Related papers: State complexity and quantum computation
Tree size ($\rm{TS}$) is an interesting measure of complexity for multiqubit states: not only is it in principle computable, but one can obtain lower bounds for it. In this way, it has been possible to identify families of states whose…
Complexity is often invoked alongside size and mass as a characteristic of macroscopic quantum objects. In 2004, Aaronson introduced the \textit{tree size} (TS) as a computable measure of complexity and studied its basic properties. In this…
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
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…
The cluster state model for quantum computation [Phys. Rev. Lett. 86, 5188] outlines a scheme that allows one to use measurement on a large set of entangled quantum systems in what is known as a cluster state to undertake quantum…
Measurement-based quantum computing enables universal quantum computing with only adaptive single-qubit measurements on certain many-qubit states, such as the graph state, the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, and several…
We study how heralded qubit losses during the preparation of a two-dimensional cluster state, a universal resource state for one-way quantum computation, affect its computational power. Above the percolation threshold we present a…
Measurement based quantum computation requires the generation of a cluster state (quantum resource) prior to starting a computation. Generation of this entangled state can be difficult with many schemes already proposed. We present an…
We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt--rank width, a measure recently introduced to assess universality of resource states,…
The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We…
Quantum computation promises applications that are thought to be impossible with classical computation. To realize practical quantum computation, the following three properties will be necessary: universality, scalability, and…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
Tree tensor network states (TTNS) generalize the notion of having low Schmidt-rank to multipartite quantum states, through a parameter known as the bond dimension. This leads to succinct representations of quantum many-body systems with a…
Measurement-based quantum computation (MQC) is a paradigm for studying quantum computation using many-body entanglement and single-qubit measurements. While MQC has inspired wide-ranging discoveries throughout quantum information, our…
We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
Quantum computers can revolutionize science and technology, but their realization remains challenging across all platforms. A promising route to scalability is photonic measurement-based quantum computation, where single-qubit measurements…
Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a…