{"arxiv_id":"2111.07933","incoming":{"papers":13,"sentences":18,"groups":[{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2302.03888","title":"Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions","url":"/paper/2302.03888","section":"Comparison with Previous Work","sentence":"Hence, the total gate count for this variational algorithm is $Ω(n^2)$ whereas the classical time and space complexity is exponential in $n$ [ref] .","intent_p":0.81,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":5,"sentences":6,"quotes":[{"arxiv_id":"2204.03495","title":"Covariance matrix preparation for quantum principal component analysis","url":"/paper/2204.03495","section":"Introduction","sentence":"We consider a dataset that has been amplitude encoded [ref] , such that the dataset is described by an ensemble ${p_i, |ψ_i⟩}$ of normalized quantum states $|ψ_i⟩$.","intent_p":0.86,"contests_p":null},{"arxiv_id":"2309.13108","title":"Data is often loadable in short depth: Quantum circuits from tensor networks for finance, images, fluids, and proteins","url":"/paper/2309.13108","section":"Introduction","sentence":"There are several previous methods that attempt to address the input problem [ref] ; we highlight some prominent approaches here.","intent_p":0.96,"contests_p":null},{"arxiv_id":"2409.07332","title":"Quantum state preparation via piecewise QSVT","url":"/paper/2409.07332","section":"Introduction","sentence":"Multiple techniques utilising these approaches have been developed including: preparing Matrix Product States (MPS) [ref] , sparse states [ref] , truncated series expansions [ref] , training variational circuits [ref] , compressing repeated values [ref] , preparing states via coherent arithmetic [ref] , and QSVT polynomial approximation [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"2309.10087","title":"Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes","url":"/paper/2309.10087","section":"Introduction","sentence":"Another example is the proposal in Ref. [ref] based on the Grover-Rudolph algorithm [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"2311.11751","title":"Quantum approximated cloning-assisted density matrix exponentiation","url":"/paper/2311.11751","section":"Introduction","sentence":"These encodings and their applications range from loading probability distributions into the amplitudes of quantum states as a means to implement a Monte Carlo integration or as an initial condition of a differential equation [ref] , to calculate the exponentiation of a certain matrix in order to calculate its principal components [ref] or to solve an associated linear system of equations [ref] .","intent_p":0.89,"contests_p":null}]}],"unlabelled_sentences":11},"outgoing":{"papers":13,"sentences":27,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":1,"quotes":[{"arxiv_id":"quant-ph/0208112","title":"Creating superpositions that correspond to efficiently integrable probability distributions","url":"/paper/quant-ph/0208112","section":"Ansatz","sentence":"The circuit proposed as an ansatz, $U(θ)$, for our model is based on the Grover-Rudolph circuit [ref] .","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":26},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2111.07933"}}