Related papers: Non-Haar random circuits form unitary designs as f…
We introduce random-LCHS, a circuit-efficient randomized-compilation framework for simulating linear non-unitary dynamics of the form $\partial_t u(t) = -A(t) u(t) + b(t)$ built on the linear combination of Hamiltonian simulation (LCHS). We…
Parameterized quantum circuits play a key role for the development of quantum variational algorithms in the realm of the NISQ era. Knowing their actual capability of performing different kinds of tasks is then of the utmost importance. By…
Recently introduced dual unitary brickwork circuits have been recognised as paradigmatic exactly solvable quantum chaotic many-body systems with tunable degree of ergodicity and mixing. Here we show that regularity of the circuit lattice is…
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…
The famous Johnson-Lindenstrauss lemma states that for any set of n vectors, there is a linear transformation into a space of dimension O(log n) that approximately preserves all their lengths. In fact, a Haar random unitary transformation…
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 establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…
While many statistical properties of deep random quantum circuits can be deduced, often rigorously and other times heuristically, by an approximation to global Haar-random unitaries, the statistics of constant-depth random quantum circuits…
Random unitaries are an important resource for quantum information processing. While their universal properties have been thoroughly analyzed, it is not known what happens to these properties when the unitaries are sampled on the…
We prove a new concentration result for non-catalytic decoupling by showing that, for suitably large $t$, applying a unitary chosen uniformly at random from an approximate $t$-design on a quantum system followed by a fixed quantum operation…
We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudo-random distribution, a k-design. k-designs have the first k moments equal to those of the Haar…
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices…
Until very recently, it was generally believed that the (approximate) 2-design property is strictly stronger than anti-concentration of random quantum circuits, mainly because it was shown that the latter anti-concentrate in logarithmic…
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…
We present a systematic study of how quantum circuit design, specifically the depth of the variational ansatz and the choice of quantum feature mapping, affects the performance of hybrid quantum-classical neural networks on a causal…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…
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…
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…
We identify a \emph{universal functional form} that governs anticoncentration in random quantum circuits-one that holds across diverse circuit architectures and depths, and crucially remains valid even at finite system sizes and shallow…