Related papers: Real-Valued Somewhat-Pseudorandom Unitaries
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two…
We consider a random quantum channel obtained by taking a selection of $d$ independent and Haar distributed $N$ dimensional unitaries. We follow the argument of Hastings to bound the spectral gap in terms of eigenvalues and adapt it to give…
Orthogonal polynomials with respect to the hypergeometric distribution on lattices in polyhedral domains in ${\mathbb R}^d$, which include hexagons in ${\mathbb R}^2$ and truncated tetrahedrons in ${\mathbb R}^3$, are defined and studied.…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…
Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak…
In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the…
Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-known dimension reduction maps, including SRHT and Gaussian…
A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the…
Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional…
We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude…
We explore the implementation of pseudo-random single-qubit rotations and multi-qubit pseudo-random circuits constructed only from Clifford gates and the T-gate, a phase rotation of pi/4. Such a gate set would be appropriate for…
Common random string model is a popular model in classical cryptography with many constructions proposed in this model. We study a quantum analogue of this model called the common Haar state model, which was also studied in an independent…
In quantum cryptography, a one-way permutation is a bounded unitary operator $U:\mathcal{H} \to \mathcal{H}$ on a Hilbert space $\mathcal{H}$ that is easy to compute on every input, but hard to invert given the image of a random input.…