Related papers: Non-Haar random circuits form unitary designs as f…
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…
At its core a $t$-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics. We construct…
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…
We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium…
We construct $\varepsilon$-approximate unitary $k$-designs on $n$ qubits in circuit depth $O(\log k \log \log n k / \varepsilon)$. The depth is exponentially improved over all known results in all three parameters $n$, $k$, $\varepsilon$.…
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…
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…
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…
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…
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 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…
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…
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…
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…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…
Dual-unitary circuits are a class of quantum systems for which exact calculations of various quantities are possible, even for circuits that are nonintegrable. The array of known exact results paints a compelling picture of dual-unitary…
(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the…
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…