Related papers: Convergence rates for arbitrary statistical moment…
Characterization of experimental systems is an essential step in developing and improving quantum hardware. A collection of protocols known as Randomized Benchmarking (RB) was developed in the past decade, which provides an efficient way to…
To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…
We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
We apply the operation of random independent thinning on the eigenvalues of $n\times n$ Haar distributed unitary random matrices. We study gap probabilities for the thinned eigenvalues, and we study the statistics of the eigenvalues of…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a…
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of…
We describe a practical experimental protocol for robustly characterizing the error rates of non-Clifford gates associated with dihedral groups, including gates in SU(2) associated with arbitrarily small angle rotations. Our dihedral…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary invariant ensembles, converge in law to Gaussian…
Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
A major line of questions in quantum information and computing asks how quickly locally random circuits converge to resemble global randomness. In particular, approximate k-designs are random unitary ensembles that resemble random circuits…
A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal…
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external…
We study the universal structure of late-time ensembles obtained from unitary dynamics in quantum chaotic systems with symmetries, such as charge or energy conservation. We find that although quantum states do not ergodically explore the…
Averaging physical quantities over Lie groups appears in many contexts across the rapidly developing branches of physics like quantum information science or quantum optics. Such an averaging process can be always represented as averaging…
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…