Related papers: Efficient quantum pseudorandomness under conservat…

Fastness and robustness are both critical in the implementation of high-fidelity gates for quantum computation, but in practice, a trade-off has to be made between them. In this paper, we investigate the underlying robust time-optimal…

Quantum computers will need effective error-correcting codes. Current quantum processors require precise control of each particle, so having fewer particles to control might be beneficial. Although traditionally quantum computers are…

We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…

TThe problem of finding the resource free, closest local unitary, to any bipartite unitary gate $U$ is addressed. Previously discussed as a measure of nonlocality, the distance $K_D(U)$ to the nearest product unitary has implications for…

We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…

We consider a family of quantum spin systems which includes as special cases the ferromagnetic XY model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any…

The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…

We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…

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 describe a quantum error-detecting and error-correcting code embedded within irreducible representations of SU(3). These logical qutrits inherit the He(3) symmetries induced by the representation, while protecting against small SU(3)…

In this paper we tackle the problem of generating uniform designs in very small subregions of computer model input space that have been identified in previous experiments as worthy of further study. The method is capable of producing…

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…

Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum…

Quantum algorithms leverage the use of quantumly-controlled data in order to achieve computational advantage. This implies that the programs use constructs depending on quantum data and not just classical data such as measurement outcomes.…

Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively…

In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…

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…

The main aim of this work is to present an explicit construction of a 2-design of ${\rm U}(2)$, relying only on a tool that belongs to every physicists toolbox: the theory of angular momentum. Unitary designs are a rich and fundamental…

We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the…

We examined the possibility of recovering the losses of entanglement and the non-local advantage by using the local symmetric operations. The improvement efficiency may be increased by applying the symmetric operations on both qubits. The…