Related papers: Direct dialling of Haar random unitary matrices
Any lossless transformation on $n_{s}$ spatial and $n_{p}$ internal modes of light can be described by an $n_{s}n_{p}\times n_{s}n_{p}$ unitary matrix, but there is no known procedure to effect an arbitrary $n_{s}n_{p}\times n_{s}n_{p}$…
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…
We study the amount of interference in random quantum algorithms using a recently derived quantitative measure of interference. To this end we introduce two random circuit ensembles composed of random sequences of quantum gates from a…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
Implementing arbitrary unitary transformations is crucial for applications in quantum computing, signal processing, and machine learning. Unitaries govern quantum state evolution, enabling reversible transformations critical in quantum…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates…
Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…
BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this…
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…
Linear optics underpins tests of fundamental quantum mechanics and computer science, as well as quantum technologies. Here we experimentally demonstrate the longstanding goal of a single reprogrammable optical circuit that is sufficient to…
Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum information processing. We suggest a scheme to implement random circuits in a weighted graph state. The…
In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…
We give a new quantum circuit approximation of quantum multiplexors based on the idea of complexity theory oracles. As an added bonus, our multiplexor approximation immediately gives a quantum circuit approximation of diagonal unitary…
It has been proven that Boson sampling is a much promising model of optical quantum computation, which has been applied to designing quantum computer successfully, such as "Jiuzhang". However, the meaningful randomness of Boson sampling…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
We introduce a novel approach to solve optimization problems on a boson sampling device assisted by classical machine-learning techniques. By virtue of the parity function, we map all measurement patterns, which label the basis spanning an…