How many qubits are needed for quantum computational supremacy?

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of classical computation. One common assumption is that the polynomial hierarchy (PH) does not collapse, a stronger version of the statement that P $\neq$ NP, which leads to the conclusion that any classical simulation of certain families of quantum circuits requires time scaling worse than any polynomial in the size of the circuits. However, the asymptotic nature of this conclusion prevents us from calculating exactly how many qubits these quantum circuits must have for their classical simulation to be intractable on modern classical supercomputers. We refine these quantum computational supremacy arguments and perform such a calculation by imposing fine-grained versions of the non-collapse assumption. Each version is parameterized by a constant $a$ and asserts that certain specific computational problems with input size $n$ require $2^{an}$ time steps to be solved by a non-deterministic algorithm. Then, we choose a specific value of $a$ for each version that we argue makes the assumption plausible, and based on these conjectures we conclude that Instantaneous Quantum Polynomial-Time (IQP) circuits with 208 qubits, Quantum Approximate Optimization Algorithm (QAOA) circuits with 420 qubits and boson sampling circuits (i.e. linear optical networks) with 98 photons are large enough for the task of producing samples from their output distributions up to constant multiplicative error to be intractable on current technology. In the first two cases, we extend this to constant additive error by introducing an average-case fine-grained conjecture.Comment: 24 pages + 3 appendices, 8 figures. v2: number of qubits calculation updated and conjectures clarified after becoming aware of Ref. [42]. v3: Section IV and Appendix C added to incorporate additive-error simulation

Efficient classical simulation of random shallow 2D quantum circuits

Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random gates, approximate simulation of typical instances is almost as hard as exact simulation. We prove that this is not the case by exhibiting a shallow circuit family with uniformly random gates that cannot be efficiently classically simulated near-exactly under standard hardness assumptions, but can be simulated approximately for all but a superpolynomially small fraction of circuit instances in time linear in the number of qubits and gates. We furthermore conjecture that sufficiently shallow random circuits are efficiently simulable more generally. To this end, we propose and analyze two simulation algorithms. Implementing one of our algorithms numerically, we give strong evidence that it is efficient both asymptotically and, in some cases, in practice. To argue analytically for efficiency, we reduce the simulation of 2D shallow random circuits to the simulation of a form of 1D dynamics consisting of alternating rounds of random local unitaries and weak measurements -- a type of process that has generally been observed to undergo a phase transition from an efficient-to-simulate regime to an inefficient-to-simulate regime as measurement strength is varied. Using a mapping from quantum circuits to statistical mechanical models, we give evidence that a similar computational phase transition occurs for our algorithms as parameters of the circuit architecture like the local Hilbert space dimension and circuit depth are varied

Prospectus, April 28, 1982

BOARD PLANS FOR COLLEGE EXPANSION; News Digest; Candidates present views; Previewing really is censorship; Second StuGo forum flops on its back; ERA supporters rally together at capital; Don\u27t push your opinions, beliefs on others; Variety of students enroll in art transfer program; P.C. Happenings...: May Day festival to be featured, Music program to be performed, Phi Beta Lambda attends convention, Walks planned through woods, Help yourself to health, Learning to adjust to newborn baby; Parkland serves area through TV classes; Event offers chance to sell food; Origin of Arbor Day hazy; Parkland plans for Arbor Day activity; Soft pretzels make good party snacks; Rathskeller jams at 1st Parkland outdoor concert; Classifieds; Gettin\u27 lucky rocking with Loverboy; \u27Swamp Thing\u27 nothing but entertainment; Talking with the roadies; Tornado Shelter Guide; Mother Nature at her worst...: Watch for tornadoes; Mayor discusses Champaign projectshttps://spark.parkland.edu/prospectus_1982/1020/thumbnail.jp

Grouping of UVCB substances with dose-response transcriptomics data from human cell-based assays

The application of in vitro biological assays as new approach methodologies (NAMs) to support grouping of UVCB (unknown or variable composition, complex reaction products, and biological materials) substances has recently been demonstrated. In addition to cell-based phenotyping as NAMs, in vitro transcriptomic profiling is used to gain deeper mechanistic understanding of biological responses to chemicals and to support grouping and read-across. However, the value of gene expression profiling for characterizing complex substances like UVCBs has not been explored. Using 141 petroleum substance extracts, we performed dose-response transcriptomic profiling in human induced pluripotent stem cell (iPSC)-derived hepatocytes, cardiomyocytes, neurons, and endothelial cells, as well as cell lines MCF7 and A375. The goal was to determine whether transcriptomic data can be used to group these UVCBs and to further characterize the molecular basis for in vitro biological responses. We found distinct transcriptional responses for petroleum substances by manufacturing class. Pathway enrichment informed interpretation of effects of substances and UVCB petroleum-class. Transcriptional activity was strongly correlated with concentration of polycyclic aromatic compounds (PAC), especially in iPSC-derived hepatocytes. Supervised analysis using transcriptomics, alone or in combination with bioactivity data collected on these same substances/cells, suggest that transcriptomics data provide useful mechanistic information, but only modest additional value for grouping. Overall, these results further demonstrate the value of NAMs for grouping of UVCBs, identify informative cell lines, and provide data that could be used for justifying selection of substances for further testing that may be required for registration

