Related papers: Encoding Hypergraphs into Quantum States
Graph states are a large class of multipartite entangled quantum states that form the basis of schemes for quantum computation, communication, error correction, metrology, and more. In this work, we consider verification of graph states…
Cubelike graphs are the Cayley graphs of the elementary abelian group (Z_2)^n (e.g., the hypercube is a cubelike graph). We give conditions for perfect state transfer between two particles in quantum networks modeled by a large class of…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure - the stabilizer group - encodes all possible…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…
Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML,…
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a…
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC)…
We discuss representations and colorings of orthogonality hypergraphs in terms of their two-valued states interpretable as classical truth assignments. Such hypergraphs, if they allow for a faithful orthogonal representation, have quantum…
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…
Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize…
Fathoming out quantum state space is a challenging endeavor due to its exponentially growing dimensionality. At the expense of being bound in its expressiveness, the discrete and finite subspace of graph states is easier to investigate via…
It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across \Omega(n \log n) coset states. One of the only known models…
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized…
We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see for example how it can be used…
A graph is said to exhibit perfect state transfer (PST) if one of its corresponding Hamiltonian matrices, which are based on the vertex-edge structure of the graph, gives rise to PST in a quantum information-theoretic context, namely with…
One of the interesting topics in quantum contextuality is the construction for various non-contextual inequalities. By introducing a new structure called hyper-graph, we present a general method, which seems to be analytic and extensible,…
Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli…