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
Simulating quantum mechanics on a quantum computer
PhysComp96 Proceedings of the fourth workshop on Physics and computation
Quantum computation and quantum information
Quantum computation and quantum information
Algebric Decision Diagrams and Their Applications
Formal Methods in System Design
Improving Gate-Level Simulation of Quantum Circuits
Quantum Information Processing
Gate-level simulation of quantum circuits
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
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
Binary superposed quantum decision diagrams
Quantum Information Processing
Fault Models for Quantum Mechanical Switching Networks
Journal of Electronic Testing: Theory and Applications
Robustness of Shor's algorithm
Quantum Information & Computation
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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 array-based 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 for these circuits.