On the realistic worst case analysis of quantum arithmetic circuits

Alexandru Paler, Oumarou Oumarou, Robert Basmadjian

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular, we show that 1) reducing the T-count can increase the total depth; 2) it may be beneficial to trade controlled NOTs for measurements in noisy intermediate-scale quantum (NISQ) circuits; 2) measurement-based uncomputation of relative phase Toffoli ancillae can make up to 30% of a circuit's depth; and 4) area and volume cost metrics can misreport the resource analysis. Our findings assume that qubits are and will remain a very scarce resource. The results are applicable for both NISQ and quantum error-corrected protected circuits. Our method uses multiple ways of decomposing Toffoli gates into Clifford+T gates. We illustrate our method on addition and multiplication circuits using ripple-carry. As a byproduct result, we show systematically that for a practically significant range of circuit widths, ripple-carry addition circuits are more resource-efficient than the carry-lookahead addition ones. The methods and circuits were implemented in the open-source QUANTIFY software.

Original languageEnglish
Article number3101311
JournalIEEE Transactions on Quantum Engineering
Publication statusPublished - 2022
MoE publication typeA1 Journal article-refereed


  • Adders
  • Arithmetic
  • Costs
  • Logic gates
  • Optimization
  • Quantum computing
  • Qubit


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