Related papers: On the statistical complexity of quantum circuits
A statistical analysis of the prime numbers indicates possible traces of quantum chaos. We have computed the nearest neighbor spacing distribution, number variance, skewness, and excess for sequences of the first N primes for various values…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…
Considering the recently established arbitrariness the Schroedinger equation has to be interpreted as an equation of motion for a statistical ensemble of particles. The statistical qualities of individual particles derive from the unknown…
In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a…
We give a new algorithm for computing the robustness of magic - a measure of the utility of quantum states as a computational resource. Our work is motivated by the magic state model of fault-tolerant quantum computation. In this model, all…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
We introduce the notion of empirical coordination for quantum correlations. Quantum mechanics enables the calculation of probabilities for experimental outcomes, emphasizing statistical averages rather than detailed descriptions of…
Quantifying the complexity of quantum states that possess intrinsic structure, such as symmetry or encoding, in a fair manner constitutes a core challenge in the benchmarking of quantum technologies. This paper introduces the…
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
We study the effect of quantum memory in magic squares game when played in quantum domain. We consider different noisy quantum channels and analyze their influence on the magic squares quantum pseudo-telepathy game. We show that the…
One of the key issues in quantum discrimination problems is understanding the extent of the advantages in discrimination performance when using resource states compared to resourceless states. We show that in any resource theory of states,…
The paper presents a generalization bound for quantum neural networks based on a dynamical Lie algebra. Using covering numbers derived from a dynamical Lie algebra, the Rademacher complexity is derived to calculate the generalization bound.…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
Magic states are the resource that allows quantum computers to attain an advantage over classical computers. This resource consists in the deviation from a property called stabilizerness which in turn implies that stabilizer circuits can be…
It has been conjectured that the size of the black hole interior captures the quantum gate complexity of the underlying boundary evolution. In this short note we aim to provide a further microscopic evidence for this by directly relating…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…