A new quantum ripple-carry addition circuit

By S. Cuccaro, Thomas G. Draper, Samuel Kutin, D. Moulton. 2004

630 citations recorded by the source corpus.

We present a new linear-depth ripple-carry quantum addition circuit. Previous addition circuits required linearly many ancillary qubits; our new adder uses only a single ancillary qubit. Also, our circuit has lower depth and fewer gates than previous ripple-carry adders.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/fe5c54cfa999706c217da3a0622adbdffc915b11

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum Computing for Finance: State-of-the-Art and Future Prospects (2020, positive): “This implies that we start with a weighted-sum operator, discussed in detail in [7], and then continue with adder circuits [52] to iteratively combine the intermediate results.”
Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning (2013, neutral): “1 RC-Adder6 [9] 14 104 77 30 234 63 29 0.”
Halving the cost of quantum addition (2017, methodology): “Existing constructions implement the Cuccaro adder’s Toffolis using 8n + O(1) T gates [1, 3, 6].”
An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures (2017, background): “6 Besides that, benchmarks that are relevant for existing quantum algorithms such as quantum ripple-carry adders (based on the realization proposed in [37] and denoted adder ) and small versions of Shor’s algorithm (based on the realization proposed in [38] and denoted shor ) have been considered.”
Open Quantum Assembly Language (2017, background): “[0]j0i X X X X X majority 0 2 1 majority 0 2 1 majority 0 2 1 majority 0 2 1 unmaj unmaj 0 unmaj 1 unmaj 2 1 ans[0] ans[1] ans[2] ans[3] ans[4] Figure 11: Example of a quantum ripple-carry adder from [29]. This circuit prepares a= 1, b= 15 and computes the sum into b with an output carry cout[0]. h ”
Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects (2012, background): “When only local interactions are available without dedicated buses for entanglement distribution, a quantum ripple-carry adder (QRCA) is the adequate adder of choice [49], for which the execution time goes as O(n).”
Option Pricing using Quantum Computers (2019, methodology): “This operation can be implemented by a quantum comparator [36] based on CNOT and Toffoli gates.”
A logarithmic-depth quantum carry-lookahead adder (2004, background): “We denote the n − 1 ancillae which store the carry string as Z [1] , . . . , Z [ n − 1], and the remaining ancillae as X .”
Hamiltonian Simulation in the Interaction Picture (2018, methodology): “[22] Steven A Cuccaro, Thomas G Draper, Samuel A Kutin, and David Petrie Moulton.”