Pauli Transfer Matrices

• URL: http://arxiv.org/abs/2411.00526v1
• Date: Fri, 01 Nov 2024 11:52:51 GMT
• Title: Pauli Transfer Matrices
• Authors: Lukas Hantzko, Lennart Binkowski, Sabhyata Gupta,
• Abstract summary: 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.
• Score: 0.0
• License:
• Abstract: Analysis of quantum processes, especially in the context of noise, errors, and decoherence is essential for the improvement of quantum devices. An intuitive representation of those processes modeled by quantum channels are Pauli transfer matrices. They display the action of a linear map in the $n$-qubit Pauli basis in a way, that is more intuitive, since Pauli strings are more tangible objects than the standard basis matrices. We set out to investigate classical algorithms that convert the various representations into Pauli transfer matrices. We propose new algorithms that make explicit use of the tensor product structure of the Pauli basis. They convert a quantum channel in a given representation (Chi or process matrix, Choi matrix, superoperator, or Kraus operators) to the corresponding Pauli transfer matrix. Moreover, the underlying principle can also be used to calculate the Pauli transfer matrix of other linear operations over $n$-qubit matrices such as left-, right-, and sandwich multiplication as well as forming the (anti-)commutator with a given operator. Finally, we investigate the runtime of these algorithms, derive their asymptotic scaling and demonstrate improved performance using instances with up to seven qubits.

Related papers

• Pauli Decomposition via the Fast Walsh-Hadamard Transform [0.0]
  We present a new exact and explicit formula for the Pauli string coefficients. We show that up to a permutation of the matrix elements, the decomposition coefficients are related to the original matrix by a multiplication of a generalised Hadamard matrix. A numerical implementation of our equation outperforms currently available solutions.
  arXiv  Detail & Related papers  (2024-08-12T14:56:45Z)
• Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
  We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems. The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
  arXiv  Detail & Related papers  (2024-08-02T10:15:26Z)
• Efficiently manipulating Pauli strings with PauliArray [0.0]
  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.
  arXiv  Detail & Related papers  (2024-05-29T17:18:08Z)
• A tree-approach Pauli decomposition algorithm with application to quantum computing [0.0]
  We propose an algorithm with a parallel implementation that optimize this decomposition using a tree approach. We also explain how some particular matrix structures can be exploited to reduce the number of operations.
  arXiv  Detail & Related papers  (2024-03-18T10:38:06Z)
• Polynomial-depth quantum algorithm for computing matrix determinant [46.13392585104221]
  We propose an algorithm for calculating the determinant of a square matrix, and construct a quantum circuit realizing it. Each row of the matrix is encoded as a pure state of some quantum system. The admitted matrix is therefore arbitrary up to the normalization of quantum states of those systems.
  arXiv  Detail & Related papers  (2024-01-29T23:23:27Z)
• 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)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• 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 algorithms for matrix operations and linear systems of equations [65.62256987706128]
  We propose quantum algorithms for matrix operations using the "Sender-Receiver" model. These quantum protocols can be used as subroutines in other quantum schemes.
  arXiv  Detail & Related papers  (2022-02-10T08:12:20Z)
• Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors [54.936314353063494]
  We provide recovery guarantees for a correlation-based optimization algorithm for robust 1-bit compressive sensing. We make use of a practical iterative algorithm, and perform numerical experiments on image datasets to corroborate our results.
  arXiv  Detail & Related papers  (2021-08-08T05:28:06Z)
• 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)

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.