Categorical computation

• URL: http://arxiv.org/abs/2102.04814v2
• Date: Mon, 6 Feb 2023 12:20:46 GMT
• Title: Categorical computation
• Authors: Liang Kong and Hao Zheng
• Abstract summary: In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors between two (higher) categories.
• Score: 7.452142897055281
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors between two (higher) categories. If from Turing computing to quantum computing is the first quantization of computation, then this new scheme can be viewed as the second quantization of computation. The fundamental problem in realizing this idea is how to realize a (higher) functor physically. We provide a theoretical idea of realizing (higher) functors physically based on the physics of topological orders.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Quantum vs. Symplectic Computers [0.0]
  symplectic computation involves a sequence of symplectic transformations and measurements. The Schr"odinger equation in its standard complex form describes the unitary evolution of a quantum system. This quantum-symplectic duality can be leveraged to enhance the capabilities of quantum and symplectic computers.
  arXiv  Detail & Related papers  (2024-07-17T17:29:41Z)
• Supervised binary classification of small-scale digits images with a trapped-ion quantum processor [56.089799129458875]
  We show that a quantum processor can correctly solve the basic classification task considered. With the increase of the capabilities quantum processors, they can become a useful tool for machine learning.
  arXiv  Detail & Related papers  (2024-06-17T18:20:51Z)
• Quantum computing topological invariants of two-dimensional quantum matter [0.0]
  We present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. First algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. Second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits.
  arXiv  Detail & Related papers  (2024-04-09T06:22:50Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Towards Quantum Computational Mechanics [1.530480694206666]
  We show how quantum computing can be used to solve representative element volume (RVE) problems in computational homogenisation. Our quantum RVE solver attains exponential acceleration with respect to classical solvers.
  arXiv  Detail & Related papers  (2023-12-06T12:53:02Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Benchmarking Small-Scale Quantum Devices on Computing Graph Edit Distance [52.77024349608834]
  Graph Edit Distance (GED) measures the degree of (dis)similarity between two graphs in terms of the operations needed to make them identical. In this paper we present a comparative study of two quantum approaches to computing GED.
  arXiv  Detail & Related papers  (2021-11-19T12:35:26Z)
• Quantum algorithmic differentiation [0.0]
  We present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step.
  arXiv  Detail & Related papers  (2020-06-23T22:52:22Z)
• Quadratic Sieve Factorization Quantum Algorithm and its Simulation [16.296638292223843]
  We have designed a quantum variant of the second fastest classical factorization algorithm named "Quadratic Sieve" We have constructed the simulation framework of quantized quadratic sieve algorithm using high-level programming language Mathematica.
  arXiv  Detail & Related papers  (2020-05-24T07:14:19Z)
• An Application of Quantum Annealing Computing to Seismic Inversion [55.41644538483948]
  We apply a quantum algorithm to a D-Wave quantum annealer to solve a small scale seismic inversions problem. The accuracy achieved by the quantum computer is at least as good as that of the classical computer.
  arXiv  Detail & Related papers  (2020-05-06T14:18:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.