Accrediting outputs of noisy intermediate-scale quantum computing devices

We present an accreditation protocol for the outputs of noisy intermediate-scale quantum devices. By testing entire circuits rather than individual gates, our accreditation protocol can provide an upper-bound on the variation distance between noisy and noiseless probability distribution of the outputs of the target circuit of interest. Our accreditation protocol requires implementation of quantum circuits no larger than the target circuit, therefore it is practical in the near term and scalable in the long term. Inspired by trap-based protocols for the verification of quantum computations, our accreditation protocol assumes that noise in single-qubit gates is bounded (but potentially gate-dependent) in diamond norm. We allow for arbitrary spatial and temporal correlations in the noise affecting state preparation, measurements and two-qubit gates. We describe how to implement our protocol on real-world devices, and we also present a novel cryptographic protocol (which we call `mesothetic' protocol) inspired by our accreditation protocol.Comment: Accepted versio

Predicting consumer biomass, size-structure, production, catch potential, responses to fishing and associated uncertainties in the world's marine ecosystems

Existing estimates of fish and consumer biomass in the world’s oceans are disparate. This creates uncertainty about the roles of fish and other consumers in biogeochemical cycles and ecosystem processes, the extent of human and environmental impacts and fishery potential. We develop and use a size-based macroecological model to assess the effects of parameter uncertainty on predicted consumer biomass, production and distribution. Resulting uncertainty is large (e.g. median global biomass 4.9 billion tonnes for consumers weighing 1 g to 1000 kg; 50% uncertainty intervals of 2 to 10.4 billion tonnes; 90% uncertainty intervals of 0.3 to 26.1 billion tonnes) and driven primarily by uncertainty in trophic transfer efficiency and its relationship with predator-prey body mass ratios. Even the upper uncertainty intervals for global predictions of consumer biomass demonstrate the remarkable scarcity of marine consumers, with less than one part in 30 million by volume of the global oceans comprising tissue of macroscopic animals. Thus the apparently high densities of marine life seen in surface and coastal waters and frequently visited abundance hotspots will likely give many in society a false impression of the abundance of marine animals. Unexploited baseline biomass predictions from the simple macroecological model were used to calibrate a more complex size- and trait-based model to estimate fisheries yield and impacts. Yields are highly dependent on baseline biomass and fisheries selectivity. Predicted global sustainable fisheries yield increases ≈4 fold when smaller individuals (< 20 cm from species of maximum mass < 1kg) are targeted in all oceans, but the predicted yields would rarely be accessible in practice and this fishing strategy leads to the collapse of larger species if fishing mortality rates on different size classes cannot be decoupled. Our analyses show that models with minimal parameter demands that are based on a few established ecological principles can support equitable analysis and comparison of diverse ecosystems. The analyses provide insights into the effects of parameter uncertainty on global biomass and production estimates, which have yet to be achieved with complex models, and will therefore help to highlight priorities for future research and data collection. However, the focus on simple model structures and global processes means that non-phytoplankton primary production and several groups, structures and processes of ecological and conservation interest are not represented. Consequently, our simple models become increasingly less useful than more complex alternatives when addressing questions about food web structure and function, biodiversity, resilience and human impacts at smaller scales and for areas closer to coasts

RNAi Effector Diversity in Nematodes

While RNA interference (RNAi) has been deployed to facilitate gene function studies in diverse helminths, parasitic nematodes appear variably susceptible. To test if this is due to inter-species differences in RNAi effector complements, we performed a primary sequence similarity survey for orthologs of 77 Caenorhabditis elegans RNAi pathway proteins in 13 nematode species for which genomic or transcriptomic datasets were available, with all outputs subjected to domain-structure verification. Our dataset spanned transcriptomes of Ancylostoma caninum and Oesophagostomum dentatum, and genomes of Trichinella spiralis, Ascaris suum, Brugia malayi, Haemonchus contortus, Meloidogyne hapla, Meloidogyne incognita and Pristionchus pacificus, as well as the Caenorhabditis species C. brenneri, C. briggsae, C. japonica and C. remanei, and revealed that: (i) Most of the C. elegans proteins responsible for uptake and spread of exogenously applied double stranded (ds)RNA are absent from parasitic species, including RNAi-competent plant-nematodes; (ii) The Argonautes (AGOs) responsible for gene expression regulation in C. elegans are broadly conserved, unlike those recruited during the induction of RNAi by exogenous dsRNA; (iii) Secondary Argonautes (SAGOs) are poorly conserved, and the nuclear AGO NRDE-3 was not identified in any parasite; (iv) All five Caenorhabditis spp. possess an expanded RNAi effector repertoire relative to the parasitic nematodes, consistent with the propensity for gene loss in nematode parasites; (v) In spite of the quantitative differences in RNAi effector complements across nematode species, all displayed qualitatively similar coverage of functional protein groups. In summary, we could not identify RNAi effector deficiencies that associate with reduced susceptibility in parasitic nematodes. Indeed, similarities in the RNAi effector complements of RNAi refractory and competent nematode parasites support the broad applicability of this research genetic tool in nematodes