Related papers: Phase map decompositions for unitaries
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We introduce a novel approach that exploits the intersection of quantum computing, machine learning and reduced density matrix functional theory to leverage the potential of quantum computing to improve simulations of interacting quantum…
The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and…
We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential $\mu$ and effective magnetic…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
One-way quantum computation, or measurement-based quantum computation, is a universal model of quantum computation alternative to the circuit model. The computation progresses by measurements of a pre-prepared resource state together with…
We consider graph states of arbitrary number of particles undergoing generic decoherence. We present methods to obtain lower and upper bounds for the system's entanglement in terms of that of considerably smaller subsystems. For an…
In one-way quantum computation (1WQC) model, an initial highly entangled state called a graph state is used to perform universal quantum computations by a sequence of adaptive single-qubit measurements and post-measurement Pauli-X and…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Quantum graph states are critical resources for various quantum algorithms, and also determine essential interconnections in distributed quantum computing. There are two schemes for generating graph states probabilistic scheme and…
Topological order has been proposed to go beyond Landau symmetry breaking theory for more than twenty years. But it is still a challenging problem to generally detect it in a generic many-body state. In this paper, we will introduce a…
Both completely positive and completely copositive maps stay decomposable under tensor powers, i.e under tensoring the linear map with itself. But are there other examples of maps with this property? We show that this is not the case: Any…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
We propose a method for decomposing continuous-variable operations into a universal gate set, without the use of any approximations. We fully characterize a set of transformations admitting exact decompositions and describe a process for…
We introduce the flag decomposition as a central tool for unitary synthesis. It lets us carve out a diagonal unitary with $2^n$ degrees of freedom in such a way that the remaining flag circuit is parametrized by the optimal number of…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
The problem of the estimation of multiple phases (or of commuting unitaries) is considered. This is a sub-model of the estimation of a completely unknown unitary operation where it has been shown in recent works that there are considerable…
Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation…