Quantum Gates and Circuits

Holger Boche, Yannik N. Bock, Zoe Garcia del Toro +1 more

We investigate the feasibility of computing quantum gate-circuit emulation (QGCE) and quantum gate-circuit concatenation (QGCC) on digital hardware. QGCE serves the purpose of rewriting gate circuits comprised of gates from a varying input gate set to gate circuits formed of gates from a fixed target gate set. Analogously, QGCC serves the purpose of finding an approximation to the concatenation of two arbitrary elements of a varying list of input gate circuits in terms of another element from the same list. Problems of this kind occur regularly in quantum computing and are often assumed an easy task for the digital computers controlling the quantum hardware. Arguably, this belief is due to analogical reasoning: The classical Boolean equivalents of QGCE and QGCC are natively computable on digital hardware. In the present paper, we present two insights in this regard: Upon applying a rigorous theory of computability, QGCE and QGCC turn out to be uncomputable on digital hardware. The results remain valid when we restrict the set of feasible inputs for the relevant functions to one parameter families of fixed gate sets. Our results underline the possibility that several ideas from quantum-computing theory may require a rethinking to become feasible for practical implementation.

Wolfgang Scherer

Nathan O. Scott, Gerhard W. Dueck

Quantum circuit synthesis is the procedure of automatically generating quantum circuits to represent specified functions. A common gate in quantum circuits is the reversible Toffoli gate, a type of generalized controlled NOT operation. There are physical barriers to implementing large quantum gates. Large Toffoli gates can be decomposed into equivalent sets of smaller, quantum elementary gates. The cost of a quantum circuit can be measured by counting the number of elementary gates in the circuit after all gates have been decomposed. Traditionally this decomposition is done independently for each gate in the circuit. This thesis identifies pairs of gates that, if decomposed together, result in fewer total elementary gates than they would otherwise. These improvements are incorporated into a simple decomposition algorithm which manipulates the circuit in order to search for such pairs. The decomposition algorithm is compared to a naive implementation, and the resulting gate costs are presented and compared.

Leporati

Majid Mohammadi, Mohammad Eshghi

Quantum gates which are represented by unitary matrices have potentials to implement reversible logic circuits. V and V+gates are two well known quantum gates which are used to synthesize the reversible logic circuits. In this paper we have used behavioral description of these gates, instead of unitary matrix description, to synthesize reversible logic circuits. By this method, V and V+gates are shown in the truth table form. Results show that bigger circuits with more number of gates can be synthesized using proposed method. Some benchmarks of reversible logic circuits are also optimized and compared to other works.