Computing quopit Clifford circuit amplitudes by the sum-over-paths technique (pp1081-1095)
          Dax E. Koh, Mark D. Penney, and Robert W. Spekkens
By the Gottesman-Knill Theorem, the outcome probabilities of Clifford circuits can be computed efficiently. We present an alternative proof of this result for quopit Clifford circuits (i.e., Clifford circuits on collections of $p$-level systems, where $p$ is an odd prime) using Feynman's sum-over-paths technique, which allows the amplitudes of arbitrary quantum circuits to be expressed in terms of a weighted sum over computational paths. For a general quantum circuit, the sum over paths contains an exponential number of terms, and no efficient classical algorithm is known that can compute the sum. For quopit Clifford circuits, however, we show that the sum over paths takes a special form: it can be expressed as a product of Weil sums with quadratic polynomials, which can be computed efficiently. This provides a method for computing the outcome probabilities and amplitudes of such circuits efficiently, and is an application of the circuit-polynomial correspondence which relates quantum circuits to low-degree polynomials.

Efficient implementation of quantum circuits with limited qubit interactions (pp1096-1104)
          Stephen Brierley
The quantum circuit model allows gates between \emph{any} pair of qubits yet physical instantiations allow only limited interactions. We address this problem by providing an interaction graph together with an efficient method for compiling quantum circuits so that gates are applied only locally. The graph requires each qubit to interact with $4$ other qubits and yet the time-overhead for implementing any $n$-qubit quantum circuit is $4\log n$. Building a network of quantum computing nodes according to this graph enables the network to emulate a single monolithic device with minimal overhead.

On quantum tensor product codes (pp1105-1122)
          Jihao Fan, Yonghui Li, Min-Hsiu Hsieh, and Hanwu Chen
We present a general  framework for the construction of quantum tensor product codes (QTPC).  In a classical tensor product code (TPC),  its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding  some constraints  on  the component codes,    several classes  of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then   QTPCs  have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with  concatenated quantum codes (CQC),   the component code selections of QTPCs  are much more  flexible than those of CQCs  since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction.  We show that it is possible to construct QTPCs with  parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes.  Many QTPCs  are obtained with parameters better than previously known quantum codes available   in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.

Efficient rate-adaptive reconciliation for CV-QKD protocol (pp1123-1134)
          Xiangyu Wang, Yichen Zhang, Zhengyu Li, Bingjie Xu, Song Yu, and Hong Guo
Information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CV-QKD) systems. We propose an efficient rate-adaptive reconciliation protocol suitable for practical CV-QKD systems with time-varying quantum channel. This protocol changes the code rate of multi-edge type low density parity check codes, by puncturing (increasing the code rate) and shortening (decreasing the code rate) techniques, to enlarge the correctable signal-to-noise ratios regime, thus improves the overall reconciliation efficiency comparing to the original fixed rate reconciliation protocol. We verify our rate-adaptive reconciliation protocol with three typical code rate, i.e., 0.1, 0.05 and 0.02, the reconciliation efficiency keep around 93.5\%, 95.4\% and 96.4\% for different signal-to-noise ratios, which shows the potential of implementing high-performance CV-QKD systems using single code rate matrix.

Topological proofs of contextuality in quantum mechanics (pp1135-1166)
          Cihan Okay, Sam Roberts, Stephen D. Bartlett, and Robert Raussendorf
We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by Mermin, as well as a different type of contextuality proofs based on symmetry transformations. The topological arguments presented can be used in the state-dependent and the state-independent case.

Robustness of QMA against witness noise (pp1167-1190)
          Friederike Anna Dziemba
Using the tool of concatenated stabilizer coding, we prove that the complexity class $\QMA$ remains unchanged even if every witness qubit is disturbed by constant noise. This result may not only be relevant for physical implementations of verifying protocols but also attacking the relationship between the complexity classes $\QMA$, $\QCMA$ and $\BQP$, which can be reformulated in this unified framework of a verifying protocol receiving a disturbed witness. While $\QCMA$ and $\BQP$ are described by fully dephasing and depolarizing channels on the witness qubits, respectively, our result proves $\QMA$ to be robust against 27% dephasing and 18% depolarizing noise.

Small Majorana fermion codes (pp1191-1205)
          Mathew B. Hastings
We consider Majorana fermion stabilizer codes with small number of modes and distance.  We give an upper bound on the number of logical qubits for distance $4$ codes, and we construct Majorana fermion codes similar to the classical Hamming code that saturate this bound.  We perform numerical studies and find other distance $4$ and $6$ codes that we conjecture have the largest possible number of logical qubits for the given number of physical Majorana modes.  Some of these codes have more logical qubits than any Majorana fermion code derived from a qubit stabilizer code.

A note on cohering power and de-cohering power (pp1206-1220)
          Kaifeng Bu and Chunhe Xiong
Cohering power and de-cohering power have recently been proposed to quantify the ability of a quantum operation to produce and erase coherence respectively. In this paper, we investigate the properties of cohering power and de-cohering power. First, we prove the equivalence between two different kinds of cohering power   for any quantum operation on single qubit systems, which implies that $l_1$ norm of coherence is monotone under Maximally incoherent operation (MIO) and Dephasing-covariant operation (DIO) in 2-dimensional space. In higher dimensions, however, we show that the monotonicity under MIO or DIO  does not hold. Besides, we compare the set of quantum operations with zero cohering power with Maximally incoherent operation (MIO) and Incoherent operation (IO). Moreover, two different types of de-cohering power are defined and we find that they are not equal  in single qubit systems. Finally, we make a comparison between cohering power and de-cohering power for single qubit unitary operations and show that cohering power is always larger than de-cohering power.