Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Feynman and computation: exploring the limits of computers
Feynman and computation: exploring the limits of computers
Quantum computation and quantum information
Quantum computation and quantum information
Algebric Decision Diagrams and Their Applications
Formal Methods in System Design
Gate-level simulation of quantum circuits
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
High-Performance QuIDD-Based Simulation of Quantum Circuits
Proceedings of the conference on Design, automation and test in Europe - Volume 2
Accurate Reliability Evaluation and Enhancement via Probabilistic Transfer Matrices
Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Computing in Science and Engineering
Analysis and synthesis of quantum circuits by using quantum decision diagrams
Proceedings of the conference on Design, automation and test in Europe: Proceedings
Probabilistic transfer matrices in symbolic reliability analysis of logic circuits
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Checking equivalence of quantum circuits and states
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Improved BDD Algorithms for the Simulation of Quantum Circuits
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An XQDD-Based Verification Method for Quantum Circuits
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Fast equivalence-checking for quantum circuits
Proceedings of the 2010 IEEE/ACM International Symposium on Nanoscale Architectures
Fast equivalence-checking for quantum circuits
Quantum Information & Computation
Graph-based simulation of quantum computation in the density matrix representation
Quantum Information & Computation
Quantum walks: a comprehensive review
Quantum Information Processing
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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.PACS: 03.67.Lx, 03.65.Fd, 03.65.Vd, 07.05.Bx