Golden codes: quantum LDPC codes from regular tessellations of hyperbolic 4-manifolds (pp0361-0391)
          Vivien Londe and Anthony Leverrier
We adapt a construction of Guth and Lubotzky \cite{GL14} to obtain a family of quantum LDPC codes with non-vanishing rate and minimum distance scaling like $n^{0.1}$ where $n$ is the number of physical qubits. Similarly as in Ref.~\cite{GL14}, our homological code family stems from hyperbolic 4-manifolds equipped with tessellations. The main novelty of this work is that we consider a regular tessellation consisting of hypercubes. We exploit this strong local structure to design and analyze an efficient decoding algorithm.

Periodic Fourier representation of Boolean functions (pp0392-0412)
          Ryuhei Mori
In this work, we consider a new type of Fourier-like representation of Boolean function $f\colon\{+1,-1\}^n\to\{+1,-1\}$  $f(x) = \cos\left(\pi\sum_{S\subseteq[n]}\phi_S \prod_{i\in S} x_i\right).$ This representation, which we call the periodic Fourier representation, of Boolean function is closely related to a certain type of multipartite Bell inequalities and non-adaptive measurement-based quantum computation with linear side-processing (\NMQCp). The minimum number of non-zero coefficients in the above representation, which we call the periodic Fourier sparsity, is equal to the required number of qubits for the exact computation of $f$ by \NMQCp. Periodic Fourier representations are not unique, and can be directly obtained both from the Fourier representation and the $\mathbb{F}_2$-polynomial representation. In this work, we first show that Boolean functions related to $\ZZZZ$-polynomial have small periodic Fourier sparsities. Second, we show that the periodic Fourier sparsity is at least $2^{\deg_{\mathbb{F}_2}(f)}-1$, which means that \NMQCp efficiently computes a Boolean function $f$ if and only if $\mathbb{F}_2$-degree of $f$ is small. Furthermore, we show that any symmetric Boolean function, e.g., $\mathsf{AND}_n$, $\mathsf{Mod}^3_n$, $\mathsf{Maj}_n$, etc, can be exactly computed by depth-2 \NMQCp using a polynomial number of qubits, that implies exponential gaps between \NMQCp and depth-2 \NMQCp.

Quantum fidelity evolution of Penning trap coherent states in an asymmetric open quantum system (pp0413-0423)
          Somayeh Mehrabankar, Davood Afshar, and Mojtaba Jafarpour
Assuming the Born-Markov approximation, we study the evolution of quantum fidelity in asymmetric systems consisting of two and three-mode independent oscillators interacting with a thermal bath. To this end, considering the Penning trap coherent states as the initial states of the system, we have studied the evolution of the quantum fidelity as a function of the parameters of the system, the environment and the initial state, in the framework of open systems theory. It is observed that fidelity is a decreasing function of the temperature and dissipation coefficient for both two and three-mode states. However, for the two-mode state, the fidelity is an oscillating function of time but a decreasing one in the low values of the magnetic field. In the case of a three-mode state, although the fidelity decreases with the magnetic field, dissipation coefficient and temperature, it is an irregular function of the asymmetric coefficient.

Bang-bang control as a design principle for classical and quantum optimization algorithms (pp0424-0446)
          Aniruddha Bapat and Stephen Jordan
Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such as tunneling may give quantum algorithms advantage in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instances that are considered classically hard. Here, building on previous observations from \cite{mcclean2016, Yang2017}, we argue that the type of \emph{control} strategy used by the optimization algorithm may be crucial to its success. Along with SA, QAO, and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the quasistatic analogues on the same instances. Lastly, we construct O(1)-depth QAOA protocols for a class of symmetric cost functions, and provide an accompanying physical picture.