We provide an alternative proof of Wallman's [Quantum 2, 47 (2018)] and
Proctor's [Phys. Rev. Lett. 119, 130502 (2017)] bounds on the effect of
gate-dependent noise on randomized benchmarking (RB). Our primary insight is
that a RB sequence is a convolution amenable to Fourier space analysis, and we
adopt the mathematical framework of Fourier transforms of matrix-valued
functions on groups established in recent work from Gowers and Hatami [Sbornik:
Mathematics 208, 1784 (2017)]. We show explicitly that as long as our faulty

Quantum gates (unitary gates) on physical systems are usually implemented by
controlling the Hamiltonian dynamics. When full descriptions of the
Hamiltonians parameters is available, the set of implementable quantum gates is
easily characterised by quantum control theory. In many real systems, however,
the Hamiltonians may include unknown parameters due to the difficulty of
precise measurements or instability of the system. In this paper, we consider
the situation that some parameters of the Hamiltonian are unknown, but we still

We investigate the uncertainty relation for the position of one electron in a
uniform magnetic field in the framework of the quantum estimation theory. Two
kinds of momenta, canonical one and mechanical one, are used to generate a
shift in the position of the electron. We first consider pure state models
whose wave function is in the ground state with zero angular momentum. The
model generated by the two-commuting canonical momenta becomes the
quasi-classical model, in which the symmetric logarithmic derivative quantum

We have developed a software library that simulates noisy quantum logic
circuits. We represent quantum states by their density matrices, and
incorporate possible errors in initialisation, logic gates, memory and
measurement using simple models. Our quantum simulator is implemented as a new
backend on IBM's open-source Qiskit platform. In this document, we provide its
description, and illustrate it with some simple examples.

We study amorphous systems with completely random sites and find that,
through constructing and exploring a concrete model Hamiltonian, such a system
can host an exotic phase of topological amorphous metal in three dimensions. In
contrast to the traditional Weyl semimetals, topological amorphous metals break
translational symmetry, and thus cannot be characterized by the first Chern
number defined based on the momentum space band structures. Instead, their
topological properties will manifest in the Bott index and the Hall

The study and prediction of chemical reactivity is one of the most important
application areas of molecular quantum chemistry. Large-scale, fully
error-tolerant quantum computers could provide exact or near-exact solutions to
the underlying electronic structure problem with exponentially less effort than
a classical computer thus enabling highly accurate predictions for comparably
large molecular systems. In the nearer future, however, only "noisy" devices
with a limited number of qubits that are subject to decoherence will be

The parity-preserving $U_A(1)\times U_a(1)$ massive QED$_3$ is ultraviolet
finiteness -- exhibits vanishing $\beta$-functions, associated to the gauge
coupling constants (electric and chiral charges) and the Chern-Simons mass
parameter, and all the anomalous dimensions of the fields -- as well as is
parity and gauge anomaly free at all orders in perturbation theory. The proof
is independent of any regularization scheme and it is based on the quantum
action principle in combination with general theorems of perturbative quantum

We consider the problem of maximizing a homogeneous polynomial on the unit
sphere and its hierarchy of Sum-of-Squares (SOS) relaxations. Exploiting the
polynomial kernel technique, we obtain a quadratic improvement of the known
convergence rate by Reznick and Doherty & Wehner. Specifically, we show that
the rate of convergence is no worse than $O(d^2/\ell^2)$ in the regime $\ell
\geq \Omega(d)$ where $\ell$ is the level of the hierarchy and $d$ the
dimension, solving a problem left open in the recent paper by de Klerk &

Implementing high-fidelity quantum control and reducing the effect of the
coupling between a quantum system and its environment is a major challenge in
developing quantum information technologies. Here, we show that there exists a
geometrical structure hidden within the time-dependent Schr\"odinger equation
that provides a simple way to view the entire solution space of pulses that
suppress noise errors in a system's evolution. In this framework, any
single-qubit gate that is robust against quasistatic noise to first order

In order to elucidate the role of spontaneous symmetry breaking in condensed
matter systems, we explicitly construct the ground state wave function for a
nonrelativistic theory of a two-fluid system of bosons. This can model either
superconductivity or superfluidity, depending on whether we assign a charge to
the particles or not. Since each nonrelativistic field $\Psi_j$ ($j=1,2$)
carries a phase $\theta_j$ and the Lagrangian is formally invariant under
shifts $\theta_j\to\theta_j+\alpha_j$ for independent $\alpha_j$, one can