Ultrahigh Error Threshold for Surface Codes with Biased Noise

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

Tailoring surface codes: Improvements in quantum error correction with biased noise

For quantum computers to reach their full potential will require error correction. We study the surface code, one of the most promising quantum error correcting codes, in the context of predominantly dephasing (Z-biased) noise, as found in many quantum architectures. We find that the surface code is highly resilient to Y-biased noise, and tailor it to Z-biased noise, whilst retaining its practical features. We demonstrate ultrahigh thresholds for the tailored surface code: ~39% with a realistic bias of = 100, and ~50% with pure Z noise, far exceeding known thresholds for the standard surface code: ~11% with pure Z noise, and ~19% with depolarizing noise. Furthermore, we provide strong evidence that the threshold of the tailored surface code tracks the hashing bound for all biases. We reveal the hidden structure of the tailored surface code with pure Z noise that is responsible for these ultrahigh thresholds. As a consequence, we prove that its threshold with pure Z noise is 50%, and we show that its distance to Z errors, and the number of failure modes, can be tuned by modifying its boundary. For codes with appropriately modified boundaries, the distance to Z errors is O(n) compared to O(n1/2) for square codes, where n is the number of physical qubits. We demonstrate that these characteristics yield a significant improvement in logical error rate with pure Z and Z-biased noise. Finally, we introduce an efficient approach to decoding that exploits code symmetries with respect to a given noise model, and extends readily to the fault-tolerant context, where measurements are unreliable. We use this approach to define a decoder for the tailored surface code with Z-biased noise. Although the decoder is suboptimal, we observe exceptionally high fault-tolerant thresholds of ~5% with bias = 100 and exceeding 6% with pure Z noise. Our results open up many avenues of research and, recent developments in bias-preserving gates, highlight their direct relevance to experiment

Digital identity : the effect of trust and reputation information on user judgement in the sharing economy

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

The value of being virtual: User feedback on email and instant messaging reference services

https://deepblue.lib.umich.edu/bitstream/2027.42/154704/1/The_Value_of_Being_Virtual.pd

Judgments in the sharing economy: the effect of user-generated trust and reputation information on decision-making accuracy and bias

The growing ecosystem of peer-to-peer enterprise – the Sharing Economy (SE) – has brought with it a substantial change in how we access and provide goods and services. Within the SE, individuals make decisions based mainly on user-generated trust and reputation information (TRI). Recent research indicates that the use of such information tends to produce a positivity bias in the perceived trustworthiness of fellow users. Across two experimental studies performed on an artificial SE accommodation platform, we test whether users’ judgments can be accurate when presented with diagnostic information relating to the quality of the profiles they see or if these overly positive perceptions persist. In study 1, we find that users are quite accurate overall (70%) at determining the quality of a profile, both when presented with full profiles or with profiles where they selected three TRI elements they considered useful for their decision-making. However, users tended to exhibit an “upward quality bias” when making errors. In study 2, we leveraged patterns of frequently vs. infrequently selected TRI elements to understand whether users have insights into which are more diagnostic and find that presenting frequently selected TRI elements improved users’ accuracy. Overall, our studies demonstrate that – positivity bias notwithstanding – users can be remarkably accurate in their online SE judgments

Tailoring surface codes for highly biased noise

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 versio

Characterisation of a new VUV beamline at the Daresbury SRS using a dispersed fluorescence apparatus incorporating CCD detection

The design and performance of a new normal incidence monochromator at the Daresbury Synchrotron Radiation Source, optimised for experiments requiring high flux of vacuum-UV radiation, are described. The re-developed beamline 3.1, based on the Wadsworth design of monochromator, is the source of tunable vacuum-UV photons in the range 4 – 31 eV, providing over two orders of magnitude more flux than the vacuum-UV, Seya monochromator in its previous manifestation. The undispersed and dispersed fluorescence spectra resulting from photoexcitation of N$_2$, CO$_2$, CF$_4$ and C$_6$F$_6$ are presented. Emitting species observed were N$_2^+$ B$^2\Sigma_u^+$ - X$^2\Sigma_g^+$, CO$_2^+$ A$^2\Pi_u$ - X$^2\Pi_g$ and B$^2\Sigma_u^+$ - X$^2\Pi_g$, CF$_4$$^+$ C$^2$T$_2$ - X$^2$T$_1$ and C$^2$T$_2$ - A$^2$T$_2$, CF$_3$* $^2$A$^’_2$ - $^2$A$^”_2$, and C$_6$F$_6^+$ B$^2$A$_{2u}$ - X$^2$E$_{1g}$. A CCD multi-channel detector has significantly reduced the time period needed to record dispersed fluorescence spectra with a comparable signal-to-noise ratio

Selecting futures: The role of conviction, narratives, ambivalence, and constructive doubt

Institutional decisions about the future, that matter, are usually made in a context of considerable uncertainty. Although the intention is success the possibility of failure must inevitably be present, whether recognized or not. The principal purposes of this study are twofold. First, we argue that uncertainty contexts require that decisions to create the future are supported by a particular type of future oriented or foresight narrative which we call a conviction narrative. Its essential function is to combine available knowledge about how to achieve desired outcomes with the feeling that the selected action will achieve the aim. Second, we introduce two states, in which conviction may be achieved, divided, and integrated, to argue that research into how conviction is achieved by individuals or institutions making decisions, can be an extremely promising and practical avenue for foresight studies, throwing light on several issues, particularly the oft-noted reluctance to change course and attachment to single stories of the future. The focus on the reality of uncertainty and the two states in which it can be met, can also enhance the research and practice of narrative foresight, through more systematic theorization of the role of emotion and ambivalence in narrative thought and in the processes through which future-focused narratives generate action under uncertainty

Narrative expectations in financial forecasting

How do people form expectations about the future? We use amateur and expert investors’ expectations about financial asset prices to study this question. Three experiments contrast the rational expectations assumption from neoclassical economics (investors forecast according to neoclassical financial theory) against two psychological theories of expectation-formation—behaviorally-informed expectations (investors understand empirical market anomalies and expect these anomalies to occur) and narrative expectations (investors use narrative thinking to predict future prices). Whereas neoclassical financial theory maintains that past public information cannot be used to predict future prices, participants used company performance information revealed before a base price quotation to project future price trends after that quotation (Experiment 1), contradicting rational expectations. Importantly, these projections were stronger when information concerned predictions about a company’s future performance rather than actual data about its past performance, suggesting that people not only rely on financially irrelevant (but narratively relevant) information for making predictions, but erroneously impose temporal order on that information. These biased predictions had downstream consequences for asset allocation choices (Experiment 2) and these choices were driven in part by affective reactions to the company performance news (Experiment 3). There were some mild effects of expertise, but overall the effects of narrative appear to be consistent across all levels of expertise studied, including professional financial analysts. We conclude by discussing the prospects for a narrative theory of choice that provide new micro-foundational insights about economic behavior