Related papers: Counting anticommuting Pauli pairs in linear time
Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of operators allows for fewer measurements and an overall speedup of the…
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 performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained…
Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed…
Qudits with local dimension $d>2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group…
We show how to determine whether a given pattern p of length m occurs in a given text t of length n in ${\tilde O}(\sqrt{n}+\sqrt{m})$\footnote{${\tilde O}$ allows for logarithmic factors in m and $n/m$} time, with inverse polynomial…
The realisation of large-scale quantum computing is no longer simply a hardware question. The rapid development of quantum technology has resulted in dozens of control and programming problems that should be directed towards the classical…
We develop a generalized framework for constructing many-body-interaction operations either in linear time, or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given in particular for Pauli strings,…
A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N-qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting…
We present a classical algorithm based on Pauli propagation for estimating expectation values of arbitrary observables on random unstructured quantum circuits across all circuit architectures and depths, including those with all-to-all…
The commutation relations between the generalized Pauli operators of N-qudits (i. e., N p-level quantum systems), and the structure of their maximal sets of commuting bases, follow a nice graph theoretical/geometrical pattern. One may…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Efficiently calculating the low-lying eigenvalues of Hamiltonians, written as sums of Pauli operators, is a fundamental challenge in quantum computing. While various methods have been proposed to reduce the complexity of quantum circuits…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead…
The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical…
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 and explicitly construct a quantum code we coin a "Pauli Manipulation Detection" code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in…
A general error correction method is presented which is capable of correcting coherent errors originating from static residual inter-qubit couplings in a quantum computer. It is based on a randomization of static imperfections in a…
Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly,…