Related papers: A strong direct product theorem for quantum query …
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…
Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
We study the problem of finding a (pure) product state with optimal fidelity to an unknown $n$-qubit quantum state $\rho$, given copies of $\rho$. This is a basic instance of a fundamental question in quantum learning: is it possible to…
We introduce two new complexity measures for Boolean functions, or more generally for functions of the form f:S->T. We call these measures sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query…
Quantum query complexity has several nice properties with respect to composition. First, bounded-error quantum query algorithms can be composed without incurring log factors through error reduction (exactness). Second, through careful…
We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a…
The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…
Simon's problem plays an important role in the history of quantum algorithms, as it inspired Shor to discover the celebrated quantum algorithm solving integer factorization in polynomial time. Besides, the quantum algorithm for Simon's…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a…
Several well-studied models of access to data samples, including statistical queries, local differential privacy and low-communication algorithms rely on queries that provide information about a function of a single sample. (For example, a…
Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the…
Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…
We explore the use of GPU for accelerating large scale nearest neighbor search and we propose a fast vector-quantization-based exhaustive nearest neighbor search algorithm that can achieve high accuracy without any indexing construction…
Quantum computing faces a key challenge: balancing the need for low circuit depth (crucial for fault tolerance) with the high accuracy required for complex computations like quantum chemistry and error correction, which typically require…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
An XOR function is a function of the form g(x,y) = f(x + y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we completely characterise…