25 research outputs found
A logarithmic-depth quantum carry-lookahead adder
We present an efficient addition circuit, borrowing techniques from the
classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead
(QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using
O(n) ancillary qubits. We present both in-place and out-of-place versions, as
well as versions that add modulo 2^n and modulo 2^n - 1.
Previously, the linear-depth ripple-carry addition circuit has been the
method of choice. Our work reduces the cost of addition dramatically with only
a slight increase in the number of required qubits. The QCLA adder can be used
within current modular multiplication circuits to reduce substantially the
run-time of Shor's algorithm.Comment: 21 pages, 4 color figure