Related papers: Fast generation of Pauli transfer matrices utilizi…
Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
Quantum computers have enabled solving problems beyond the current computers' capabilities. However, this requires handling noise arising from unwanted interactions in these systems. Several protocols have been proposed to address efficient…
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
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 is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
The advent of fault-tolerant quantum computers marks a significant milestone, yet the development of practical quantum algorithms remains a critical challenge. Effective quantum algorithms are essential for leveraging the power of quantum…
The one-way model of Measurement-Based Quantum Computing and the gate-based circuit model give two different presentations of how quantum computation can be performed. There are known methods for converting any gate-based quantum circuit…
Transformations which convert between Fermionic modes and qubit operations have become a ubiquitous tool in quantum algorithms for simulating systems. Similarly, collections of Pauli operators might be obtained from solutions of non-local…
Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give…
In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of…
We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
Pauli-based computation (PBC) is a universal measurement-based quantum computation model steered by an adaptive sequence of independent and compatible Pauli measurements on separable magic-state qubits. Here, we propose several new…
Correlated noise is a critical failure mode in quantum error correction (QEC), as temporal memory and spatial structure concentrate faults into error bursts that undermine standard threshold assumptions. Yet, a fundamental gap persists…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding…
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…
The implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…