相关论文: Quantum vs. Classical Read-once Branching Programs
We show lower bounds of $\Omega(\sqrt{n})$ and $\Omega(n^{1/4})$ on the randomized and quantum communication complexity, respectively, of all $n$-variable read-once Boolean formulas. Our results complement the recent lower bound of…
The main conceptual contribution of this paper is investigating quantum multiparty communication complexity in the setting where communication is \emph{oblivious}. This requirement, which to our knowledge is satisfied by all quantum…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
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…
We show two results about the relationship between quantum and classical messages. Our first contribution is to show how to replace a quantum message in a one-way communication protocol by a deterministic message, establishing that for all…
Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…
Neural network-based algorithms have garnered considerable attention in condensed matter physics for their ability to learn complex patterns from very high dimensional data sets towards classifying complex long-range patterns of…
We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f(x)=1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a…
Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…
Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean function $f : \{-1, 1\}^n \to \{-1, 1\}$ and $\bullet : \{-1, 1\}^2 \to \{-1, 1\}$ the two-party bounded-error quantum communication complexity of $(f \circ \bullet)$ is…
Although `quantum contextuality' is one of the most fundamental non-classical feature, its generic role in information processing and computation is an open quest. In this article, we present a family of distributed computing tasks…
We are considering RAMs $N_{n}$, with wordlength $n=2^{d}$, whose arithmetic instructions are the arithmetic operations multiplication and addition modulo $2^{n}$, the unary function $ \min\lbrace 2^{x}, 2^{n}-1\rbrace$, the binary…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent…
We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to "width" complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. But there…
In this paper, we show that while almost all functions require exponential size branching programs to compute, for all functions $f$ there is a branching program computing a doubly exponential number of copies of $f$ which has linear size…
This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…
We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently…
We give the first exponential separation between quantum and classical multi-party communication complexity in the (non-interactive) one-way and simultaneous message passing settings. For every k, we demonstrate a relational communication…
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently,…