Related papers: State complexity and quantum computation
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing…
Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
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…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
We investigate the implementation of photonic cluster state generation protocols using quantum metasurfaces comprising sub-wavelength atomic arrays which enables quantum-controlled reflectivity. These cluster states are generated using…
Cluster states for measurement-based quantum computing can be created with entangling operations of arbitrary low success probability. This will place a lower bound on the minimum lifetime of the qubits used in the implementation. Here, we…
Recently, quantum convolutional neural networks (QCNNs) are proposed, harnessing the power of quantum computing for faster training compared to the classical counterparts. However, this framework for deep learning also relies on multiple…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
The tree reconstruction problem is to collect and analyze massive data at the $n$th level of the tree, to identify whether there is non-vanishing information of the root, as $n$ goes to infinity. Its connection to the clustering problem in…
For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures…
A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer…
Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how…
We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…