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Improving gatelevel simulation of quantum circuits
 Quantum Information Processing
"... 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 198 ..."
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Cited by 35 (8 self)
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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 polynomialtime simulation of restricted types of quantum circuits that fall short of the full power of quantum computation [7]. 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 gatelevel 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 Groverâ€™s quantum search algorithm [8]. The backend of our package, QuIDD Pro, is based on Binary Decision Diagrams, wellknown for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a wellestablished area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation. 1
Discrete Cosine Transforms on Quantum Computers
 PROCEEDINGS OF THE 2ND INTERNATIONAL SYMPOSIUM ON IMAGE AND SIGNAL PROCESSING AND ANALYSIS
, 2001
"... A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it ..."
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Cited by 10 (2 self)
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A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size N N and types I,II,III, and IV with as little as O(log 2 N) operations on a quantum computer, whereas the known fast algorithms on a classical computer need O(N log N) operations.
A Parallel Quantum Computer Simulator
, 1997
"... A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that prime factorization is computationally difficult. Errors limit ..."
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Cited by 6 (1 self)
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A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that prime factorization is computationally difficult. Errors limit the effectiveness of quantum computers. Because of the exponential nature of quantum computers, simulating the effect of errors on them requires a vast amount of processing and memory resources. In this paper we describe a parallel simulator which accesses the feasibility of quantum computers. We also derive and validate an analytical model of execution time for the simulator, which shows that parallel quantum computer simulation is very scalable. # Submitted to High Performance Computing `98 September 19, 1997 1 1.0 Introduction A quantum computer consists of atomic particles which obey the laws of quantum mechanics. The complexity of a quantum system is exponential with respect to the...
Models to Reduce the Complexity of Simulating a Quantum Computer
, 1997
"... Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum computer is limited by the effect of errors. Simulation is a useful tool for determining the feasibility of quantum ..."
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Cited by 4 (1 self)
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Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum computer is limited by the effect of errors. Simulation is a useful tool for determining the feasibility of quantum computers in the presence of errors. The size of a quantum computer that can be simulated is small because faithfully modeling a quantum computer requires an exponential amount of storage and number of operations. In this paper we define simulation models to study the feasibility of quantum computers. The most detailed of these models is based directly on a proposed implementation. We also define less detailed models which are exponentially less complex but still produce accurate results. Finally we show that the two different types of errors, decoherence and inaccuracies, are uncorrelated. This decreases the number of simulations which must be performed. Models to Reduce the Complexity of S...
QuantPh/9804044
, 2001
"... The main features of quantum computing are described in the framework of spin resonance methods. ..."
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The main features of quantum computing are described in the framework of spin resonance methods.
Entangling DipoleDipole Interactions with Neutral Atoms . . .
"... OF DISSERTATION Submitted in Partial Fulfillment of the Albuquerque, New Mexico vi ########################################## ################################### ## ################ ################################################### ############################################ ######## This diss ..."
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OF DISSERTATION Submitted in Partial Fulfillment of the Albuquerque, New Mexico vi ########################################## ################################### ## ################ ################################################### ############################################ ######## This dissertation studies the entanglement via dipoledipole interactions of a pair of neutral atoms trapped in an optical lattice. Information can be encoded in the groundstate hyperfine levels and processed by bringing atoms together pairwise to perform quantum logical operations through induced dipoledipole interactions. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate and substantial coherent evolution of the two atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states, allowing for deterministic generation of entanglement. We investigate, in progressively complex models of atomic structure, protocols to couple ground states with dipoledipole coupled excited molecular states, culminating in a realistic model of entanglement engineering between trapped alkalis with hyperfine structure. We analyze the robustness of this entangling evolution for executing quantum logic gates against sources of decoherence such as photon scattering and coherent leakage outside the logical basis and explore the power of such protocols to perform general quantum information processing tasks. vii CONTENTS List of Figures .................................................................................................................. ix List of Tables......................................................................................................................x Preface...
Reversible Logic Circuit Synthesis
 In International Conference on Computer Aided Design
, 2002
"... Reversible or informationlossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. ..."
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Reversible or informationlossless circuits have applications in digital signal processing, communication, computer graphics and cryptography.