{"id":160626,"date":"2018-11-06T17:23:55","date_gmt":"2018-11-07T01:23:55","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/a-logarithmic-depth-quantum-carry-lookahead-adder\/"},"modified":"2018-11-06T17:23:55","modified_gmt":"2018-11-07T01:23:55","slug":"a-logarithmic-depth-quantum-carry-lookahead-adder","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/a-logarithmic-depth-quantum-carry-lookahead-adder\/","title":{"rendered":"A Logarithmic-depth Quantum Carry-Lookahead Adder"},"content":{"rendered":"<div class=\"asset-content\">\n<p>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<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>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. 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