Related papers: Quantum Cellular Automata, Tensor Networks, and Ar…
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local $\epsilon$-randomizing map with non-negative probability. The idea comes from a small…
A natural way to generalise tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product…
Quantum devices featuring mid-circuit measurement and reset capabilities, such as quantum computers and dual-species Rydberg quantum simulators, enable the realization of quantum cellular automata. These systems evolve in discrete time…
We investigate the quantum capacity of noisy quantum channels which can be represented by coupling a system to an effectively small environment. A capacity formula is derived for all cases where both system and environment are…
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to…
Quantum networks of quantum objects promise to be exponentially more powerful than the objects considered independently. To live up to this promise will require the development of error mitigation and correction strategies to preserve…
There have been several non-axiomatic approaches taken to define Quantum Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we first show that any QCA can be put into the…
Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear…
In this paper we continue and extend the investigations of the ensembles of random physical states introduced in A. Hamma et al. [ http://prl.aps.org/abstract/PRL/v109/i4/e040502 Phys. Rev. Lett. 109, 040502 (2012)]. These ensembles are…
If the systems of quantum theory are thought of as elementary information carriers in the first place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
In this paper, we study linear cellular automata (CAs) on Cayley tree of order 2 over the field $\mathbb F_p$ (the set of prime numbers modulo $p$). We construct the rule matrix corresponding to finite cellular automata on Cayley tree.…
Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
An important question to be addressed regarding system control on a time interval $[0, T]$ is whether some particular target state in the configuration space is reachable from a given initial state. When the target of interest refers only…
An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set…