Related papers: Generating a state $t$-design by diagonal quantum …
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…
Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple…
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…
We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…
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…
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…
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 develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming…
A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states, w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate…
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…
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…
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…
We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al.,…
We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…
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 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.…
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…
We prove a quantum information-theoretic conjecture due to Ji, Liu and Song (CRYPTO 2018) which suggested that a uniform superposition with random \emph{binary} phase is statistically indistinguishable from a Haar random state. That is, any…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
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…