Related papers: More global randomness from less random local gate…
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the "frame potential," which is minimized by unitary $k$-designs and measures the $2$-norm…
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…
We consider Kitaev's quantum double model based on a finite group $G$ and describe quantum circuits for (a) preparation of the ground state, (b) creation of anyon pairs separated by an arbitrary distance, and (c) non-destructive topological…
We describe a practical experimental protocol for robustly characterizing the error rates of non-Clifford gates associated with dihedral groups, including gates in SU(2) associated with arbitrarily small angle rotations. Our dihedral…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
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…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
Random reversible and quantum circuits form random walks on the alternating group $\mathrm{Alt}(2^n)$ and unitary group $\mathrm{SU}(2^n)$, respectively. Known bounds on the spectral gap for the $t$-th moment of these random walks have…
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their…
We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…
Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U equal to the Shannon entropy of the vector of singular values…
This article explores search strategies for the design of parameterized quantum circuits. We propose several optimization approaches including random search plus survival of the fittest, reinforcement learning both with classical and hybrid…
Distributed quantum computing represents at present one of the most promising approaches to scaling quantum processors. Current implementations typically partition circuits into multiple cores, each composed of several qubits, with…
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…
Understanding how fast physical systems can resemble Haar-random unitaries is a fundamental question in physics. Many experiments of interest in quantum gravity and many-body physics, including the butterfly effect in quantum information…
With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of 99.95% with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between…
We investigate a class of brickwork-like quantum circuits on chains of $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these systems generate unitary dynamics not only when propagating in the time…
Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we…
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…
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…