37 problems

Let $S_{\alpha}(l)$ denote the tensor complexity at subsystem size $l$, measured by the $\alpha$-Rényi entropy. Consider tensorized recurrent architectures used for chaotic time-se…

Let $c_G$ and $L$ be the parameters appearing in the global perturbation bound, with $L=\lceil\log_2(r_{\mathrm{max}})\rceil$. $L$-independent dependence conjecture. A more refined…

Let $\tilde{\rho}$ be the estimator of a quantum state produced by sketch tomography, and let $n$ denote the number of qubits. Warm-start conjecture. Using $\tilde{\rho}$ as a warm…

Type III algebra conjecture. The type III algebras associated with half-infinite subsystems in quantum field theory might arise from this thick RT surface in the MERA for a suitabl…

Conjecture on decorated-mixture-index sampling. In future work, sampling of the decorated mixture index will be useful in parallelized algorithms which themselves might provide cru…

A gauge theory here means a spin system obtained from the tensor-network construction of a fermion-to-qubit encoding, with the gauge constraints described in the paper. Ungauging c…

Boundary Hilbert-space nonlocality conjecture. The emergent symmetries arising from bulk topological order imply that the boundary Hilbert space does not admit a local tensor produ…

Let $d(\psi)$ denote the minimum bond dimension of a translation-invariant matrix product state (TI MPS) representation with periodic boundary conditions (PBC) of a state $\psi$, a…

Let $\mathscr{Q}_{MPS}$ denote the proposed space of states represented by normal matrix product state tensors of finite bond dimension, namely … A parametrized phase in spatial di…

Fusion categories describe the symmetries of the physical models under consideration, and bimodule categories describe the corresponding models. The tensor-network condition on the…

Let $M,N\in \operatorname{Mat}_{D\times D}^d$, and write $\lvert M_n\rangle$ and $\lvert N_n\rangle$ for the corresponding matrix product states of system size $n$. The tensors are…

Gauge-point vertex conjecture. The gauge points are the vertices of a convexly parametrized family of spectral points.

Tensor-train (TT) tensors are low-rank tensor representations based on nested matricizations; more generally, tensor networks based on nested matricizations provide structured repr…

Cui et al.'s asymptotic quantum max-flow min-cut conjecture. For every quantum tensor network $\mathcal{N}=(G,d,S,T)$,

Positivity and definiteness conjecture. The dominant eigenvalue $\eta$ is real and positive, and

Dimension conjecture. For all such $d$, $\mathbf{m}$, and $\mathbf{n}$, the displayed dimension formula holds outside precisely the listed exceptional cases.

Consider tensorized recurrent neural-network architectures for forecasting chaotic time series, with tensor complexity measured by the entanglement entropy (EE), and compare matrix…

Let $G_K$ be a hypergraph defining a $K$-party state construction, and let $\Ket{G_K}$ denote the resulting $K$-party quantum state. The construction uses AME tensors at bulk verti…

Universality conjecture. The universal state-sum construction contains fixed point models for topological phases that are not captured by known constructions.

Consider the six tensor-network representations in Table: TT-rank over $\mathbb{R}$, TT-rank over $\mathbb{R}_{\geq 0}$, Born-rank over $\mathbb{R}$, Born-rank over $\mathbb{C}$, p…

Let $\Sigma$ be a network with $n\geq2$ boundary vertices. An extremal-ray realization is a subnetwork whose entropy vector realizes an extremal ray of the $n$-boundary-region holo…

Let $\Sigma$ be a network with four boundary vertices $A_1,\ldots,A_4$, and let $I(A_i:A_j)$ denote the mutual information between $A_i$ and $A_j$ on $\Sigma$. Let…

Large bond-dimension conjecture. For $d=2$ and $k$ sufficiently large, there exists a tensor $T \in \operatorname{TNS}(G_{2 \times N},d,k)$ such that all flattenings of $T$ have ma…

Let $C_m$ be a cyclic graph, and let $(S,\bar S)$ be a partition of its external edges. Write $\operatorname{QMF}'(C_m,(S,\bar S),N)$ for the quantum max-flow and…

Consider anyon condensation phase transitions between nonchiral topological orders in two spatial dimensions, and the construction using algebra-graded MPO algebras whose symmetry…