62 research outputs found
Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels
Inspired by the Solovay-Kitaev decomposition for approximating unitary
operations as a sequence of operations selected from a universal quantum
computing gate set, we introduce a method for approximating any single-qubit
channel using single-qubit gates and the controlled-NOT (CNOT). Our approach
uses the decomposition of the single-qubit channel into a convex combination of
"quasiextreme" channels. Previous techniques for simulating general
single-qubit channels would require as many as 20 CNOT gates, whereas ours only
needs one, bringing it within the range of current experiments
Quantum Fourier Addition, Simplified to Toffoli Addition
Quantum addition circuits are considered being of two types: 1)
Toffolli-adder circuits which use only classical reversible gates (CNOT and
Toffoli), and 2) QFT-adder circuits based on the quantum Fourier
transformation. We present the first systematic translation of the QFT-addition
circuit into a Toffoli-based adder. This result shows that QFT-addition has
fundamentally the same fault-tolerance cost (e.g. T-count) as the most
cost-efficient Toffoli-adder: instead of using approximate decompositions of
the gates from the QFT circuit, it is more efficient to merge gates. In order
to achieve this, we formulated novel circuit identities for multi-controlled
gates and apply the identities algorithmically. The employed techniques can be
used to automate quantum circuit optimisation heuristics.Comment: accepted in PR
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