We present an efficient addition circuit, borrowing techniques from the classical carry look-ahead 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 2n and modulo 2n \u2212 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\u2019s algorithm.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present an efficient addition circuit, borrowing techniques from the classical carry look-ahead 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 2n and modulo 2n \u2212 1. […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Tom Draper"},{"type":"text","value":"Samuel Kutin"},{"type":"text","value":"Eric Rains"},{"type":"text","value":"Krysta M. 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