Related papers: Distribution of interference in random quantum alg…
We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
We study the statistics of quantum interference for completely positive maps. We calculate analytically the mean interference and its second moment for finite dimensional quantum systems interacting with a simple environment consisting of…
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We…
We introduce an interference measure which allows to quantify the amount of interference present in any physical process that maps an initial density matrix to a final density matrix. In particular, the interference measure enables one to…
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…
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…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
We explore the interplay between symmetry and randomness in quantum information. Adopting a geometric approach, we consider states as $H$-equivalent if related by a symmetry transformation characterized by the group $H$. We then introduce…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of…
Quantum states can in a sense be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some…
We investigate the generic aspects of quantum coherence guided by the concentration of measure phenomenon. We find the average relative entropy of coherence of pure quantum states sampled randomly from the uniform Haar measure and show that…