Related papers: Wasserstein Complexity of Quantum Circuits
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
Experimental implementations of quantum computer architectures are now being investigated in many different physical settings. The full set of requirements that must be met to make quantum computing a reality in the laboratory [1] is…
The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion…
Nielsen \cite{Nielsen05} recently asked the following question: "What is the minimal size quantum circuit required to exactly implement a specified $% \mathit{n}$-qubit unitary operation $U$, without the use of ancilla qubits?" Nielsen was…
Simulating quantum dynamics is one of the most promising applications of quantum computers. While the upper bound of the simulation cost has been extensively studied through various quantum algorithms, much less work has focused on…
We investigate here the optimal transportation problem on configuration space for the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is finite, there exists one unique optimal measure and that this…
This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum…
An extension to computational mechanics complexity measure is proposed in order to tackle quantum states complexity quantification. The method is applicable to any $n-$partite state of qudits through some simple modifications. A Werner…
Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the…
We establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations:…
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
Quantum circuit complexity has played a central role in recent advances in holography and many-body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real-time) framework. In a departure from standard…
We propose a method for the implementation of one-way quantum computing in superconducting circuits. Measurement-based quantum computing is a universal quantum computation paradigm in which an initial cluster-state provides the quantum…
Rapid development of quantum computing technology has led to a wide variety of sophisticated quantum devices. Benchmarking these systems becomes crucial for understanding their capabilities and paving the way for future advancements. The…
The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum…