Related papers: Fast generation of Pauli transfer matrices utilizi…
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. The strength of this strategy is…
Pauli channels are fundamental in the context of quantum computing as they model the simplest kind of noise in quantum devices. We propose a quantum algorithm for simulating Pauli channels and extend it to encompass Pauli dynamical maps…
Several linear algebra routines for quantum computing use a basis of tensor products of identity and Pauli operators to describe linear operators, and obtaining the coordinates for any given linear operator from its matrix representation…
This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…
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…
We present a tomographic protocol for the characterization of multiqubit quantum channels. We discuss a specific class of input states, for which the set of Pauli measurements at the output of the channel directly relates to its Pauli…
We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors…
Learning about physical systems from quantum-enhanced experiments, relying on a quantum memory and quantum processing, can outperform learning from experiments in which only classical memory and processing are available. Whereas quantum…
Pauli channels are ubiquitous in quantum information, both as a dominant noise source in many computing architectures and as a practical model for analyzing error correction and fault tolerance. Here we prove several results on efficiently…
Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, especially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
The Pauli matrices are 2-by-2 matrices that are very useful in quantum computing. They can be used as elementary gates in quantum circuits but also to decompose any matrix of $\mathbb{C}^{2^n \times 2^n}$ as a linear combination of tensor…
A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we…
We propose a new quantum computing formalism named Pauli quantum computing. In this formalism, we use the Pauli basis $I$ and $X$ on the non-diagonal blocks of density matrices to encode information and treat them as the computational basis…
We introduce an approach for estimating the expectation values of arbitrary $n$-qubit matrices $M \in \mathbb{C}^{2^n\times 2^n}$ on a quantum computer. In contrast to conventional methods like the Pauli decomposition that utilize $4^n$…
The Pauli strings appearing in the decomposition of an operator can be can be grouped into commuting families, reducing the number of quantum circuits needed to measure the expectation value of the operator. We detail an algorithm to…
As quantum devices continue to grow in size but remain affected by noise, it is crucial to determine when and how they can outperform classical computers on practical tasks. A central piece in this effort is to develop the most efficient…
The decomposition of a square matrix into a sum of Pauli strings is a classical pre-processing step required to realize many quantum algorithms. Such a decomposition requires significant computational resources for large matrices. We…
We present an abstract model of quantum computation, the "Pauli Fusion" model, whose primitive operations correspond closely to generators of the ZX calculus (a formal graphical language for quantum computing). The fundamental operations of…
We investigate the problem of predicting the output behavior of unknown quantum channels. Given query access to an $n$-qubit channel $E$ and an observable $O$, we aim to learn the mapping \begin{equation*} \rho \mapsto \mathrm{Tr}(O…