On the realistic worst case analysis of quantum arithmetic circuits

TL;DR

This paper challenges common assumptions in quantum circuit design, showing that optimizing certain metrics can lead to increased depth or resource costs, with implications for both NISQ and error-corrected quantum circuits.

Contribution

It introduces new analysis methods for quantum circuit resource trade-offs, including decomposition techniques and measurement strategies, with practical implementation in open-source software.

Findings

Reducing T-count can increase circuit depth.

Measurement-based uncomputation can account for up to 30% of depth.

Ripple-carry adders are more resource-efficient than carry-lookahead for certain sizes.

Abstract

We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements in NISQ circuits; c) measurement-based uncomputation of relative phase Toffoli ancillae can make up to 30\% of a circuit's depth; d) 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 QECC 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.