Daowen Qiu

Xin Sun, Feifei He, Daowen Qiu et al.

We designed two rules of binary quantum computed vote: Quantum Logical Veto (QLV) and Quantum Logical Nomination (QLN). The conjunction and disjunction from quantum computational logic are used to define QLV and QLN, respectively. Compared to classical vote, quantum computed vote is fairer, more democratic and has stronger expressive power. Since the advantage of quantum computed vote is neither the speed of computing nor the security of communication, we believe it opens a new battlefield in the second quantum revolution. Compared to other rules of quantum computed vote, QLV and QLN have better scalability. Both QLV and QLN can be implemented by the current technology and the difficulty of implementation does not grow with the increase of the number of voters.

Daowen Qiu

Discrete event systems (DES) have been deeply developed and applied in practice, but state complexity in DES still is an important problem to be better solved with innovative methods. With the development of quantum computing and quantum control, a natural problem is to simulate DES by means of quantum computing models and to establish {\it quantum DES} (QDES). The motivation is twofold: on the one hand, QDES have potential applications when DES are simulated and processed by quantum computers, where quantum systems are employed to simulate the evolution of states driven by discrete events, and on the other hand, QDES may have essential advantages over DES concerning state complexity for imitating some practical problems. So, the goal of this paper is to establish a basic framework of QDES by using {\it quantum finite automata} (QFA) as the modelling formalisms, and the supervisory control theorems of QDES are established and proved. Then we present a polynomial-time algorithm to decide whether or not the controllability condition holds. In particular, we construct a number of new examples of QFA to illustrate the supervisory control of QDES and to verify the essential advantages of QDES over classical DES in state complexity.

Fang Yu, Daowen Qiu, Xiaoming Wang et al.

New quantum private database (with N elements) query protocols are presented and analyzed. Protocols preserve O(logN) communication complexity of known protocols for the same task, but achieve several significant improvements in security, especially concerning user privacy. For example, the randomized form of our protocol has a cheat-sensitive property - it allows the user to detect a dishonest database with a nonzero probability, while the phase-encoded private query protocols for the same task do not have such a property. Moreover, when the database performs the computational basis measurement, a particular projective measurement which can cause a significant loss of user privacy in the previous private query protocols with O(logN) communication complexity, at most half of the user privacy could leak to such a database in our protocol, while in the QPQ protocol, the entire user privacy could leak out. In addition, it is proved here that for large N, the user could detect a cheating via the computational basis measurement, with a probability close to 1/2 using O(\sqrt{N}) special queries. Finally, it is shown here, for both forms of our protocol, basic and randomized, how a dishonest database has to act in case it could not learn user's queries.

Weilin Deng, Jingkai Yang, Daowen Qiu

The supervisory control of probabilistic discrete event systems (PDESs) is investigated under the assumptions that the supervisory controller (supervisor) is probabilistic and has a partial observation. The probabilistic P-supervisor is defined, which specifies a probability distribution on the control patterns for each observation. The notions of the probabilistic controllability and observability are proposed and demonstrated to be a necessary and sufficient conditions for the existence of the probabilistic P-supervisors. Moreover, the polynomial verification algorithms for the probabilistic controllability and observability are put forward. In addition, the infimal probabilistic controllable and observable superlanguage is introduced and computed as the solution of the optimal control problem of PDESs. Several examples are presented to illustrate the results obtained.

Shenggen Zheng, Daowen Qiu, Jozef Gruska

In this paper we explore the power of AM for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA)--introduced by Ambainis and Watrous in 2002--and the communications are classical. It is of interest to consider AM with such "semi-quantum" verifiers because they use only limited quantum resources. Our main result is that such Quantum Arthur-Merlin proof systems (QAM(2QCFA)) with polynomial expected running time are more powerful than in the case verifiers are two-way probabilistic finite automata (AM(2PFA)) with polynomial expected running time. Moreover, we prove that there is a language which can be recognized by an exponential expected running time QAM(2QCFA), but can not be recognized by any AM(2PFA), and that the NP-complete language $L_{knapsack}$ can also be recognized by a QAM(2QCFA) working only on quantum pure states using unitary operators.