On machine creativity and the notion of free will

We discuss the possibility of freedom of action in embodied systems that are, with no exception and at all scales of their body, subject to physical law. We relate the discussion to a model of an artificial agent that exhibits a primitive notion of creativity and freedom in dealing with its environment, which is part of a recently introduced scheme of information processing called projective simulation. This provides an explicit proposal on how we can reconcile our understanding of universal physical law with the idea that higher biological entities can acquire a notion of freedom that allows them to increasingly detach themselves from a strict causal embedding into the surrounding world.Comment: 7 pages, 2 figure

Algorithmic complexity and entanglement of quantum states

We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.Comment: 4 pages. Replaced with published versio

Computational model underlying the one-way quantum computer

In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett. 86, 5188 (2001)]. The one-way quantum computer has the property that any quantum logic network can be simulated on it. Conversely, not all ways of quantum information processing that are possible with the one-way quantum computer can be understood properly in network model terms. We show that the logical depth is, for certain algorithms, lower than has so far been known for networks. For example, every quantum circuit in the Clifford group can be performed on the one-way quantum computer in a single step.Comment: 37 pages, 3 figures. Extended version. Some results generalized. Discussion of results adde

Quantum computing via measurements only

A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of these systems to a large number of qubits, essential for practical applications such as the Shor algorithm, represents a formidable challenge. Most of the current experiments are designed to implement sequences of highly controlled interactions between selected particles (qubits), thereby following models of a quantum computer as a (sequential) network of quantum logic gates. Here we propose a different model of a scalable quantum computer. In our model, the entire resource for the quantum computation is provided initially in form of a specific entangled state (a so-called cluster state) of a large number of qubits. Information is then written onto the cluster, processed, and read out form the cluster by one-particle measurements only. The entangled state of the cluster thus serves as a universal substrate for any quantum computation. Cluster states can be created efficiently in any system with a quantum Ising-type interaction (at very low temperatures) between two-state particles in a lattice configuration.Comment: 4 pages, 2 figure

Intra-molecular refrigeration in enzymes

We present a simple mechanism for intra-molecular refrigeration, where parts of a molecule are actively cooled below the environmental temperature. We discuss the potential role and applications of such a mechanism in biology, in particular in enzymatic reactions.Comment: 6 pages, 5 figure

Algorithmic complexity of quantum states

In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the string itself. We define the complexity of a quantum state by means of the classical description complexity of an (abstract) experimental procedure that allows us to prepare the state with a given fidelity. We argue that our definition satisfies the intuitive idea of complexity as a measure of ``how difficult'' it is to prepare a state. We apply this definition to give an upper bound on the algorithmic complexity of a number of states.Comment: 24 pages, no figure

Quantum machine learning with glow for episodic tasks and decision games

We consider a general class of models, where a reinforcement learning (RL) agent learns from cyclic interactions with an external environment via classical signals. Perceptual inputs are encoded as quantum states, which are subsequently transformed by a quantum channel representing the agent's memory, while the outcomes of measurements performed at the channel's output determine the agent's actions. The learning takes place via stepwise modifications of the channel properties. They are described by an update rule that is inspired by the projective simulation (PS) model and equipped with a glow mechanism that allows for a backpropagation of policy changes, analogous to the eligibility traces in RL and edge glow in PS. In this way, the model combines features of PS with the ability for generalization, offered by its physical embodiment as a quantum system. We apply the agent to various setups of an invasion game and a grid world, which serve as elementary model tasks allowing a direct comparison with a basic classical PS agent.Comment: 20 pages, 14 figure

Entanglement purification and quantum error correction

We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, which highlights the fact that entanglement purification is a fundamental tool in quantum information processing.Comment: review article; 48 pages, 18 figures; V2:published versio

Quantum mixing of Markov chains for special distributions

The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of classical mixing processes may offer a generic quadratic speed-up in realizing such stationary distributions. Such a speed-up would also imply a speed-up of a broad family of heuristic algorithms. However, a true quadratic speed up has thus far only been demonstrated for special classes of Markov chains. These results often presuppose a regular structure of the underlying graph of the Markov chain, and also a regularity in the transition probabilities. In this work, we demonstrate a true quadratic speed-up for a class of Markov chains where the restriction is only on the form of the stationary distribution, rather than directly on the Markov chain structure itself. In particular, we show efficient mixing can be achieved when it is beforehand known that the distribution is monotonically decreasing relative to a known order on the state space. Following this, we show that our approach extends to a wider class of distributions, where only a fraction of the shape of the distribution is known to be monotonic. Our approach is built on the Szegedy-type quantization of transition operators.Comment: 15 page

Computational Model for the One-Way Quantum Computer: Concepts and Summary

The one-way quantum computer (QCc) is a universal scheme of quantum computation consisting only of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. The computational model underlying the QCc is different from the quantum logic network model and it is based on different constituents. It has no quantum register and does not consist of quantum gates. The QCc is nevertheless quantum mechanical since it uses a highly entangled cluster state as the central physical resource. The scheme works by measuring quantum correlations of the universal cluster state.Comment: 9 pages, 4 figure