19 problems

GRK optimality conjecture. If this sequence can find the target block, then there exists a global-local-global sequence satisfying

Character bound conjecture. There is a constant $A$ such that, for sufficiently large $n$, every big $\lambda$ satisfies

Let $beta\geq 5/3$ and define … Assume there is an efficient procedure for sampling from the probability distribution induced by the normalized tensor $c/J$. Consider the quadratic…

Quantum-state preparation conjecture. The observable $u_{0,\xi^*}$ can be efficiently prepared as a quantum state. The claimed efficient preparation is relevant to the quantum algo…

Consider the stochastic nonlinear differential-equation simulation problem studied in the paper, and let $lambda_i$ denote the dissipation rates ordered increasingly. The strong di…

Let $d\geq 2$, let $\nu_{x,y}(\xi)$ be a Young-measure density analytic in $x$ and $y$, discretize $\xi$ algebraically at $N_\xi\sim\varepsilon^{-1}$, and suppose $R_1$ is polynomi…

AMP optimality conjecture. AMP algorithms are optimal for average-case sparse optimization problems.

MF-AOA asymptotic performance conjecture. In the limit $n\rightarrow\infty$, AMP algorithms such as the MF-AOA achieve a performance of approximately

High-order discrete adiabatic convergence conjecture.

The state preparation model accesses matrices and vectors through state preparation circuits, whereas the block encoding model accesses matrices through block encodings. State prep…

A function $f(x)$ may take infinitely many values, although sampling gives a finite number of evaluated values. Quantum Church–Turing thesis. Given sufficient resources, a quantum…

Tightness conjecture. This lower bound is tight: quantum algorithms for solving linear programs to constant precision should require only $\widetilde{O}(\sqrt{nd})$ row queries. Th…

Quantum speedup conjecture. A quantum speedup for semidefinite optimization should rely on techniques other than the direct quantization of a classical interior point method with l…

If the underlying graph $\mathcal{A}$ has $N$ vertices, representing the graph isomorphism problem as a quadratic unconstrained binary optimization problem in a quantum computer re…

Let $\mathcal{P}$ be a reversible, ergodic Markov chain with stationary distribution $\uppi$, and let $M$ be a set of marked states. Define … Assume that $p_M<0.5$, and consider Al…

Let $G$ be a graph with a reversible, ergodic Markov chain, let $M$ be any arrangement of marked vertices, and let $HT$ denote the hitting time of the chain from its stationary dis…

Eisenträger–Hallgren–Kitaev–Song conjecture. The methods of Eisenträger, Hallgren, Kitaev and Song should ultimately yield a quantum polynomial-time algorithm for solving the PIP.

Let $n_c$ be the number of iterations required to obtain an accuracy satisfying $f_{n_c}(\lambda_0)>1-\epsilon$, where $D=\lambda_1-\lambda_0\ll 1$ is the difference between the tw…

Consider simulation of a sparse Hamiltonian using splitting formulae, with spectral norm $Vert HVert$ and evolution time $Delta t$. Higher-order splitting formulae reduce the compl…