Related papers: Wasserstein Complexity of Quantum Circuits
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
Despite advances in the development of quantum computers, the practical application of quantum algorithms requiring deep circuit depths or high-fidelity transformations remains outside the current range of the so-called noisy…
Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time…
Quantifying the effect of noise on unitary operations is an essential task in quantum information processing. We propose the quantum Wasserstein distance between unitary operations, which shows an explanation for quantum circuit complexity…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance…
Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
The complexity of a quantum gate, defined as the minimal number of elementary gates to build it, is an important concept in quantum information and computation. It is shown recently that the complexity of quantum gates built from random…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. Recently, the quantum Wasserstein distance emerged from the theory of quantum optimal transport as a promising…
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…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…
We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields.…