Related papers: Classical-Quantum Separations in Certain Classes o…
We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Let f be a Boolean function with…
The main reason for query model's prominence in complexity theory and quantum computing is the presence of concrete lower bounding techniques: polynomial and adversary method. There have been considerable efforts to give lower bounds using…
We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexity of two primitive problems: given a function $f$ and a…
We propose a new formalism for quantum entanglement (QE), and study its generic searches at the colliders. For a general quantum system with $N$ particles, we show that the quantum space (the total spin polarization parameter space) is…
We show a partial Boolean function $f$ together with an input $x\in f^{-1}\left(*\right)$ such that both $C_{\bar{0}}\left(f,x\right)$ and $C_{\bar{1}}\left(f,x\right)$ are at least $C\left(f\right)^{2-o\left(1\right)}$. Due to recent…
We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…
We provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
We study the query complexity analogue of the class TFNP of total search problems. We give a way to convert partial functions to total search problems under certain settings; we also give a way to convert search problems back into partial…
In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded…
Density modelling is the task of learning an unknown probability density function from samples, and is one of the central problems of unsupervised machine learning. In this work, we show that there exists a density modelling problem for…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
Let $A$ be an $s$-sparse Hermitian matrix, $f(x)$ be a univariate function, and $i, j$ be two indices. In this work, we investigate the query complexity of approximating $\bra{i} f(A) \ket{j}$. We show that for any continuous function…
Aaronson and Ambainis (SICOMP `18) showed that any partial function on $N$ bits that can be computed with an advantage $\delta$ over a random guess by making $q$ quantum queries, can also be computed classically with an advantage $\delta/2$…
We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
Despite years of effort, the quantum machine learning community has only been able to show quantum learning advantages for certain contrived cryptography-inspired datasets in the case of classical data. In this note, we discuss the…