Application of Permutation Group Theory in Reversible Logic Synthesis

The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits consisting of gates from the NCT library is described. An algorithm for gate complexity reduction, based on equivalent replacements of gates compositions, is introduced. A new approach for combining a group-theory-based synthesis algorithm with a Reed-Muller-spectra-based synthesis algorithm is described. Experimental results are presented to show that the proposed synthesis techniques allow a reduction in input lines count, gate complexity or quantum cost of reversible circuits for various benchmark functions.Comment: In English, 15 pages, 2 figures, 7 tables. Proceeding of the RC 2016 conferenc

Realisation of a programmable two-qubit quantum processor

The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. Algorithms performed on such a device are predicted to offer significant gains for some important computational tasks. In the context of quantum information, "universal" refers to the ability to perform arbitrary unitary transformations in the system's computational space. The combination of arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate is a gate set capable of achieving universal control of any number of qubits, provided that these gates can be performed repeatedly and between arbitrary pairs of qubits. Although gate sets have been demonstrated in several technologies, they have as yet been tailored toward specific tasks, forming a small subset of all unitary operators. Here we demonstrate a programmable quantum processor that realises arbitrary unitary transformations on two qubits, which are stored in trapped atomic ions. Using quantum state and process tomography, we characterise the fidelity of our implementation for 160 randomly chosen operations. This universal control is equivalent to simulating any pairwise interaction between spin-1/2 systems. A programmable multi-qubit register could form a core component of a large-scale quantum processor, and the methods used here are suitable for such a device.Comment: 7 pages, 4 figure

Synthesizing Quantum Circuits via Numerical Optimization

International audienceWe provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of quantum gates required to implement any quantum algorithm. Then we present numerical experiments with random quantum operators where we compute the optimal parameters of the circuits and we illustrate the correctness of the theoretical lower bounds. We finally discuss the scalability of the method with the number of qubits

SAT-based {CNOT, T} Quantum Circuit Synthesis

The prospective of practical quantum computers has lead researchers to investigate automatic tools to program them. A quantum program is modeled as a Clifford+T quantum circuit that needs to be optimized in order to comply with quantum technology constraints. Most of the optimization algorithms aim at reducing the number of T gates. Nevertheless, a secondary optimization objective should be to minimize the number of two-qubit operations (the CNOT gates) as they show lower fidelity and higher error rate when compared to single-qubit operations. We have developed an exact SAT-based algorithm for quantum circuit rewriting that aims at reducing CNOT gates without increasing the number of T gates. Our algorithm finds the minimum {CNOT, T} circuit for a given phase polynomial description of a unitary transformation. Experiments confirm a reduction of CNOT in T-optimized quantum circuits. We synthesize quantum circuits for all single-target gates whose control functions are one of the representatives of the 48 spectral equivalence classes of all 5-input Boolean functions. Our experiments show an average CNOT reduction of 26.84%

Fungal indole alkaloid biogenesis through evolution of a bifunctional reductase/Diels-Alderase

Prenylated indole alkaloids such as the calmodulin-inhibitory malbrancheamides and anthelmintic paraherquamides possess great structural diversity and pharmaceutical utility. Here, we report complete elucidation of the malbrancheamide biosynthetic pathway accomplished through complementary approaches. These include a biomimetic total synthesis to access the natural alkaloid and biosynthetic intermediates in racemic form and in vitro enzymatic reconstitution to provide access to the natural antipode (+)-malbrancheamide. Reductive cleavage of an L-Pro–L-Trp dipeptide from the MalG non-ribosomal peptide synthetase (NRPS) followed by reverse prenylation and a cascade of post-NRPS reactions culminates in an intramolecular [4+2] hetero-Diels–Alder (IMDA) cyclization to furnish the bicyclo[2.2.2]diazaoctane scaffold. Enzymatic assembly of optically pure (+)-premalbrancheamide involves an unexpected zwitterionic intermediate where MalC catalyses enantioselective cycloaddition as a bifunctional NADPH-dependent reductase/Diels–Alderase. The crystal structures of substrate and product complexes together with site-directed mutagenesis and molecular dynamics simulations demonstrate how MalC and PhqE (its homologue from the paraherquamide pathway) catalyse diastereo- and enantioselective cyclization in the construction of this important class of secondary metabolites

Reversing Unbounded Petri Nets

International audienceIn Petri nets, computation is performed by executing transitions. An effect-reverse of a given transition b is a transition that, when executed, undoes the effect of b. A transition b is reversible if it is possible to add enough effect-reverses of b so to always being able to undo its effect, without changing the set of reachable markings. This paper studies the transition reversibility problem: in a given Petri net, is a given transition b reversible? We show that, contrarily to what happens for the subclass of bounded Petri nets, the transition reversibility problem is in general undecidable. We show, however, that the same problem is decidable in relevant subclasses beyond bounded Petri nets, notably including all Petri nets which are cyclic, that is where the initial marking is reachable from any reachable marking. We finally show that some non-reversible Petri nets can be restructured, in particular by adding new places, so to make them reversible, while preserving their behaviour