Related papers: Subquadratic Encodings for Point Configurations

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…

We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…

Qutrits, three-level quantum systems, have the advantage of potentially requiring fewer components than the typically used two-level qubits to construct equivalent quantum circuits. This work investigates the potential of qutrit parametric…

A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…

An ordered binary decision diagram (OBDD) is a directed acyclic graph that represents a Boolean function. OBDDs are also known as special cases of oblivious read-once branching programs in the field of complexity theory. Since OBDDs have…

Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…

We empirically study sorting in the evolving data model. In this model, a sorting algorithm maintains an approximation to the sorted order of a list of data items while simultaneously, with each comparison made by the algorithm, an…

We preprocess the input subdivision with $n$ points on the plane in $O(n\sqrt{\log n})$ time to facilitate point location in constant time. Previously the preprocessing time is $O(n\log n)$ and point location takes $O(\log n)$ time.

Examining the effect of different encoding techniques on entity and context embeddings, the goal of this work is to challenge commonly used Ordinal encoding for tabular learning. Applying different preprocessing methods and network…

Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE…

Recent works on machine learning for combinatorial optimization have shown that learning based approaches can outperform heuristic methods in terms of speed and performance. In this paper, we consider the problem of finding an optimal…

Owing to their rich internal structure and significant long-range interactions, ultracold molecules have been widely explored as carriers of quantum information. Several different schemes for encoding qubits into molecular states, both bare…

The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…

We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second…

Let $T$ be a string of length $n$ over an integer alphabet of size $\sigma$. In the word RAM model, $T$ can be represented in $O(n /\log_\sigma n)$ space. We show that a representation of all covers of $T$ can be computed in the optimal…

Transformer models are permutation equivariant. To supply the order and type information of the input tokens, position and segment embeddings are usually added to the input. Recent works proposed variations of positional encodings with…

The era of Big Data has spawned unprecedented interests in developing hashing algorithms for efficient storage and fast nearest neighbor search. Most existing work learn hash functions that are numeric quantizations of feature values in…

Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…

In a previous paper [quant-ph/0408045] we described a quantum algorithm to prepare an arbitrary state of a quantum register with arbitrary fidelity. Here we present an alternative algorithm which uses a small number of quantum oracles…