4,368 research outputs found
Equivalence Checking of Sequential Quantum Circuits
We define a formal framework for equivalence checking of sequential quantum
circuits. The model we adopted is a quantum state machine, which is a natural
quantum generalisation of Mealy machines. A major difficulty in checking
quantum circuits (but not present in checking classical circuits) is that the
state spaces of quantum circuits are continuums. This difficulty is resolved by
our main theorem showing that equivalence checking of two quantum Mealy
machines can be done with input sequences that are taken from some chosen basis
(which are finite) and have a length quadratic in the dimensions of the state
Hilbert spaces of the machines. Based on this theoretical result, we develop an
(and to the best of our knowledge, the first) algorithm for checking
equivalence of sequential quantum circuits. A case study and experiments are
presented
Equivalence Checking of Quantum Finite-State Machines
In this paper, we introduce the model of quantum Mealy machines and study the
equivalence checking and minimisation problems of them. Two efficient
algorithms are developed for checking equivalence of two states in the same
machine and for checking equivalence of two machines. They are applied in
experiments of equivalence checking of quantum circuits. Moreover, it is shown
that the minimisation problem is proved to be in \textbf{PSPACE}
Perfect Computational Equivalence between Quantum Turing Machines and Finitely Generated Uniform Quantum Circuit Families
In order to establish the computational equivalence between quantum Turing
machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit
simulation of QTMs, we previously introduced the class of uniform QCFs based on
an infinite set of elementary gates, which has been shown to be computationally
equivalent to the polynomial-time QTMs (with appropriate restriction of
amplitudes) up to bounded error simulation. This result implies that the
complexity class BQP introduced by Bernstein and Vazirani for QTMs equals its
counterpart for uniform QCFs. However, the complexity classes ZQP and EQP for
QTMs do not appear to equal their counterparts for uniform QCFs. In this paper,
we introduce a subclass of uniform QCFs, the finitely generated uniform QCFs,
based on finite number of elementary gates and show that the class of finitely
generated uniform QCFs is perfectly equivalent to the class of polynomial-time
QTMs; they can exactly simulate each other. This naturally implies that BQP as
well as ZQP and EQP equal the corresponding complexity classes of the finitely
generated uniform QCFs.Comment: 11page
Bounded Counter Languages
We show that deterministic finite automata equipped with two-way heads
are equivalent to deterministic machines with a single two-way input head and
linearly bounded counters if the accepted language is strictly bounded,
i.e., a subset of for a fixed sequence of symbols . Then we investigate linear speed-up for counter machines. Lower
and upper time bounds for concrete recognition problems are shown, implying
that in general linear speed-up does not hold for counter machines. For bounded
languages we develop a technique for speeding up computations by any constant
factor at the expense of adding a fixed number of counters
(Un)decidable Problems about Reachability of Quantum Systems
We study the reachability problem of a quantum system modelled by a quantum
automaton. The reachable sets are chosen to be boolean combinations of (closed)
subspaces of the state space of the quantum system. Four different reachability
properties are considered: eventually reachable, globally reachable, ultimately
forever reachable, and infinitely often reachable. The main result of this
paper is that all of the four reachability properties are undecidable in
general; however, the last three become decidable if the reachable sets are
boolean combinations without negation
Computing with Coloured Tangles
We suggest a diagrammatic model of computation based on an axiom of
distributivity. A diagram of a decorated coloured tangle, similar to those that
appear in low dimensional topology, plays the role of a circuit diagram.
Equivalent diagrams represent bisimilar computations. We prove that our model
of computation is Turing complete, and that with bounded resources it can
moreover decide any language in complexity class IP, sometimes with better
performance parameters than corresponding classical protocols.Comment: 36 pages,; Introduction entirely rewritten, Section 4.3 adde
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