Efficiently manipulating Pauli strings with PauliArray

• URL: http://arxiv.org/abs/2405.19287v1
• Date: Wed, 29 May 2024 17:18:08 GMT
• Title: Efficiently manipulating Pauli strings with PauliArray
• Authors: Maxime Dion, Tania Belabbas, Nolan Bastien,
• Abstract summary: Pauli matrices and Pauli strings are widely used in quantum computing. It is important to have a well-rounded, versatile and efficient tool to handle a large number of Pauli strings and operators expressed in this basis. This library introduces data structures to represent arrays of Pauli strings and operators as well as various methods to modify and combine them.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Pauli matrices and Pauli strings are widely used in quantum computing. These mathematical objects are useful to describe or manipulate the quantum state of qubits. They offer a convenient basis to express operators and observables used in different problem instances such as molecular simulation and combinatorial optimization. Therefore, it is important to have a well-rounded, versatile and efficient tool to handle a large number of Pauli strings and operators expressed in this basis. This is the objective behind the development of the PauliArray library presented in this work. This library introduces data structures to represent arrays of Pauli strings and operators as well as various methods to modify and combine them. Built using NumPy, PauliArray offers fast operations and the ability to use broadcasting to easily carry out otherwise cumbersome manipulations. Applications to the fermion-to-qubit mapping, to the estimation of expectation values and to the computation of commutators are considered to illustrate how PauliArray can simplify some relevant tasks and accomplish them faster than current libraries.

Related papers

• Pauli Transfer Matrices [0.0]
  Pauli transfer matrices show the action of a linear map in the $n$-qubit Pauli basis. We propose new algorithms that make explicit use of the tensor product structure of the Pauli basis.
  arXiv  Detail & Related papers  (2024-11-01T11:52:51Z)
• Quantum many-body simulations with PauliStrings.jl [0.0]
  We present the Julia package PauliStrings for quantum many-body simulations. It performs fast operations on the Pauli group by encoding Pauli strings in binary. We show that this representation allows for easy encoding of any geometry.
  arXiv  Detail & Related papers  (2024-10-12T21:18:47Z)
• Decomposing dense matrices into dense Pauli tensors [0.0]
  We derive a fixed-memory, branchless algorithm to compute the inner product between a 2N-by-2N complex matrix and an N-term Pauli tensor in O(2N) time. Our scheme permits the embarrassingly parallel decomposition of a matrix into a weighted sum of Pauli strings in O(8N) time.
  arXiv  Detail & Related papers  (2024-01-29T18:18:11Z)
• The Basis of Design Tools for Quantum Computing: Arrays, Decision Diagrams, Tensor Networks, and ZX-Calculus [55.58528469973086]
  Quantum computers promise to efficiently solve important problems classical computers never will. A fully automated quantum software stack needs to be developed. This work provides a look "under the hood" of today's tools and showcases how these means are utilized in them, e.g., for simulation, compilation, and verification of quantum circuits.
  arXiv  Detail & Related papers  (2023-01-10T19:00:00Z)
• PauliComposer: Compute Tensor Products of Pauli Matrices Efficiently [0.0]
  We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. As a side product, we provide an optimized method for one key calculus in quantum simulations: the Pauli basis decomposition of Hamiltonians.
  arXiv  Detail & Related papers  (2023-01-02T08:48:47Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers [0.0]
  We prove the obtainable lower-bound for the number of qubits needed to represent such Pauli operations. We provide a procedure for determining such a set of minimal register Pauli operations.
  arXiv  Detail & Related papers  (2022-06-27T04:22:30Z)
• Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-calculus [55.2480439325792]
  Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. We refine the PBS-calculus, a graphical language for coherent control inspired by quantum optics.
  arXiv  Detail & Related papers  (2022-02-10T18:59:52Z)
• Coherent randomized benchmarking [68.8204255655161]
  We show that superpositions of different random sequences rather than independent samples are used. We show that this leads to a uniform and simple protocol with significant advantages with respect to gates that can be benchmarked.
  arXiv  Detail & Related papers  (2020-10-26T18:00:34Z)
• Anchor & Transform: Learning Sparse Embeddings for Large Vocabularies [60.285091454321055]
  We design a simple and efficient embedding algorithm that learns a small set of anchor embeddings and a sparse transformation matrix. On text classification, language modeling, and movie recommendation benchmarks, we show that ANT is particularly suitable for large vocabulary sizes.
  arXiv  Detail & Related papers  (2020-03-18T13:07:51Z)
• Torch-Struct: Deep Structured Prediction Library [138.5262350501951]
  We introduce Torch-Struct, a library for structured prediction. Torch-Struct includes a broad collection of probabilistic structures accessed through a simple and flexible distribution-based API.
  arXiv  Detail & Related papers  (2020-02-03T16:43:02Z)

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.