Related papers: The Quantum Complexity of Set Membership
We consider the following problem: Given a set S of at most n elements from a universe of size m, represent it in memory as a bit string so that membership queries of the form "Is x in S?" can be answered by making at most t probes into the…
We consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in S?" by…
This survey summarizes several results about quantum computing related to (mostly static) data structures. First, we describe classical data structures for the set membership and the predecessor search problems: Perfect Hash tables for set…
We consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in…
We introduce a new model for studying quantum data structure problems -- the "quantum cell probe model". We prove a lower bound for the static predecessor problem in the address-only version of this model where we allow quantum parallelism…
The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a…
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 present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether $S$ is a semigroup or has an identity element. If S is a monoid, we want to…
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
We are studying the adaptive bitprobe model to store an arbitrary subset S of size at most five from a universe U of size m and answer the membership queries of the form "Is x in S?" in two bitprobes. In this paper, we present a data…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. This setting is related to the worst case setting on a classical…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
We study probabilistic bit-probe schemes for the membership problem. Given a set A of at most n elements from the universe of size m we organize such a structure that queries of type "Is x in A?" can be answered very quickly. H.Buhrman,…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
We consider a fundamental problem in data structures, static predecessor searching: Given a subset S of size n from the universe [m], store S so that queries of the form "What is the predecessor of x in S?" can be answered efficiently. We…
Quantum query complexity is a fundamental model for analyzing the computational power of quantum algorithms. It has played a key role in characterizing quantum speedups, from early breakthroughs such as Grover's and Simon's algorithms to…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…