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<p>The space and time complexity of many quantum algorithms, including Shor’s algorithm, depends strongly on the efficiency of the underlying arithmetic circuits. Since many mathematical operation gates include controlled adders, optimizing controlled adders is important for improving the practical efficiency of quantum arithmetic. In this paper, we propose an optimized circuit of controlled CDKM adder (including carryless version) using Bennett’s trick, gate substitution and rearrangement. In addition, by applying gate substitution and rearrangement, we modified the circuit of controlled ripple carry adder (including carryless version) and reduced the <Emphasis FontCategory="NonProportional">Toffoli</Emphasis> depth from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(3n+O(1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mi>n</mi> <mo>+</mo> <mi>O</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2n+O(1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mi>O</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Construction and depth optimization of quantum controlled adder

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Chanho Jeon,
  • Donghoe Heo,
  • Hyojun Shin,
  • Seokhie Hong

摘要

The space and time complexity of many quantum algorithms, including Shor’s algorithm, depends strongly on the efficiency of the underlying arithmetic circuits. Since many mathematical operation gates include controlled adders, optimizing controlled adders is important for improving the practical efficiency of quantum arithmetic. In this paper, we propose an optimized circuit of controlled CDKM adder (including carryless version) using Bennett’s trick, gate substitution and rearrangement. In addition, by applying gate substitution and rearrangement, we modified the circuit of controlled ripple carry adder (including carryless version) and reduced the Toffoli depth from \(3n+O(1)\) 3 n + O ( 1 ) to \(2n+O(1)\) 2 n + O ( 1 ) .