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In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
The ability to identify cause-effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against…
In many predictive decision-making scenarios, such as credit scoring and academic testing, a decision-maker must construct a model that accounts for agents' propensity to "game" the decision rule by changing their features so as to receive…
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here we…
We consider online algorithms as a request-answer game. An adversary that generates input requests, and an online algorithm answers. We consider a generalized version of the game that has a buffer of limited size. The adversary loads data…
We study a version of the minority game in which one agent is allowed to join the game in a random fashion. It is shown that in the crowded regime, i.e., for small values of the memory size $m$ of the agents in the population, the agent…
The human mind is known to be sensitive to complexity. For instance, the visual system reconstructs hidden parts of objects following a principle of maximum simplicity. We suggest here that higher cognitive processes, such as the selection…
How do incentive levels affect strategic behaviour? We address this with an experiment that separately identifies own- and opponent-incentive effects in two dominance-solvable games that differ in strategic complexity. Higher own incentives…
When humans are subject to an algorithmic decision system, they can strategically adjust their behavior accordingly (``game'' the system). While a growing line of literature on strategic classification has used game-theoretic modeling to…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced,…
Humans spend a remarkable fraction of waking life engaged in acts of "mental time travel". We dwell on our actions in the past and experience satisfaction or regret. More than merely autobiographical storytelling, we use these event…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
As a schematic model of the complexity economic agents are confronted with, we introduce the ``SK-game'', a discrete time binary choice model inspired from mean-field spin-glasses. We show that even in a completely static environment,…