Combining SWAPs and Remote Toffoli Gates in the Mapping to IBM QX Architectures

AbstractWe report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous demonstration. We go beyond this work by using a configuration of approximate Toffoli gates with residual phase shifts, which preserves the functional correctness and allows us to achieve a complete factoring of $$N=21$$ N = 21 . We implemented the algorithm on IBM quantum processors using only five qubits and successfully verified the presence of entanglement between the control and work register qubits, which is a necessary condition for the algorithm’s speedup in general. The techniques we employ may be useful in carrying out Shor’s algorithm for larger integers, or other algorithms in systems with a limited number of noisy qubits.

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Comment on “Linear-depth quantum circuits forn-qubit Toffoli gates with no ancilla”

Physical Review A ◽

10.1103/physreva.94.026301 ◽

2016 ◽

Vol 94 (2) ◽

Cited By ~ 1

Author(s):

Ming-Xing Luo ◽

Hui-Ran Li

Keyword(s):

Quantum Circuits ◽

Toffoli Gates

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Quantum circuits for simple periodic functions

Quantum Information and Computation ◽

10.26421/qic14.9-10-4 ◽

2014 ◽

Vol 14 (9&10) ◽

pp. 763-776

Author(s):

Omar Gamel ◽

Daniel F.V. James

Keyword(s):

Quantum Computing ◽

Periodic Function ◽

Quantum Circuits ◽

Special Importance ◽

Periodic Functions ◽

Single Period ◽

Shor's Algorithm ◽

Toffoli Gates ◽

One To One

Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for a simple monoperiodic function, that is one-to-one within a single period, of a given period $p$. We conjecture that to create a simple periodic function of period $p$, where $p$ is an $n$-bit number, one needs at most $n$ Toffoli gates.

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