Related papers: Unitary designs from statistical mechanics in rand…
Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of…
We map the dynamics of entanglement in random unitary circuits, with finite on-site Hilbert space dimension $q$, to an effective classical statistical mechanics, and develop general diagrammatic tools for calculations in random unitary…
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…
We consider quantum circuits consisting of randomly chosen two-local gates and study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated, roughly meaning that the…
Stochasticity is ubiquitous in the world around us. However, our predominant computing paradigm is deterministic. Random number generation (RNG) can be a computationally inefficient operation in this system especially for larger workloads.…
Recent years have seen unprecedented advance in the design and control of quantum computers. Nonetheless, their applicability is still restricted and access remains expensive. Therefore, a substantial amount of quantum algorithms research…
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…
Sampling from a probability distribution is a core task in many quantum and classical algorithms. Variational quantum circuits provide a natural approach to generating such distributions, as measurement outcomes directly define the…
Unitary randomness underpins both fundamental tasks in quantum information and the modern theory of quantum chaos. On one side, a central concept is that of approximate unitary designs: circuits that look random according to small moments…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases:…
Constructing ensembles of circuits which efficiently approximate the Haar measure over various groups is a long-standing and fundamental problem in quantum information theory. Recently it was shown that one can obtain approximate designs…
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.…
Variational quantum algorithms are a promising class of algorithms that can be performed on currently available quantum computers. In most settings, the free parameters of a variational circuit are optimized using a classical optimizer that…
We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium…
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…
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…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Quantum Supremacy is a demonstration of a computation by a quantum computer that can not be performed by the best classical computer in a reasonable time. A well-studied approach to demonstrating this on near-term quantum computers is to…
We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the…