Quantum Circuit Simplification and Level Compaction
arXiv:quant-ph/0604001 · doi:10.1109/TCAD.2007.911334
Abstract
Quantum circuits are time dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed. With the use of heuristics, the optimality of circuits is no longer guaranteed. In this paper, we consider a local optimization technique based on templates to simplify and reduce the depth of non-optimal quantum circuits. We present and analyze templates in the general case, and provide particular details for the circuits composed of NOT, CNOT and controlled-sqrt-of-NOT gates. We apply templates to optimize various common circuits implementing multiple control Toffoli gates and quantum Boolean arithmetic circuits. We also show how templates can be used to compact the number of levels of a quantum circuit. The runtime of our implementation is small while the reduction in number of quantum gates and number of levels is significant.
13 pages, 6 figures. New author, improved presentation, more results
References in corpus (13)
- Elementary gates for quantum computation
- Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
- Quantum Amplitude Amplification and Estimation
- Scalable multi-particle entanglement of trapped ions
- Synthesis of Quantum Logic Circuits
- A geometric theory of non-local two-qubit operations
- Fast Quantum Modular Exponentiation
- Improved Quantum Cost for n-bit Toffoli Gates
- Efficient Refocussing of One Spin and Two Spin Interactions for NMR Quantum Computation
- Quantum Logic Gates and Nuclear Magnetic Resonance Pulse Sequences
- Decompositions of general quantum gates
- Quantum Circuit Identities
- New Structural Quantum Circuit Simulating a Toffoli Gate
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