Related papers: Reducing circuit depth with qubitwise diagonalizat…
Characterization of quantum devices generates insights into their sources of disturbances. State-of-the-art characterization protocols often focus on incoherent noise and eliminate coherent errors when using Pauli or Clifford twirling…
GCD computations and variants of the Euclidean algorithm enjoy broad uses in both classical and quantum algorithms. In this paper, we propose quantum circuits for GCD computation with $O(n \log n)$ depth with O(n) ancillae. Prior circuit…
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…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
A central aspect for operating future quantum computers is quantum circuit optimization, i.e., the search for efficient realizations of quantum algorithms given the device capabilities. In recent years, powerful approaches have been…
We propose a Hamiltonian-based quantum state preparation method implemented via a shallow parametrized quantum circuit. The approach learns the parameters of a diagonal Hamiltonian through a classical training phase, while the quantum…
Portfolio optimization is a cornerstone of financial decision-making, traditionally relying on classical algorithms to balance risk and return. Recent advances in quantum computing offer a promising alternative, leveraging quantum…
In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We…
Current quantum computers suffer from noise due to lack of error correction. Several techniques to mitigate the effect of noise have been studied, in particular to extract the expectation value of observables. One such technique, circuit…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and…
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
The Pauli matrices are a set of three 2x2 complex Hermitian, unitary matrices. In this article, we investigate the relationships between certain roots of the Pauli matrices and how gates implementing those roots are used in quantum…
Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
We describe a compilation strategy for Variational Quantum Eigensolver (VQE) algorithms which use the Unitary Coupled Cluster (UCC) ansatz, designed to reduce circuit depth and gate count. This is achieved by partitioning Pauli exponential…