相关论文: Optimal lower bounds for quantum automata and rand…

Affine finite automata (AfA) can be more succinct than probabilistic and quantum finite automata when recognizing some regular languages with bounded-error. In this paper, we improve previously known constructions given for the succinctness…

The approximate degree of a Boolean function f is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly…

Quantum finite automata (QFA) are basic computational devices that make binary decisions using quantum operations. They are known to be exponentially memory efficient compared to their classical counterparts. Here, we demonstrate an…

{\it Two-way finite automata with quantum and classical states} (2qcfa's) were introduced by Ambainis and Watrous. Though this computing model is more restricted than the usual {\it two-way quantum finite automata} (2qfa's) first proposed…

Quantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based…

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r + r)$ on the communication required for…

In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x, y \in\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that…

The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the…

We show that for any two distinct words $ s_1, s_2 $ over an arbitrary alphabets, there exists a deterministic finite automaton with $ O(\log^2 n) $ states that accepts $ s_1 $ and rejects $ s_2 $. This improves the previous upper bound of…

In a recent paper we have described an optical implementation of a measure-once one-way quantum finite automaton recognizing a well-known family of unary periodic languages, accepting words not in the language with a given error…

The goal of the ordered search problem is to find a particular item in an ordered list of n items. Using the adversary method, Hoyer, Neerbek, and Shi proved a quantum lower bound for this problem of (1/pi) ln n + Theta(1). Here, we find…

Let $\eta_0$ be the supremum of those $\eta$ for which every poly-size quantum circuit can be simulated by another poly-size quantum circuit with gates of fan-in $\leq 2$ that tolerates random noise independently occurring on all wires at…

We present a family of easily computable upper bounds for the Holevo quantity of ensemble of quantum states depending on a reference state as a free parameter. These upper bounds are obtained by combining probabilistic and metric…

We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…

We present new results on realtime alternating, private alternating, and quantum alternating automaton models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we…

We study a model of one-way quantum automaton where only measurement operations are allowed (MOn-1qfa). We give an algebraic characterization of LMO, showing that the syntactic monoids of the languages in LMO are exactly the literal…

The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Theta(n^{1/5}) on the number of queries needed by a quantum computer to…

We show that Durr-Hoyer's quantum algorithm of searching for extreme point of integer function can not be sped up for functions chosen randomly. Any other algorithm acting in substantially shorter time $o(\sqrt{2^n})$ gives incorrect answer…

It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…

Every language in NL has a $k$-head two-way nondeterministic finite automaton (2nfa($k$)) recognizing it. It is known how to build a constant-space verifier algorithm from a 2nfa($k$) for the same language with constant-randomness, but with…