Abstract
Algorithms to resolve multiple-qubit unitary transformations into a sequence of simple operations on one-qubit subsystems are central to the methods of quantum-circuit simulators. We adapt Householder’s theorem to the tensor-product character of multi-qubit state vectors and translate it to a combinatorial procedure to assemble cascades of quantum gates that recreate any unitary operation U acting on n-qubit systems. U may be recreated by any cascade from a set of combinatorial options that, in number, are not lesser than super-factorial of 2n. Cascades are assembled with one-qubit controlled-gates of a single type. We complement the assembly procedure with a new algorithm to generate Gray codes that reduce the combinatorial options to cascades with the least number of CNOT gates. The combined procedure —factorization, gate assembling, and Gray ordering — is illustrated on an array of three qubits.
Original language | English |
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Pages (from-to) | 150-157 |
Journal | Canadian Journal of Physics |
Volume | 94 |
Issue number | 2 |
DOIs | |
Publication status | Published - 28 Oct 2015 |
Keywords
- Householder factorizations in tensor-product spaces
- algorithmic synthesis of quantum circuits
- quantum simulators