Towards optimization of quantum circuits

Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for a short sequence of gates - efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et.al [1]. We also created a computer program which realizes both Barenco's decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.Comment: 10 pages, 11 figures, minor changes+typo

Minimal Universal Two-qubit Quantum Circuits

We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare favorably to previously published results. Temporary storage is not used because it tends to be expensive in physical implementations. For each gate library, best gate counts can be achieved by a single universal circuit. To compute gate parameters in universal circuits, we only use closed-form algebraic expressions, and in particular do not rely on matrix exponentials. Our algorithm has been coded in C++.Comment: 8 pages, 2 tables and 4 figures. v3 adds a discussion of asymetry between Rx, Ry and Rz gates and describes a subtle circuit design problem arising when Ry gates are not available. v2 sharpens one of the loose bounds in v1. Proof techniques in v2 are noticeably revamped: they now rely less on circuit identities and more on directly-computed invariants of two-qubit operators. This makes proofs more constructive and easier to interpret as algorithm

Performance Evaluation of Adaptive Scientific Applications using TAU

Fueled by increasing processor speeds and high speed interconnection networks, advances in high performance computer architectures have allowed the development of increasingly complex large scale parallel systems. For computational scientists, programming these systems efficiently is a challenging task. Understanding the performance of their parallel applications i

Measurements of scattering observables for the pdpd break-up reaction

High-precision measurements of the scattering observables such as cross sections and analyzing powers for the proton-deuteron elastic and break-up reactions have been performed at KVI in the last two decades and elsewhere to investigate various aspects of the three-nucleon force (3NF) effects simultaneously. In 2006 an experiment was performed to study these effects in $\vec{p}+d$ break-up reaction at 135 MeV with the detection system, Big Instrument for Nuclear polarization Analysis, BINA. BINA covers almost the entire kinematical phase space of the break-up reaction. The results are interpreted with the help of state-of-the-art Faddeev calculations and are partly presented in this contribution.Comment: Proceedings of 19th International IUPAP Conference on Few-Body Problems in Physics, Bonn University, 31.08 - 05.09.2009, Bonn, GERMAN

A Similarity Measure for GPU Kernel Subgraph Matching

Accelerator architectures specialize in executing SIMD (single instruction, multiple data) in lockstep. Because the majority of CUDA applications are parallelized loops, control flow information can provide an in-depth characterization of a kernel. CUDAflow is a tool that statically separates CUDA binaries into basic block regions and dynamically measures instruction and basic block frequencies. CUDAflow captures this information in a control flow graph (CFG) and performs subgraph matching across various kernel's CFGs to gain insights to an application's resource requirements, based on the shape and traversal of the graph, instruction operations executed and registers allocated, among other information. The utility of CUDAflow is demonstrated with SHOC and Rodinia application case studies on a variety of GPU architectures, revealing novel thread divergence characteristics that facilitates end users, autotuners and compilers in generating high performing code

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author

An Arbitrary Two-qubit Computation In 23 Elementary Gates

Quantum circuits currently constitute a dominant model for quantum computation. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2 CNOTs. To this end, we constructively prove a worst-case upper bound of 23 elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail much larger quantum circuits than ours in the special case of two qubits. One such algorithm has a worst case of 61 gates of which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie theory as well as the polar and spectral (symmetric Shur) matrix decompositions from numerical analysis and operator theory. They are related to the canonical decomposition of a two-qubit gate with respect to the ``magic basis'' of phase-shifted Bell states, published previously. We further extend this decomposition in terms of elementary gates for quantum computation.Comment: 18 pages, 7 figures. Version 2 gives correct credits for the GQC "quantum compiler". Version 3 adds justification for our choice of elementary gates and adds a comparison with classical library-less logic synthesis. It adds acknowledgements and a new reference, adds full details about the 8-gate decomposition of topC-V and stealthily fixes several minor inaccuracies. NOTE: Using a new technique, we recently improved the lower bound to 18 gates and (tada!) found a circuit decomposition that requires 18 gates or less. This work will appear as a separate manuscrip

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons

We discuss the quantum-circuit realization of the state of a nucleon in the scope of simple symmetry groups. Explicit algorithms are presented for the preparation of the state of a neutron or a proton as resulting from the composition of their quark constituents. We estimate the computational resources required for such a simulation and design a photonic network for its implementation. Moreover, we highlight that current work on three-body interactions in lattices of interacting qubits, combined with the measurement-based paradigm for quantum information processing, may also be suitable for the implementation of these nucleonic spin states.Comment: 5 pages, 2 figures, RevTeX4; Accepted for publication in Quantum Information Processin

High statistics study of the reaction γp→p 2π0\gamma p\to p\;2\pi^0

The photoproduction of 2$\pi^0$ mesons off protons was studied with the Crystal Barrel/TAPS experiment at the electron accelerator ELSA in Bonn. The energy of photons produced in a radiator was tagged in the energy range from 600\,MeV to 2.5\,GeV. Differential and total cross sections and $p\pi^0\pi^0$ Dalitz plots are presented. Part of the data was taken with a diamond radiator producing linearly polarized photons, and beam asymmetries were derived. Properties of nucleon and $\Delta$ resonances contributing to the $p\pi^0\pi^0$ final state were determined within the BnGa partial wave analysis. The data presented here allow us to determine branching ratios of nucleon and $\Delta$ resonances for their decays into $p\pi^0\pi^0$ via several intermediate states. Most prominent are decays proceeding via $\Delta(1232)\pi$, $N(1440)1/2^+\pi$, $N(1520)3/2^-\pi$, $N(1680)5/2^+\pi$, but also $pf_0(500)$, $pf_0(980)$, and $pf_2(1270)$ contribute to the reaction.Comment: 28 pages, 17 figures, 7 table