Related papers: Unitary property testing lower bounds by polynomia…
Understanding the power and limitations of classical and quantum information and how they differ is a fundamental endeavor. In property testing of distributions, a tester is given samples over a typically large domain $\{0,1\}^n$. An…
We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or…
We address the problem of testing the dimensionality of classical and quantum systems in a `black-box' scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension…
This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats,…
We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
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…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
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…
We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…
We introduce a reinforcement learning algorithm designed to identify the fixed points of a given quantum operation. The method iteratively constructs the unitary transformation that maps the computational basis onto the basis of fixed…
This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum…
We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution…
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 introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…
QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical…
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of…