Related papers: Three Hamiltonians are Sufficient for Unitary $k$-…
We present a single-quench protocol that generates unitary $k$-designs with minimal control. A system first evolves under a random Hamiltonian $H_1$; at a switch time $t_s \geq t_{\mathrm{Th}}$ (the Thouless time), it is quenched to an…
The realization of unitary designs is of fundamental interest in quantum science and typically requires the ability to implement structured quantum circuits. Recent developments have explored the possibility of generating unitary designs…
Local random circuits scramble efficiently and accordingly have a range of applications in quantum information and quantum dynamics. With a global $U(1)$ charge however, the scrambling ability is reduced; for example, such random circuits…
We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic…
The nature of randomness and complexity growth in systems governed by unitary dynamics is a fundamental question in quantum many-body physics. This problem has motivated the study of models such as local random circuits and their…
Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused…
Unitary $2$-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries. They are used in a wide variety of theoretical and…
Unitary Designs have become a vital tool for investigating pseudorandomness since they approximate the statistics of the uniform Haar ensemble. Despite their central role in quantum information, their relation to quantum chaotic evolution…
Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple…
We investigate circuit complexity of unitaries generated by time evolution of randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. Specifically, we focus on two ensembles of random generators -- the so…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
Random unitaries are useful in quantum information and related fields, but hard to generate with limited resources. An approximate unitary $k$-design is an ensemble of unitaries with an underlying measure over which the average is close to…
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
A unitary state $t$-design is an ensemble of pure quantum states whose moments match up to the $t$-th order those of states uniformly sampled from a $d$-dimensional Hilbert space. Typically, unitary state $t$-designs are obtained by…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating…
Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially…
The generation of $k$-designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive…
As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide…