Related papers: Unitary Designs from Random Symmetric Quantum Circ…
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…
Quantum circuits with symmetry-respecting gates have attracted broad interest in quantum information science. While recent work has developed a theory for circuits with Abelian symmetries, revealing important distinctions between Abelian…
In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the…
We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is…
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their…
Unitary t-designs are distributions on the unitary group whose first t moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate…
Unitary $k$-designs are distributions of unitary gates that match the Haar distribution up to its $k$-th statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical…
An important result in the theory of quantum control is the "universality" of $2$-local unitary gates, i.e. the fact that any global unitary evolution of a system of $L$ qudits can be implemented by composition of $2$-local unitary gates.…
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…
The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary $t$-design is designed to tackle this challenge in an efficient way, yet constructions to date rely…
Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…
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…
We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed $2$-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
We prove new lower bounds on the growth of robust quantum circuit complexity -- the minimal number of gates $C_{\delta}(U)$ to approximate a unitary $U$ up to an error of $\delta$ in operator norm distance. More precisely we show two bounds…
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…
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…
For a random set $\mathcal{S} \subset U(d)$ of quantum gates we provide bounds on the probability that $\mathcal{S}$ forms a $\delta$-approximate $t$-design. In particular we have found that for $\mathcal{S}$ drawn from an exact $t$-design…
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…
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.…