Gate-Level Simulation of Quantum Circuits

While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomial-time simulation of restricted types of quantum circuits that fall short of the full power of quantum computation. Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gate-level simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover's quantum search algorithm. The back-end of our package, QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a well-established area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation

Improving Gate-Level Simulation of Quantum Circuits

Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and the vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a novel data structure called the Quantum Information Decision Diagram (QuIDD) that exploits the structure of quantum operators, a useful subset of operator matrices and state vectors can be represented in a form that grows polynomially with the number of qubits. This subset contains, but is not limited to, any equal superposition of n qubits, any computational basis state, n-qubit Pauli matrices, and n-qubit Hadamard matrices. It does not, however, contain the discrete Fourier transform (employed in Shor's algorithm) and some oracles used in Grover's algorithm. We first introduce and motivate decision diagrams and QuIDDs. We then analyze the runtime and memory complexity of QuIDD operations. Finally, we empirically validate QuIDD-based simulation by means of a general-purpose quantum computing simulator QuIDDPro implemented in C++. We simulate various instances of Grover's algorithm with QuIDDPro, and the results demonstrate that QuIDDs asymptotically outperform all other known simulation techniques. Our simulations also show that well-known worst-case instances of classical searching can be circumvented in many specific cases by data compression techniques.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45525/1/11128_2004_Article_482625.pd

Efficient quantum circuit simulation

Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.Ph.D.Applied SciencesComputer scienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126583/2/3253425.pd

Graph-based Simulation of Quantum Computation in the Density Matrix Representation

Quantum-mechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication. Simulating such phenomena efficiently is exceedingly difficult because of the vast size of the quantum state space involved. A major complication is caused by errors (noise) due to unwanted interactions between the quantum states and the environment. Consequently, simulating quantum circuits and their associated errors using the density matrix representation is potentially significant in many applications, but is well beyond the computational abilities of most classical simulation techniques in both time and memory resources. The size of a density matrix grows exponentially with the number of qubits simulated, rendering array-based simulation techniques that explicitly store the density matrix intractable. In this work, we propose a new technique aimed at efficiently simulating quantum circuits that are subject to errors. In particular, we describe new graph-based algorithms implemented in the simulator QuIDDPro/D. While previously reported graph-based simulators operate in terms of the state-vector representation, these new algorithms use the density matrix representation. To gauge the improvements offered by QuIDDPro/D, we compare its simulation performance with an optimized arraybased simulator called QCSim. Empirical results, generated by both simulators on a set of quantum circuit benchmarks involving error correction, reversible logic, communication, and quantum search, show that the graph-based approach far outperforms the array-based approach

New aminoacid -schiff bases and Ni(II) complexes synthesis, characterization and evaluation of biological activity

Bu çalışmada, 5 - Flor - Salisilaldehit ve 5 - Flor - 3 - Klor Salisilaldehit ile D - glisin ve D- alaninden Schiff bazları ve onun Ni(II) kompleksleri hazırlanarak, karakterizasyon ve biyolojik aktivitelerinin değerlendirilmesi yapıldı. Schiff bazları ve Ni(II) komplekslerinin yapıları, element analizleri FTIR, 1H-NMR, 13C-NMR, UV-GB spektrumları ile aydınlatıldı. Bütün komplekslerde Schiff bazlarının Ni(II) iyonuna imin azotu, karbonil oksijeni ve hidroksil oksijeninden bağlanarak üç dişli şelat olarak davrandığı ve Ni(II) : L oranının 1:1 olduğu öngörüldü. 5 - Flor - Salisilaldehitten hazırlanan Schiff bazı komplekslerinin ise kare düzlem yapıya sahip olduğu öngörüldü. Aminoasit - Schiff bazları ve onun Ni(II) komplekslerinin Staphylococcus aureus (RSKK-07035), Escherichia coli (ATCC-1230), Salmonella typhi H (NCTC- 901.8394), Brucella abortus (RSKK-03026), Micrococcus luteus, Listeria monocytogenes 4b (ATCC 19115), Staphylococcus epidermidis, Sh.dys. typ 10 ve maya olarak Candida albicans (Y-1200-NIH), Tokyo`ya karşı biyolojik aktiviteleri değerlendirildi.In this study, by using 5- Floro- Salisilaldehyde and 5- Floro 3- Chloride Salisilaldehyde with D-glycine and D-alanine, Schiff bases and their Ni(II) complexes were prepared. Characterization and biological activities were evaluated. The structure and element analysis of Schiff bases and Ni (II) complexes are lightened by using FTIR, 1H-NMR, 13C-NMR and UV- GB spectras. In the all complexes, the Schiff bases act as three dentate chelate connecting to Ni(II) ion from imine nitrogen, carbonyl oxygen and hydroxyl oxygen. The result of it, Ni(II): L ratio 1:1 was foreseen. Schiff base complexes prepared by 5 - Floro - Salisilaldehyde were foreseen square planar structure. The biological activities of amino acid - Schiff bases and their Ni(II) complexes were evaluated against Staphylococcus aureus (RSKK-07035), Escherichia coli (ATCC-1230), Salmonella typhi H (NCTC- 901.8394), Brucella abortus (RSKK-03026), Micrococcus luteus, Listeria monocytogenes 4b (ATCC 19115), Staphylococcus epidermidis, Sh.dys. typ 10 and Candida albicans (Y-1200-NIH) used as a yeast, Toky