Related papers: Matrix concentration inequalities and efficiency o…
For a Haar random set $\mathcal{S}\subset U(d)$ of quantum gates we consider the uniform measure $\nu_\mathcal{S}$ whose support is given by $\mathcal{S}$. The measure $\nu_\mathcal{S}$ can be regarded as a…
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…
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…
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…
We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial"…
Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit…
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…
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.…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
The efficiency of locally generating unitary designs, which capture statistical notions of quantum pseudorandomness, lies at the heart of wide-ranging areas in physics and quantum information technologies. While there are extensive potent…
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…
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…
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…
The problem of finding good approximations of arbitrary 1-qubit gates is identical to that of finding a dense group generated by a universal subset of $SU(2)$ to approximate an arbitrary element of $SU(2)$. The Solovay-Kitaev Theorem is a…
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…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
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.…
Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider…
In this work we give an efficient construction of unitary $k$-designs using $\tilde{O}(k\cdot poly(n))$ quantum gates, as well as an efficient construction of a parallel-secure pseudorandom unitary (PRU). Both results are obtained by giving…
In [A.W. Harrow and R.A. Low, Commun. Math. Phys. 291, 257-302 (2009)], it was shown that a quantum circuit composed of random 2-qubit gates converges to an approximate quantum 2-design in polynomial time. We point out and correct a flaw in…