Related papers: Non-Haar random circuits form unitary designs as f…
To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively…
Information scrambling, the process by which quantum information spreads and becomes effectively inaccessible, is central to modern quantum statistical physics and quantum chaos. These lecture notes provide an introduction to information…
Random circuit sampling (RCS) is a leading approach to demonstrate quantum advantage, with its believed classical hardness rooted in anticoncentration of output distributions and average-case hardness of probability estimation. Here we show…
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…
Haar random states are fundamental objects in quantum information theory and quantum computing. We study the density matrix resulting from sampling $t$ copies of a $d$-dimensional quantum state according to the Haar measure on the…
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…
We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum many-body Hamiltonians. We show that generic high-depth circuits, performing a sequence of layer unitaries of the same form, can…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
Standard randomized benchmarking protocols entail sampling from a unitary 2 design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2…
Unitary designs are essential tools in several quantum information protocols. Similarly to other design concepts, unitary designs are mainly used to facilitate averaging over a relevant space, in this case, the unitary group…
We construct random walks on simple Lie groups that quickly converge to the Haar measure for all moments up to order $t$. Specifically, a step of the walk on the unitary or orthognoal group of dimension $2^{\mathsf n}$ is a random Pauli…
We show that noiseless random quantum circuits pass the linear cross-entropy benchmark (LXEB) test with high probability. If the circuits are linear depth, and thus form unitary 4-designs, the LXEB test is passed with probability…
In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the…
Gluing theorem for random unitaries [Schuster, Haferkamp, Huang, QIP 2025] have found numerous applications, including designing low depth random unitaries [Schuster, Haferkamp, Huang, QIP 2025], random unitaries in ${\sf QAC0}$ [Foxman,…
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of a large number of neurons per hidden layer. In this work we prove an analogous…
Recent years have enjoyed a strong interest in exploring properties and applications of random quantum circuits. In this work, we explore the ensemble of $t$-doped Clifford circuits on $n$ qubits, consisting of Clifford circuits…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
Quantum circuits with local unitaries have emerged as a rich playground for the exploration of many-body quantum dynamics of discrete-time systems. While the intrinsic locality makes them particularly suited to run on current quantum…
We study the problem of efficiently learning an unknown $n$-qubit unitary channel in diamond distance given query access. We present a general framework showing that if Pauli operators remain low-complexity under conjugation by a unitary,…