Every quantum algorithm worth knowing about, written down the same way: what it takes, what it returns, what it costs, and who proved it.
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The defining behavior was checked exactly: a mathematical identity, a full statevector or stabilizer simulation, or an exhaustive basis-state truth table.
The design was verified by construction plus measured evidence: statistical re-execution, small-instance analytic agreement, sub-block, echo, or invariant checks. Scale-specific bugs can still survive.
The record rests on external authority: peer-reviewed papers, standard textbooks, expert review, or evidence carried over from related verified entries. Nothing here was re-executed by this catalog.
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13 public entries
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The general framework behind Grover's algorithm: boosting the success probability of any subroutine with a known reflection structure.
A finance- and Monte-Carlo-facing primitive that makes the oracle and error model visible.
Price discretely monitored Asian options over T monitoring points, where the underlying asset is modeled by a geometric Brownian motion.
Given N coins of which exactly k are counterfeit, where the real coins all share one weight and the counterfeit coins all share another, and given a pan balance that can compare the weight of any pair of subsets of the coins but reports only whether they balance or tilt, identify all of the counterfeit coins in as few weighings as possible.
Bound the quantum-computing resources a fault-tolerant quantum computer would need to price derivatives — autocallable and Target Accrual Redemption Forward (TARF) instruments serving as the paper's benchmark use cases — at a scale offering a quantum advantage over classical pricing.
The canonical search primitive, paired with the linear classical baseline it is meant to improve.
A block-encoding primitive that turns a weighted sum of unitary operations into one larger unitary circuit.
Price an option, or a portfolio of options — vanilla contracts, multi-asset contracts, and path-dependent contracts such as barrier options — on a gate-based quantum computer, in the setting where the paper takes classical Monte Carlo methods as its point of comparison.
Estimates how many items in an unstructured search space satisfy an oracle, without checking them one by one.
Price rainbow options — a type of path-independent multi-asset derivative — on a quantum computer.
Evaluate risk measures of a financial position — Value at Risk and Conditional Value at Risk among them — where the classical route is a Monte Carlo simulation over sampled realisations of the uncertainty.
In the spiked tensor model, an unknown signal vector v_sig in R^N of magnitude √N is hidden inside a p-th order tensor T0 = λ v_sig^⊗p + G, where G is noise whose entries are chosen independently from a Gaussian distribution of zero mean and unit variance and λ is a scalar representing a signal-to-noise ratio; the task called recovery is to infer v_sig to some accuracy given T0, and the simpler task called detection is to distinguish the case λ = 0 from λ = λ̄ for some λ̄ > 0, again just given T0. The paper treats the symmetrized and non-symmetrized cases as reducible to each other, and says that for odd p it is convenient in the analysis not to symmetrize T0 and to take complex G. Recovery is information-theoretically possible for λ much larger than N^((1-p)/2), but no polynomial-time algorithm is known that achieves that performance; the two best known algorithms are spectral and sum-of-squares, and for even p the spectral method works for λ much larger than N^(-p/4), with a variant conjectured to perform similarly for odd p. The regime this record is about is the hard one at and below that spectral threshold: write λ = α N^(-p/4), and the question is what recovery costs as α shrinks.
The Viterbi algorithm finds the most likely sequence of hidden states a hidden Markov model passed through, given a sequence of emissions. Applied to decoding, the hidden states are the encoder states of a classical convolutional code and the emissions are the received symbols, so the most likely path is the decoded message.