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There is growing interest in the role of sentiment in economic decision-making. However, most research on the subject has focused on positive and negative valence. Conviction Narrative Theory (CNT) places Approach and Avoidance sentiment (that which drives action) at the heart of real-world decision-making, and argues that it better captures emotion in financial markets. This research, bringing together psychology and machine learning, introduces new techniques to differentiate Approach and Avoidance from positive and negative sentiment on a fundamental level of meaning. It does this by comparing word-lists, previously constructed to capture these concepts in text data, across a large range of semantic features. The results demonstrate that Avoidance in particular is well defined as a separate type of emotion, which is evaluative/cognitive and action-orientated in nature. Refining the Avoidance word-list according to these features improves macroeconomic models, suggesting that they capture the essence of Avoidance and that it plays a crucial role in driving real-world economic decision-making.

Tensor-network codes enable the construction of large stabilizer codes out of tensors describing smaller stabilizer codes. An application of tensor-network codes was an efficient and exact decoder for holographic codes. Here, we show how to write some topological codes, including the surface code and colour code, as simple tensor-network codes. We also show how to calculate distances of stabilizer codes by contracting a tensor network. The algorithm actually gives more information, including a histogram of all logical coset weights. We prove that this method is efficient in the case of holographic codes. Using our tensor-network distance calculator, we find a modification of the rotated surface code that has the same distance but fewer minimum-weight logical operators by injecting the non-CSS five-qubit code tensor into the tensor network. This corresponds to an improvement in successful error correction of up to 2% against depolarizing noise (in the perfect-measurement setting), but comes at the cost of introducing four higher-weight stabilizers. Our general construction lets us pick a network geometry (e.g., a Euclidean lattice in the case of the surface code), and, using only a small set of seed codes (constituent tensors), build extensive codes with the potential for optimisation., Comment: 6+5 pages, 6 figures

The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes, and the underlying physical qubits upon which they are built, in tandem. Following this design principle we demonstrate remarkable error correction performance by concatenating the XZZX surface code with Kerr-cat qubits. We contrast several variants of fault-tolerant systems undergoing different circuit noise models that reflect the physics of Kerr-cat qubits. Our simulations show that our system is scalable below a threshold gate infidelity of $p_\mathrm{CX} \sim 6.5\%$ within a physically reasonable parameter regime, where $p_\mathrm{CX}$ is the infidelity of the noisiest gate of our system; the controlled-not gate. This threshold can be reached in a superconducting circuit architecture with a Kerr-nonlinearity of $10$MHz, a $\sim 6.25$ photon cat qubit, single-photon lifetime of $\gtrsim 64\mu$s, and thermal photon population $\lesssim 8\%$. Such parameters are routinely achieved in superconducting circuits.

Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code -- the XZZX code -- offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation., Comment: 10+6 pages, 11 figures; v2 - minor clarifying changes; v3 - final author version. Data and code used to produce our results available at https://bitbucket.org/qecsim/qsdxzzx/. The available software extends and uses services from the quantum error correction simulation package qecsim

Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the noise is biased towards dephasing. Here we introduce an efficient high-threshold decoder for a noise-tailored surface code based on minimum-weight perfect matching. The decoder exploits the symmetries of its syndrome under the action of biased noise and generalises to the fault-tolerant regime where measurements are unreliable. Using this decoder, we obtain fault-tolerant thresholds in excess of $6\%$ for a phenomenological noise model in the limit where dephasing dominates. These gains persist even for modest noise biases: we find a threshold of $\sim 5\%$ in an experimentally relevant regime where dephasing errors occur at a rate one hundred times greater than bit-flip errors., Comment: 6 pages, 4 figures, comments welcome; v2 published version, now includes supplemental material with a technical description of the implemented decoders

The surface code, with a simple modification, exhibits ultra-high error correction thresholds when the noise is biased towards dephasing. Here, we identify features of the surface code responsible for these ultra-high thresholds. We provide strong evidence that the threshold error rate of the surface code tracks the hashing bound exactly for all biases, and show how to exploit these features to achieve significant improvement in logical failure rate. First, we consider the infinite bias limit, meaning pure dephasing. We prove that the error threshold of the modified surface code for pure dephasing noise is $50\%$, i.e., that all qubits are fully dephased, and this threshold can be achieved by a polynomial time decoding algorithm. We demonstrate that the sub-threshold behavior of the code depends critically on the precise shape and boundary conditions of the code. That is, for rectangular surface codes with standard rough/smooth open boundaries, it is controlled by the parameter $g=\gcd(j,k)$, where $j$ and $k$ are dimensions of the surface code lattice. We demonstrate a significant improvement in logical failure rate with pure dephasing for co-prime codes that have $g=1$, and closely-related rotated codes, which have a modified boundary. The effect is dramatic: the same logical failure rate achievable with a square surface code and $n$ physical qubits can be obtained with a co-prime or rotated surface code using only $O(\sqrt{n})$ physical qubits. Finally, we use approximate maximum likelihood decoding to demonstrate that this improvement persists for a general Pauli noise biased towards dephasing. In particular, comparing with a square surface code, we observe a significant improvement in logical failure rate against biased noise using a rotated surface code with approximately half the number of physical qubits., Comment: 18+4 pages, 24 figures; v2 includes additional coauthor (ASD) and new results on the performance of surface codes in the finite-bias regime, obtained with beveled surface codes and an improved tensor network decoder; v3 published version

The Sharing Economy (SE) is a growing ecosystem focusing on peer-to-peer enterprise. In the SE the information available to assist individuals (users) in making decisions focuses predominantly on community generated trust and reputation information. However, how such information impacts user judgement is still being understood. To explore such effects, we constructed an artificial SE accommodation platform where we varied the elements related to hosts' digital identity, measuring users' perceptions and decisions to interact. Across three studies, we find that trust and reputation information increases not only the users' perceived trustworthiness, credibility, and sociability of hosts, but also the propensity to rent a private room in their home. This effect is seen when providing users both with complete profiles and profiles with partial user-selected information. Closer investigations reveal that three elements relating to the host's digital identity are sufficient to produce such positive perceptions and increased rental decisions, regardless of which three elements are presented. Our findings have relevant implications for human judgment and privacy in the SE, and question its current culture of ever increasing information-sharing.

We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is in fact at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes., Comment: 6 pages, 5 figures, comments welcome; v2 includes minor improvements to the numerical results, additional references, and an extended discussion; v3 published version (incorporating supplementary material into main body of paper)

Following the financial crisis of the late 2000s, policy makers have shown considerable interest in monitoring financial stability. Several central banks now publish indices of financial stress, which are essentially based upon market related data. In this paper, we examine the potential for improving the indices by deriving information about emotion shifts in the economy. We report on a new approach, based on the content analysis of very large text databases, and termed directed algorithmic text analysis. The algorithm identifies, very rapidly, shifts through time in the relations between two core emotional groups. The method is robust. The same word-list is used to identify the two emotion groups across different studies. Membership of the words in the lists has been validated in psychological experiments. The words consist of everyday English words with no specific economic meaning. Initial results show promise. An emotion index capturing shifts between the two emotion groups in texts potentially referring to the whole US economy improves the one-quarter ahead consensus forecasts for real GDP growth. More specifically, the same indices are shown to Granger cause both the Cleveland and St Louis Federal Reserve Indices of Financial Stress., Comment: 14 pages plus Supplementary Material