Related papers: Quantum State Designs from Minimally Random Quantu…
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…
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…
Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we…
The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
We investigate protocols for generating a state $t$-design by using a fixed separable initial state and a diagonal-unitary $t$-design in the computational basis, which is a $t$-design of an ensemble of diagonal unitary matrices with random…
We study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be…
We review the generation of random pure states using a protocol of repeated two qubit gates. We study the dependence of the convergence to states with Haar multipartite entanglement distribution. We investigate the optimal generation of…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed…
The applications of random quantum circuits range from quantum computing and quantum many-body systems to the physics of black holes. Many of these applications are related to the generation of quantum pseudorandomness: Random quantum…
We explicitly construct a quantum circuit which exactly generates random three-qubit states. The optimal circuit consists of three CNOT gates and fifteen single qubit elementary rotations, parametrized by fourteen independent angles. The…
An algorithm is proposed for constructing quasi-random "peaked" quantum circuits, i.e., circuits whose final qubit state exhibits a high probability concentration on a specific computational basis state. These circuits consist of random…
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs.…
Randomness is an essential tool in many disciplines of modern sciences, such as cryptography, black hole physics, random matrix theory and Monte Carlo sampling. In quantum systems, random operations can be obtained via random circuits…
$k$-Uniform states are fundamental to quantum information and computing, with applications in multipartite entanglement and quantum error-correcting codes (QECCs). Prior work has primarily focused on constructing exact $k$-uniform states or…
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…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…
We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem,…
In recent years, we have witnessed an explosion of experimental tools by which quantum systems can be manipulated in a controlled and coherent way. One of the most important goals now is to build quantum simulators, which would open up the…