Related papers: Unitary Complexity and the Uhlmann Transformation …
Quantum information processing is the use of inherently quantum mechanical phenomena to perform information processing tasks that cannot be achieved using conventional classical information technologies. One famous example is quantum…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space…
Quantum entanglement is a key physical resource in quantum information processing that allows for performing basic quantum tasks such as teleportation and quantum key distribution, which are impossible in the classical world. Ever since the…
Classical-quantum computational complexity separations are an important motivation for the long-term development of digital quantum computers, but classical-quantum complexity equivalences are just as important in our present era of noisy…
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
The analysis of multiparticle quantum states is a central problem in quantum information processing. This task poses several challenges for experimenters and theoreticians. We give an overview over current problems and possible solutions…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…
Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent…
Being able to reliably transfer the quantum state from one system to another is crucial to developing quantum networks. A standard way to accomplish this transfer of information is by making use of an intermediate information carrier (e.g.,…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of…
This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum…
Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of…
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus…