Related papers: Convergence Conditions for Random Quantum Circuits
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…
We prove a quantum information-theoretic conjecture due to Ji, Liu and Song (CRYPTO 2018) which suggested that a uniform superposition with random \emph{binary} phase is statistically indistinguishable from a Haar random state. That is, any…
In a recently demonstrated quantum-state tomography scheme [Phys. Rev. Lett. 124, 010405 (2020)], a random control field is locally applied to a multipartite system to reconstruct the full quantum state of the system through…
We propose a new method to extend the size of a quantum computation beyond the number of physical qubits available on a single device. This is accomplished by randomly inserting measure-and-prepare channels to express the output state of a…
Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum channel. The codes are random subspaces…
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true…
In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
We introduce a simulation-free method to estimate the fidelity of large quantum circuits based on the order statistics of measured output probabilities from highly entangled, chaotic states. The approach requires only the…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several…
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group, one often resorts to $t$-designs. Unitary…
Continuous-variable quantum cryptographic systems, including random number generation and key distribution, are often based on coherent detection. The essence of the security analysis lies in the randomness quantification. Previous analyses…
We analyze the optimal basis for generating the maximum relative entropy of quantum coherence by an arbitrary gate on a two-qubit system. The optimal basis is not unique, and the high quantum coherence generating gates are also typically…
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of a large number of neurons per hidden layer. In this work we prove an analogous…
Given a closed quantum system, the states that can be reached with a cyclic process are those with the same spectrum as the initial state. Here we prove that, under a very general assumption on the Hamiltonian, the distribution of the mean…
Distributed quantum computing represents at present one of the most promising approaches to scaling quantum processors. Current implementations typically partition circuits into multiple cores, each composed of several qubits, with…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
We investigate randomized benchmarking in a general setting with quantum gates that form a representation, not necessarily an irreducible one, of a finite group. We derive an estimate for the average fidelity, to which experimental data may…