Summer School on New Directions in Quantum and Quantum Reservoir Computing, Quantum Devices and Related Technologies

Simulation of non-Hermitian quantum mechanics with a superconducting quantum processor

Recent rapid advancements in quantum computing allow for tests of unconventional concepts that extend the theoretical framework of standard quantum mechanics. The observation of genuine quantum effects in systems governed by non-Hermitian Hamiltonians is one such intriguing direction. Here we simulate the evolution under such Hamiltonians in the quantum regime on a superconducting quantum processor by using a dilation procedure involving an ancillary qubit. We observe the parity–time (PT )-symmetry breaking phase transition at the exceptional points, discuss the characteristic recurrence and decay times, show the apparent violations of no-go theorems on quantum state distinguishability and entanglement monotonicity in one and two-qubit systems, respectively. We also present a quantum simulation of non-Hermitian non-PT symmetric time-dependent Hamiltonian with real eigenvalues.

Slides available here: https://www.aalto.fi/sites/default/files/2025-09/ShrutiDogra_slides_QRC2025.pdf

Slides available here: https://www.aalto.fi/sites/default/files/2025-09/Ivan_Ivanov-Experiments.pdf

Benchmarking and Optimizing Quantum Reservoirs

Quantum systems are an example of a physical platform capable of generating feature vectors for reservoir computing and extreme learning machine schemes. Their performance depends on how well their nonlinear transformation and memory properties align with the requirements of a given task. This talk will explore how the computational capabilities of such systems can be accessed, how benchmarking tasks can be selected and interpreted, and how the intrinsic properties of quantum systems can be harnessed for optimal performance.

Slides available here: https://www.aalto.fi/sites/default/files/2025-09/Aalto_QRC_workshop_LJaurigue.pdf

The Finnish Quantum-Computing Infrastructure FiQCI

The Finnish Quantum-Computing Infrastructure (FiQCI) was established in 2020, with the mission to provide state-of-the-art hybrid quantum-computing services such as computing time and training to national users. The first hybrid HPC+QC service was opened in 2022, when the VTT Q5 "Helmi" quantum computer was integrated to the LUMI supercomputer. Since the beginning of 2025, the hybrid service has incorporated the national VTT Q50 quantum computer. Efficient emulation is also available through the infrastructure — full state-vector simulations of up to 44 qubits, utilising 4000 GPUs in parallel, is now available through LUMI. 

In this presentation, I will give an overview of the journey, lessons learned so far, and thought on future directions for the infrastructure, including the incorporation of AI tools for enhancing hybrid classical/quantum workflows.

Slides available here: https://www.aalto.fi/sites/default/files/2025-09/FiQCI-Johansson-2025-08-22.pdf

Slides available here: https://www.aalto.fi/sites/default/files/2025-09/slides_Lado.pdf

Slides available here: https://www.aalto.fi/sites/default/files/2025-09/Aalto---Moghaddam---QRC.pdf

Slides for all lectures are available here: https://www.aalto.fi/sites/default/files/2025-08/OQS_Lecturs_all_2025.pdf

From single photon detection to quantum reservoir computing  in a superconducting qubit array embedded in a microwave cavity

We review theoretically the quantum electrodynamics of a set of superconducting qubits inserted into a cavity connected to 2 or 3 ports of microwave waveguides. In the case of a detection of a fainted microwave beam, an additional probe beam is used to analyze the resulting distribution of the photon number inside the cavity by means of the Stark shift effect. The obtained theory is compared with the experimental data on the response of the probe signal to the photon number. We calculate the fluorescence radiation resulting from the non-linear behavior of the qubits. We examine the design possibilities of this system for generating entangled quantum states that could be useful for quantum reservoir computing. 

Slides available here: https://www.aalto.fi/sites/default/files/2025-09/qrc2025talk.pdf

Slides available here: https://www.aalto.fi/en/media/446013

Analysing Reservoir Computing Through the Lens of Filter Theory

This talk will provide a pedagogical introduction to the theory of filters [Wiener 1964, Wiener 1958] and its connection to reservoir computing. Although this connection is relatively straightforward, especially in light of work on Liquid State Machines [Maass 2007, Maass 2011], it is largely overlooked in more recent literature on reservoir computing [Lukosevicius 2012, Tanaka 2019, Nakajima 2020, Ghosh 2021].

