorithms (VQAs), which combine a classical optimization procedure with quantum evaluation of a cost function, have emerged as particularly promising. However, barren plateaus and ill-conditioned optimization landscapes remain among the primary obstacles faced by VQAs, often leading to unstable convergence and high sensitivity to initialization. Motivated by this challenge, we investigate whether a purely classical remedy, standard L2 squared-norm regularization, can systematically stabilize hybrid quantum-classical optimization. Specifically, we augment the Variational Quantum Eigensolver (VQE) objective with a quadratic penalty proportional to the squared norm of the parameters, without modifying the quantum circuit or measurement process. Across all tested Hamiltonians, H2, LiH, and the Random Field Ising Model (RFIM), we observe improved performance over a broad window of the regularization strength. Our large-scale numerical results demonstrate that classical regularization provides a robust, system-independent mechanism for mitigating VQE instability, enhancing the reliability and reproducibility of variational quantum optimization without altering the underlying quantum circuit.

quant-ph↗

arXiv2026

Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space

Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding that maps a system with $N$ physical sites onto only $\lceil \log_2 N \rceil$ qubits while maintaining a clear correspondence with the underlying physical model. Within this reduced register, we construct a compatible variational circuit and a Gray-code-inspired measurement strategy whose number of global settings grows only logarithmically with system size. To quantify the overall hardware load, we introduce a volumetric efficiency metric that combines the number of qubit, circuit depth, and the number of measurement settings into a single measure, expressing the overall computation costs. Using this metric, we show that the total space-time-sampling volume required in a variational loop can be reduced dramatically from $N^2$ to $(logN)^3$ for hardware efficient ansatz, allowing an exponential reduction in time and size of the quantum hardware. These results demonstrate that large, structured solid-state Hamiltonians can be simulated on substantially smaller quantum registers with controlled sampling overhead and manageable circuit complexity, extending the reach of variational quantum algorithms on near-term devices.

quant-ph↗

arXiv2025

Optics experiments as a tool for developing critical thinking in physics education

Experimental activities are an essential part of physics education. In addition to conveying scientific knowledge, they play a significant role in developing scientific literacy, inquiry skills, and critical thinking. In today's world, where students are exposed to vast amounts of information of varying quality, the ability to analyse, evaluate, and interpret information correctly has become increasingly important. This paper presents a series of physics experiments in the field of optics, specifically designed to foster critical thinking at various stages of the inquiry process. The topic of optics was chosen deliberately, as many optical phenomena occur naturally in everyday life, are familiar to students, and stimulate their curiosity. At the same time, they provide space for formulating hypotheses, designing experiments, interpreting data, and evaluating alternative explanations. Each experiment begins with a real-life problem situation that students are expected to explore and resolve through their own investigative work. The tasks are structured to encourage discussion, require argumentation, and promote reflection on both the process and the outcomes. The proposed experiments are suitable for students at both primary and secondary school levels and can be implemented in formal as well as non-formal educational settings. The aim of this contribution is to demonstrate how well-designed and pedagogically grounded experiments can not only enhance the understanding of physical concepts but also systematically develop critical thinking skills - one of the key competencies of 21st-century education.

physics.ed-ph↗

arXiv2025

The use of a simple digital weather station (not only) in teaching physics

One of key goals of contemporary physics (and, realistically, STEM) education is to develop students' science literacy and critical thinking skills. In this paper, we present the construction and use of several versions of a simple school-based digital weather station that students can use to measure fundamental physical quantities (temperature, pressure, air humidity, light intensity) as part of school activities. The weather stations were constructed at our workplace using an Arduino microcontroller, BBC micro: bit, and the school measurement system Coach. This paper proposes not only the design and related programming of the weather stations but also how students can collect, analyse, and interpret measured data, thereby learning scientific methods and developing science literacy and critical thinking. This hands-on approach also develops students' experimental skills, emphasizes the cross-curricular relationships between physics, computer science and geography, and teaches them to work with accurate data in the context of real environmental problems.

physics.ed-ph↗

arXiv2025

Minimum measurements quantum protocol for band structure calculation

Protocols for quantum measurement are an essential part of quantum computing. Measurements are no longer confined to the final step of computation but are increasingly embedded within quantum circuits as integral components of noise-resilient algorithms. However, each observable typically requires a distinct measurement basis, often demanding a different circuit configuration. As the number of such configurations typically grows with the number of qubits, measurements constitute a major bottleneck. Focusing on electronic structure calculations in crystalline systems, we propose a measurement protocol that restricts the required measurement configurations to an absolute minimum of just three, independent of the number of qubits. This makes it one of the few known protocols that do not scale with qubit number. In particular, we derive the measurement protocol from the symmetries of tight-binding (TB) Hamiltonians and implement it within the Orthogonal-Ansatz Variational Quantum Eigensolver (OA-VQE) algorithm. We demonstrate its performance on three systems, namely a two-dimensional CuO$_2$ square lattice (3 qubits), bilayer graphene with hexagonal (Honeycomb) lattice (4 qubits) and three-dimensional diamond lattice (10 qubits). Beyond tight-binding systems, the protocol can be extended to enable efficient initial state preparation for many-body Hamiltonians, such as multi-orbital Hubbard models in a momentum space.

