Related papers: Quantum t-designs: t-wise independence in the quan…
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…
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…
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body…
Unitary $t$-designs are `good' finite subsets of the unitary group $U(d)$ that approximate the whole unitary group $U(d)$ well. Unitary $t$-designs have been applied in randomized benchmarking, tomography, quantum cryptography and many…
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…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…
Random unitary matrices sampled from the uniform Haar ensemble have a number of important applications both in cryptography and in the simulation of a variety of fundamental physical systems. Since the Haar ensemble is very expensive to…
It was recently observed that in certain thermalizing many-body systems, measuring the complement of a subsystem that thermalized to infinite temperature in a suitable orthonormal basis gives rise to approximate quantum state k-designs as…
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…
A unitary state $t$-design is an ensemble of pure quantum states whose moments match up to the $t$-th order those of states uniformly sampled from a $d$-dimensional Hilbert space. Typically, unitary state $t$-designs are obtained by…
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…
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state…
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…
Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics.…
In this paper, we study the quantum-state estimation problem in the framework of optimal design of experiments. We first find the optimal designs about arbitrary qubit models for popular optimality criteria such as A-, D-, and E-optimal…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
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 t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…
The computational power of quantum computers poses major challenges to new design tools since representing pure quantum states typically requires exponentially large memory. As shown previously, decision diagrams can reduce these memory…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…