We will first introduce key aspects of filter theory and then demonstrate how reservoir computing aligns with these theoretical insights. In particular, we will translate important reservoir computing concepts, such as «  fading memory » , «  echo state property » , and «  echo state function »  [Jaeger 2001, Yildiz 2012], into the language of filter theory.

The main conclusions of this comparison are as follows:

• For a given task, there exists a unique reservoir that minimizes the mean-squared error between the predicted and expected outputs.
• A given reservoir can be interpreted as a sub-optimal nonlinear filter or, put differently, a partially optimal nonlinear filter.
• For a given task, if the reservoir exhibits the fading memory property, its mean-squared error is bounded by that of a nonlinear filter of the same order of nonlinearity.

This comparison also sheds light on why, for many tasks, prediction performance of the reservoir computing algorithm improves near unstable dynamical regimes, often referred to as «  The edge of instability »  [Hsu 2023], or as «  The edge of chaos »  [H. Jäger in Nakajima 2021], and eventually as «  The edge of the echo state property »  [H. Jäger in Nakajima 2021].

[Ghosh 2021] Ghosh, S., Nakajima, K., Krisnanda, T., Fujii, K., & Liew, T. C. (2021). Quantum neuromorphic computing with reservoir computing networks. Advanced Quantum Technologies, 4(9), 2100053.

[Hsu 2023] Hsu, A., & Marzen, S. E. (2023). Strange properties of linear reservoirs in the infinitely large limit for prediction of continuous-time signals. Journal of Statistical Physics, 190(2), 32.

[Jaeger 2001] Jaeger, H. (2001). The “echo state” approach to analysing and training recurrent neural networks-with an erratum note. Bonn, Germany: German national research center for information technology gmd technical report, 148(34), 13.

[Lukosevicius 2012]: Lukoševičius, M., Jaeger, H., & Schrauwen, B. (2012). Reservoir computing trends. KI-Künstliche Intelligenz, 26(4), 365-371.

[Maass 2007] Maass, W., Joshi, P., & Sontag, E. D. (2007). Computational aspects of feedback in neural circuits. PLoS computational biology, 3(1), e165.

[Maass 2011] Maass, W. (2011). Liquid state machines: motivation, theory, and applications. Computability in context: computation and logic in the real world, 275-296.

[Nakajima 2020] Nakajima, K. (2020). Physical reservoir computing—an introductory perspective. Japanese Journal of Applied Physics, 59(6), 060501.

[Nakajima 2021] Nakajima, K., & Fischer, I. (2021). Reservoir computing. Singapore: Springer Singapore.

[Tanaka 2019] Tanaka, G., Yamane, T., Héroux, J. B., Nakane, R., Kanazawa, N., Takeda, S., ... & Hirose, A. (2019). Recent advances in physical reservoir computing: A review. Neural Networks, 115, 100-123.

[Wiener 1964] Wiener, N. (1964). Extrapolation, interpolation, and smoothing of stationary time series. The MIT press.  Technology Press of Massachusetts Institute of Technology, 1964. ISBN: 9780262730051

[Wiener 1958] Wiener, N. (1958). Nonlinear problems in random theory. Mit Press. Technology Press of Massachusetts Institute of Technology, 1958. ISBN: 9780262230049

[Yildiz 2012] Yildiz, I. B., Jaeger, H., & Kiebel, S. J. (2012). Re-visiting the echo state property. Neural networks, 35, 1-9.

Density dependence of thermal conductivity in nanoporous and amorphous
carbon with machine-learned molecular dynamics

Yanzhou Wang , Zheyong Fan , Ping Qian , Miguel A. Caro and Tapio Ala-
Nissilä

Disordered forms of carbon are an important class of materials for applications such
as thermal management. However, a comprehensive theoretical understanding of the
structural dependence of thermal transport and the underlying microscopic
mechanisms is lacking. Here we study the structure-dependent thermal conductivity of
disordered carbon^[1] by employing molecular dynamics (MD) simulations driven by a
machine-learned interatomic potential based on the efficient neuroevolution potential
approach^[2]. Using large-scale MD simulations^[3], we generate realistic nanoporous
carbon (NP-C) samples with density varying from 0.3 to 1.5 g cm^-3 dominated by
sp² motifs, and amorphous carbon (a-C) samples with density varying from 1.5 to 3.5
g cm^-3 exhibiting mixed sp² and sp³ motifs. Structural properties including
short- and medium-range order are characterized by atomic coordination, pair
correlation function, angular distribution function and structure factor. Using the
homogeneous nonequilibrium MD method and the associated quantum-statistical
correction scheme, we predict a linear and a superlinear density dependence of
thermal conductivity for NP-C and a-C, respectively, in good agreement with relevant
experiments. The distinct density dependences are attributed to the different impacts
of the sp² and sp³ motifs on the spectral heat capacity, vibrational mean free paths
and group velocity. We additionally highlight the significant role of structural order in
regulating the thermal conductivity of disordered carbon.
 

