Arunava Majumder, Marius Krumm, Tina Radkohl et al.
Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and unitary, but are rather augmented with probabilistic byproducts. Yet, the main algorithmic use of MBQC so far has been to completely counteract this probabilistic nature in order to simulate unitary computations expressed in the circuit model. In this work, we propose designing MBQC algorithms that embrace this inherent randomness and treat the random byproducts in MBQC as a resource for computation. As a natural application where randomness can be beneficial, we consider generative modeling, a task in machine learning centered around generating complex probability distributions. To address this task, we propose a variational MBQC algorithm equipped with control parameters that allow one to directly adjust the degree of randomness to be admitted in the computation. Our algebraic and numerical findings indicate that this additional randomness can lead to significant gains in expressivity and learning performance for certain generative modeling tasks, respectively. These results highlight the potential advantages in exploiting the inherent randomness of MBQC and motivate further research into MBQC-based algorithms.
Lea M. Trenkwalder, Andrea López Incera, Hendrik Poulsen Nautrup et al.
In recent years, reinforcement learning (RL) has become increasingly successful in its application to science and the process of scientific discovery in general. However, while RL algorithms learn to solve increasingly complex problems, interpreting the solutions they provide becomes ever more challenging. In this work, we gain insights into an RL agent's learned behavior through a post-hoc analysis based on sequence mining and clustering. Specifically, frequent and compact subroutines, used by the agent to solve a given task, are distilled as gadgets and then grouped by various metrics. This process of gadget discovery develops in three stages: First, we use an RL agent to generate data, then, we employ a mining algorithm to extract gadgets and finally, the obtained gadgets are grouped by a density-based clustering algorithm. We demonstrate our method by applying it to two quantum-inspired RL environments. First, we consider simulated quantum optics experiments for the design of high-dimensional multipartite entangled states where the algorithm finds gadgets that correspond to modern interferometer setups. Second, we consider a circuit-based quantum computing environment where the algorithm discovers various gadgets for quantum information processing, such as quantum teleportation. This approach for analyzing the policy of a learned agent is agent and environment agnostic and can yield interesting insights into any agent's policy.
Arunava Majumder, Hendrik Poulsen Nautrup, Hans J. Briegel
Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as $N \times D$, where $N$ is the number of logical qubits (width) and $D$ is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.
Paulin de Schoulepnikoff, Hendrik Poulsen Nautrup, Hans J. Briegel et al.
Interpretable machine learning techniques are becoming essential tools for extracting physical insights from complex quantum data. We build on recent advances in variational autoencoders to demonstrate that such models can learn physically meaningful and interpretable representations from a broad class of unlabeled quantum datasets. From raw measurement data alone, the learned representation reveals rich information about the underlying structure of quantum phase spaces. We further augment the learning pipeline with symbolic methods, enabling the discovery of compact analytical descriptors that serve as order parameters for the distinct regimes emerging in the learned representations. We demonstrate the framework on experimental Rydberg-atom snapshots, classical shadows of the cluster Ising model, and hybrid discrete-continuous fermionic data, revealing previously unreported phenomena such as a corner-ordering pattern in the Rydberg arrays. These results establish a general framework for the automated and interpretable discovery of physical laws from diverse quantum datasets. All methods are available through qdisc, an open-source Python library designed to make these tools accessible to the broader community.
Measurement-based quantum computation (MBQC) is a paradigm for quantum computation where computation is driven by local measurements on a suitably entangled resource state. In this work we show that MBQC is related to a model of quantum computation based on Clifford quantum cellular automata (CQCA). Specifically, we show that certain MBQCs can be directly constructed from CQCAs which yields a simple and intuitive circuit model representation of MBQC in terms of quantum computation based on CQCA. We apply this description to construct various MBQC-based Ansätze for parameterized quantum circuits, demonstrating that the different Ansätze may lead to significantly different performances on different learning tasks. In this way, MBQC yields a family of Hardware-efficient Ansätze that may be adapted to specific problem settings and is particularly well suited for architectures with translationally invariant gates such as neutral atoms.
Paulin de Schoulepnikoff, Gorka Muñoz-Gil, Hendrik Poulsen Nautrup et al.
Interpretable machine learning is rapidly becoming a crucial tool for scientific discovery. Among existing approaches, variational autoencoders (VAEs) have shown promise in extracting the hidden physical features of some input data, with no supervision nor prior knowledge of the system at study. Yet, the ability of VAEs to create meaningful, interpretable representations relies on their accurate approximation of the underlying probability distribution of their input. When dealing with quantum data, VAEs must hence account for its intrinsic randomness and complex correlations. While VAEs have been previously applied to quantum data, they have often neglected its probabilistic nature, hindering the extraction of meaningful physical descriptors. Here, we demonstrate that two key modifications enable VAEs to learn physically meaningful latent representations: a decoder capable of faithfully reproduce quantum states and a probabilistic loss tailored to this task. Using benchmark quantum spin models, we identify regimes where standard methods fail while the representations learned by our approach remain meaningful and interpretable. Applied to experimental data from Rydberg atom arrays, the model autonomously uncovers the phase structure without access to prior labels, Hamiltonian details, or knowledge of relevant order parameters, highlighting its potential as an unsupervised and interpretable tool for the study of quantum systems.
Sofiene Jerbi, Lukas J. Fiderer, Hendrik Poulsen Nautrup et al.
Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and studied extensively. Yet, our understanding of how these models compare, both mutually and to classical models, remains limited. In this work, we identify a constructive framework that captures all standard models based on parametrized quantum circuits: that of linear quantum models. In particular, we show using tools from quantum information theory how data re-uploading circuits, an apparent outlier of this framework, can be efficiently mapped into the simpler picture of linear models in quantum Hilbert spaces. Furthermore, we analyze the experimentally-relevant resource requirements of these models in terms of qubit number and amount of data needed to learn. Based on recent results from classical machine learning, we prove that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points. Our results provide a more comprehensive view of quantum machine learning models as well as insights on the compatibility of different models with NISQ constraints.
Hendrik Poulsen Nautrup, Tony Metger, Raban Iten et al.
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical structure present in the training data; however, these methods do not allow us to specify explicit and operationally meaningful requirements on the representation. Here, we present a neural network architecture based on the notion that agents dealing with different aspects of a physical system should be able to communicate relevant information as efficiently as possible to one another. This produces representations that separate different parameters which are useful for making statements about the physical system in different experimental settings. We present examples involving both classical and quantum physics. For instance, our architecture finds a compact representation of an arbitrary two-qubit system that separates local parameters from parameters describing quantum correlations. We further show that this method can be combined with reinforcement learning to enable representation learning within interactive scenarios where agents need to explore experimental settings to identify relevant variables.
Alexey A. Melnikov, Hendrik Poulsen Nautrup, Mario Krenn et al.
How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. A major motivation for the present work is the unknown reachability of various entanglement classes in quantum experiments. We investigate this question by using the projective simulation model, a physics-oriented approach to artificial intelligence. In our approach, the projective simulation system is challenged to design complex photonic quantum experiments that produce high-dimensional entangled multiphoton states, which are of high interest in modern quantum experiments. The artificial intelligence system learns to create a variety of entangled states, and improves the efficiency of their realization. In the process, the system autonomously (re)discovers experimental techniques which are only now becoming standard in modern quantum optical experiments - a trait which was not explicitly demanded from the system but emerged through the process of learning. Such features highlight the possibility that machines could have a significantly more creative role in future research.