quant-ph↗

arXiv2025

Development of soft and hard skills of high-school students via Young Physicists' Tournament

The Young Physicists' Tournament (YPT) inspires high-school students to immerse themselves into an inquiry process closely resembling the real physics research. Using questionnaires' replies from the students and their teachers engaged in YPT, we investigated the perception of teachers and students on how the preparation for YPT contributes to the development of hard skills (physics content knowledge, mathematics, modelling...) and soft skills (communication, team work, organization...) of the students, and how it compares to regular classes and other activities. This comparison shows a positive role of YPT among students, and even a more positive perception among teachers. The significant development of a wide range of advanced skills justifies the substantial effort, resources and dedication of both teachers and students required for the participation in YPT.

physics.ed-ph↗

arXiv2025

HOPSO: A Robust Classical Optimizer for VQE

Variational Quantum Eigensolver (VQE) algorithm is one of few approaches where the hope for near-term quantum advantage concentrates. However, they face challenges connected with measurement stochastic noise, barren plateaus, and optimization difficulties in periodic parameter spaces. While most of the efforts concentrates on optimizing the quantum part of the procedure, here we aim to enhance the classical optimization by utilizing a modified version of Harmonic Oscillator-based Particle Swarm Optimization (HOPSO). By adapting its dynamics to respect the periodicity of quantum parameters and enhance noise resilience, we show its strengths on hydrogen (H2) and lithium hydride (LiH) molecules modeled as 4- and 8-qubit Hamiltonians. HOPSO achieves competitive ground-state energy approximations and demonstrates improved robustness compared to COBYLA, Differential Evolution (DE), and standard Particle Swarm Optimization (PSO) methods in all situations and outperforms other methods under realistic noise conditions. These results suggest that a properly tailored classical part of VQE algorithms can tackle with current problems and gives hope for its scalability for larger systems.

quant-ph↗

arXiv2024

Harmonic Oscillator based Particle Swarm Optimization

Numerical optimization techniques are widely used in a broad area of science and technology, from finding the minimal energy of systems in Physics or Chemistry to finding optimal routes in logistics or optimal strategies for high speed trading. In general, a set of parameters (parameter space) is tuned to find the lowest value of a function depending on these parameters (cost function). In most cases the parameter space is too big to be completely searched and the most efficient techniques combine stochastic elements (randomness included in the starting setting and decision making during the optimization process) with well designed deterministic process. Thus there is nothing like a universal best optimization method; rather than that, different methods and their settings are more or less efficient in different contexts. Here we present a method that integrates Particle Swarm Optimization (PSO), a highly effective and successful algorithm inspired by the collective behavior of a flock of birds searching for food, with the principles of Harmonic Oscillators. This physics-based approach introduces the concept of energy, enabling a smoother and a more controlled convergence throughout the optimization process. We test our method on a standard set of test functions and show that in most cases it can outperform its natural competitors including the original PSO as well as the broadly used COBYLA and Differential Evolution optimization methods.

cs.NE↗

arXiv2023

Resource-efficient utilization of quantum computers

The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all information encoded in the calculation. Even if the technology advances fast within the next years, any use of quantum computers will be limited to short and simple tasks, serving as subroutines of more complex classical procedures. Even for these applications the resource efficiency, measured in the number of quantum computer runs, will be a key parameter. Here we suggest a general optimization procedure for hybrid quantum-classical algorithms that allows finding the optimal approach with limited quantum resources. We demonstrate this procedure on a specific example of variational quantum algorithm used to find the ground state energy of a hydrogen molecule.

quant-ph↗

arXiv2022

Development of Scientific Skills via IYPT -- How does YPT participation lead to hard-skill development?

physics.ed-ph↗

arXiv2022

Development of Soft Skills via IYPT

We investigated how students perceive the role of IYPT (www.iypt.org) participation in their development of soft skills. We also investigated how students teachers assess the contribution of YPT participation to students soft skills development. Third, we link self-reported soft-skill development to performance in research tasks, as assessed by international panels of experts in the context of a physics competition. Taken together, the three steps, by triangulating the relationship between inquiry-based learning and soft-skill development, allow building inference about how inquiry-based learning helps students build soft skills, and how these soft skills influence student performance in research tasks. The data for the three stages includes 308 student responses for stage one, 33 teacher responses for stage two, and 794 expert (teachers, researchers, and university professors) assessments of student performance for stage three. Condensing the detailed findings from our analysis, we suggest thirteen guidelines for developing soft skills in students below.