[1] Wang, Yanzhou, et al. "Density dependence of thermal conductivity in nanoporous
and amorphous carbon with machine-learned molecular dynamics." Physical Review B
111.9 (2025): 094205.
[2] Fan, Zheyong, et al. "Neuroevolution machine learning potentials: Combining high
accuracy and low cost in atomistic simulations and application to heat transport."
Physical Review B 104.10 (2021): 104309.
[3] Fan, Zheyong, et al. "Efficient molecular dynamics simulations with many-body
potentials on graphics processing units." Computer Physics Communications 218
(2017): 10-16.

Numerical investigation of minimal quantum reservoirs 

We present a quantum reservoir computing framework using minimal single-qubit systems for signal processing and time series prediction. Data encoded into Hamiltonians naturally transforms into the Fourier domain through the unitary time evolution, with  measurements extracting cosine and sine frequency components. Our experiments show strong performance in signal reconstruction and time series tasks. We were able to confirm the idea that qubits naturally decompose the learned signal into Fourier components. 

Entropy and SVD analyses confirm efficient compression and learning so that we can determine the minimum number of samples we can reconstruct from a signal. We investigated how sampling affects the signal reconstruction accuracy barrier.  We have succeeded in creating a single qubit recursive perdito and investigated the relationship between the target signal and the sampling window.

Understanding Decoherence of the Boron Vacancy Center in Hexagonal Boron Nitride

András Tárkányi_^1,2, Viktor Ivády<sup>_1,2

1 Department of Physics of Complex Systems, Eötvös Loránd University,
Egyetem tér 1-3, H-1053 Budapest, Hungary
2 MTAELTE Lendület "Momentum" NewQubit Research Group, Pázmány Péter, Sétány 1/A, 1117 Budapest, Hungary</sup>

Hexagonal boron nitride (hBN) has emerged as a significant material for quantum sensing,
particularly due to its ability to host spin active defects, such as the negatively charged boron
vacancy (V—B center). The optical addressability of the V–B center and hBN’s 2D structure enable high spatial resolution and integration into various platforms.

However, decoherence due to the strong magnetic noise in hBN imposes fundamental limitations
on the sensitivity of V–B center-based applications. Understanding the phenomena behind
decoherence and identifying parameter settings that provide the highest performance are
essential for advancing V–B sensors.

In this study, we employ state-of-the-art computational methods to investigate the decoherence
of the V–B center in hexagonal boron nitride across a wide range of magnetic field values
from 0 T up to 3 T. The provided in-depth numerical and analytical analysis reveals an intricate
interplay of various decoherence mechanisms.

We identify five distinct magnetic field regions governed by different types of magnetic
interactions with and within the abundant nuclear spin bath. In addition to magnetic field, the
effects of zero-field splitting, nuclear polarization, and different hyperfine coupling terms are
studied, representing an important step forward in utilizing V–B ensembles in sensing.

In particular, this study proposes operation in the moderate 180–350 mT magnetic field
range in chemically pure h¹¹B¹⁵N samples, where the coherence time can reach 1–20 microseconds, significantly exceeding the O(100 ns) low-field T₂ values.

Preprint available here: https://arxiv.org/pdf/2505.03292

Understanding the environment-driven spectral drift of semiconductor
quantum defects

Oscar Bulancea-Lindvall_{^{1, 2}}, Danial Shafizadeh_¹, Nguyen Tien Son_¹, and Igor A. Abrikosov_¹

^{1 Linköping University, IFM, SE-58183 Linköping, Sweden
2 MTA–ELTE Lendület ”Momentum” NewQubit Research Group, Pázmany Péter, Sétány 1/A, 1117 Budapest, Hungary}

