Related papers: Local random quantum circuits are approximate poly…
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…
A major line of questions in quantum information and computing asks how quickly locally random circuits converge to resemble global randomness. In particular, approximate k-designs are random unitary ensembles that resemble random circuits…
Motivated by practical concerns in cryptography, we study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a…
Random reversible and quantum circuits form random walks on the alternating group $\mathrm{Alt}(2^n)$ and unitary group $\mathrm{SU}(2^n)$, respectively. Known bounds on the spectral gap for the $t$-th moment of these random walks have…
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…
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…
A unitary $t$-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general $t$. In this paper, we provide for the first time quantum…
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…
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…
We study the formation of short-depth designs beyond the unitary group. We provide a range of results on several groups of broad interest in quantum information science: the Clifford group, the orthogonal group, the unitary symplectic…
The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with $T$ gates whose underlying graph has treewidth $d$ can be simulated deterministically in…
Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However, our understanding of the…
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 study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided…
Unitary $t$-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary $t$-designs. Building on results by Aubrun (Comm.…
Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…
Epsilon-nets and approximate unitary $t$-designs are natural notions that capture properties of unitary operations relevant for numerous applications in quantum information and quantum computing. The former constitute subsets of unitary…
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…
It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at $\omega(\log n)$ depth, where $n$ is the number of qubits, making them classically simulable. We show…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…