physics.ed-ph↗

arXiv2022

Implementation of quantum compression on IBM quantum computers

Advances in development of quantum computing processors brought ample opportunities to test the performance of various quantum algorithms with practical implementations. In this paper we report on implementations of quantum compression algorithm that can efficiently compress unknown quantum information. We restricted ourselves to compression of three pure qubits into two qubits, as the complexity of even such a simple implementation is barely within the reach of today's quantum processors. We implemented the algorithm on IBM quantum processors with two different topological layouts - a fully connected triangle processor and a partially connected line processor. It turns out that the incomplete connectivity of the line processor affects the performance only minimally. On the other hand, it turns out that the transpilation, i.e. compilation of the circuit into gates physically available to the quantum processor, crucially influences the result. We also have seen that the compression followed by immediate decompression is, even for such a simple case, on the edge or even beyond the capabilities of currently available quantum processors.

quant-ph↗

arXiv2021

Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality

Self-testing protocols enable certification of quantum devices without demanding full knowledge about their inner workings. A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in Bell experiment known as Hardy's test of nonlocality not only the maximally nonlocal correlation self-tests a quantum state, rather a non-maximal nonlocal behavior can serve the same purpose. We, in fact, completely characterize all such behaviors leading to self-test of every pure two qubit entangled state except the maximally entangled ones. Apart from originating a novel self-testing protocol, our method provides a powerful tool towards characterizing the complex boundary of the set of quantum correlations.

quant-ph↗

arXiv2021

Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule

Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we have performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting best-practice aspects of these calculations. In order to compare the performance of different set-ups, the ground-state energy of hydrogen molecule has been chosen as a benchmark for which the exact solution exists in literature. Applying variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi-Kitaev transformation we have analyzed the impact of various computational technicalities. These include (i) the choice of optimization methods, (ii) the architecture of quantum circuits, as well as (iii) different types of noise when simulating real quantum processors. On these we eventually performed a series of experimental runs as a complement to our simulations. The SPSA and COBYLA optimization methods have clearly outperformed the Nelder-Mead and Powell methods. The results obtained when using the $R_{\mathrm{y}}$ variational form were better than those obtained when the $R_{\mathrm{y}}R_{\mathrm{z}}$ form was used. The choice of an optimum {entangling layer} was sensitively interlinked with the choice of the optimization method. The circular {entangling layer} has been found to worsen the performance of the COBYLA method while the full {entangling layer} improved it. All four optimization methods sometimes lead to an energy that corresponds to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight.

quant-ph↗

arXiv2021

The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE) -- an algorithm to calculate the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE, and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, as well as physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal way of running the hybrid classical-quantum optimization is to (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but require high final readout precision, (ii) emphasize efficient problem encoding and ansatz parametrization, and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently it is quite difficult to obtain trustworthy calculations of molecular energies.

quant-ph↗

arXiv2021

Device-independent bounds from Cabello's nonlocality argument

Hardy-type arguments manifest Bell nonlocality in one of the simplest possible ways. Except for demonstrating nonclassical signature of entangled states in question, they can also serve for device-independent self-testing of states, as shown, e.g., in Phys. Rev. Lett. 109, 180401 (2012). Here we develop and broaden these results to an extended version of Hardy's argument, often referred to as Cabello's nonlocality argument. We show that, as in the simpler case of Hardy's nonlocality argument, the maximum quantum value for Cabello's nonlocality is achieved by a pure two-qubit state and projective measurements that are unique up to local isometries. We also examine the properties of a more realistic case when small errors in the ideal constraints are accepted within the probabilities obtained and prove that also in this case the two-qubit state and measurements are sufficient for obtaining the maximum quantum violation of the classical bound.

quant-ph↗

arXiv2020

Choice of mutually unbiased bases and outcome labelling affects measurement outcome secrecy

Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove randomness or secrecy of measurement results. In this work we show that certain properties of sets of MUBs crucially depend on their specific choice, including, somewhat surprisingly, measurement outcome labelling. If measurements are chosen in a coherent way, the secrecy of the result can be completely lost for specific sets of MUB measurements, while partially retained for others. This can potentially impact a broad spectrum of applications, where MUBs are utilized.

quant-ph↗

arXiv2020

Quantum key distribution overcoming extreme noise: simultaneous subspace coding using high-dimensional entanglement

High-dimensional entanglement promises to increase the information capacity of photons and is now routinely generated exploiting spatio-temporal degrees of freedom of single photons. A curious feature of these systems is the possibility to certify entanglement despite strong noise in the data. We show that it is also possible to exploit this noisy high-dimensional entanglement for quantum key distribution by introducing a protocol that uses mutliple subspaces of the high-dimensional system simultaneously. Our protocol can be used to establish a secret key even in extremely noisy experimental conditions, where qubit protocols fail. To show that, we analyze the performance of our protocol for noise models that apply to the two most commonly used sources of high-dimensional entanglement: time bins and spatial modes.

quant-ph↗