Defects in wide band-gap semiconductors such as silicon carbide (SiC) are of high interest in various areas of quantum technology, utilizing their spin-optical properties for highly reliable single photon generation as well as photo-driven sensing schemes. Defects are susceptible to its solid-state environment, while simultaneously exhibiting coherent quantum states even up to room temperature, providing excellent opportunities for environment-driven dynamics and allowing for spectral tuning by external and host stimuli. However, for the same reasons, defects can experience great variation in their observed photoluminescence signals, leading to increased linewidths and spectral drift that require calibration and careful design of the host material for reliable use of the defect. One leading attribution to the spectral drift is the ionization of electrically active defects in the local environment created together with the central defect during irradiation and/or implantation. In this study, we apply first-principle simulations such as density functional theory, and statistical models of the defect environment, to model and estimate the size and behavior of the spectral drift from local electron sources for the silicon vacancy (V_Si) in 4H-SiC, a highly promising quantum defect emitting in the near-infrared.

Coherent Interaction-Free Detection with Superconducting Qutrits

Interaction-free measurement (IFM) enables detection without energy exchange. We implement a fully coherent IFM protocol using a transmon qutrit, inferring the presence of a resonant microwave pulse without exciting the third level. Unlike conventional IFM schemes based on projective measurements, our protocol uses unitary evolution, yielding higher detection efficiency and robustness to experimental imperfections. We also demonstrate IFM-based noise sensing, where the qutrit outperforms qubit sensors in detecting amplitude and phase noise and revealing noise correlations. These results showcase the advantages of coherent quantum protocols for minimally invasive detection and precision metrology.

From Pixels to Qubits: On-demand Game Level Generation with Quantum Reservoir Computing

We propose a quantum reservoir computing (QRC) method for procedural content generation (PCG) in games, adapted from music generation to sequential level design. Using minimal training data on Super Mario Bros and a custom Roblox lobby, QRC produces novel yet coherent layouts controllable via a temperature parameter. It outperforms Markov and uncorrelated baselines in balancing originality and gameplay integrity, and supports parallel, real‑time generation within noisy intermediate‑scale quantum (NISQ) hardware limits. This highlights QRC’s potential for fast, adaptive game content on emerging quantum devices.

Predicting Mechanical Properties using Coordinate Free Representations

Timothy H Lees, Abhijith S Parackal, Florian Trybel and Rickard Armiento

Recent advances in machine learning have significantly accelerated materials discovery. Despite these advances, the space of all possible crystal structures is enormous, and full exploration is computationally infeasible. Exploring the combinatorial space of Wyckoff positions is a more tractable problem. The WREN (Wyckoff REpresentation regressioN) framework can be used to efficiently navigate this space. While WREN has proven highly effective in relating symmetry properties to formation energies, we extend its application to mechanical properties. Specifically, we predict the essential mechanical properties of bulk (K) and shear (G) modulus by descriptors that are independent of atomic positions.

Dynamics of a dissipative Kerr Cavity-Oscillator system in phase space

Controlled PT symmetric loss and gain mediated Quantum Mpemba Effect in a driven dissipative Kerr nonlinear oscillator - towards better computing

Dynamical Learning and Quantum Memory with Non-Hermitian Many-Body Systems

Non-Hermitian (NH) quantum systems, arising naturally from continuous measurement and postselection, host rich dynamical phases that can be further realized through engineered dissipation which make them an increasingly promising platform for many-body physics and quantum information processing. Within the quantum measurement trajectory framework, the spectral properties of effective NH Hamiltonians can be tuned via measurement strength, disorder, and interactions. With sufficiently high dissipation, these systems experience a spectral phase transition—a spontaneous breaking of parity–time symmetry—distinguished by the appearance of complex eigenvalues and exceptional points.

Here it is shown that such an exceptional point marks also a computational phase transition in learnability where the system abruptly shifts from a non-learning phase with functionally absent memory capacity to a learning phase characterized by finite memory, contractive dynamics, and accurate temporal prediction. In parameter space this transition defines a controllable "learnability line"—the position of which can be tuned using local disorder and interaction strength. Using pseudo-Hermitian interacting spin systems on random graphs as a NH reservoir we demonstrate this where dynamical phases, entanglement properties, and learning performance are shown to be closely linked.

These results potentially indicate the emergence of computation as a dynamical phase transition in open quantum systems. Beyond the exceptional point the NH reservoir undergoes a type of reorganization into a memory-capable learning phase where disorder serves to prevent collapse and enriches the structure of the quantum state space. Notably, moderate disorder and interactions in addition to reducing the cost of simulation also stabilize learning performance, establishing non-Hermitian quantum reservoirs as an efficient and extensible paradigm for temporal quantum machine learning.