TY - JOUR
T1 - Optimization of lattice surgery is NP-hard
AU - Herr, Daniel
AU - Nori, Franco
AU - Devitt, Simon J.
N1 - Copyright the Author(s) 2017. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.
PY - 2017/9/11
Y1 - 2017/9/11
N2 - The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates. However, this is not the only way to achieve universal, fault-tolerant computation. In this work, we focus on the lattice surgery representation, which realizes transversal logic operations without destroying the intrinsic 2D nearest-neighbor properties of the braid-based surface code and achieves universality without defects and braid-based logic. For both techniques there are open questions regarding the compilation and resource optimization of quantum circuits. Optimization in braid-based logic is proving to be difficult and the classical complexity associated with this problem has yet to be determined. In the context of lattice-surgery-based logic, we can introduce an optimality condition, which corresponds to a circuit with the lowest resource requirements in terms of physical qubits and computational time, and prove that the complexity of optimizing a quantum circuit in the lattice surgery model is NP-hard.
AB - The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates. However, this is not the only way to achieve universal, fault-tolerant computation. In this work, we focus on the lattice surgery representation, which realizes transversal logic operations without destroying the intrinsic 2D nearest-neighbor properties of the braid-based surface code and achieves universality without defects and braid-based logic. For both techniques there are open questions regarding the compilation and resource optimization of quantum circuits. Optimization in braid-based logic is proving to be difficult and the classical complexity associated with this problem has yet to be determined. In the context of lattice-surgery-based logic, we can introduce an optimality condition, which corresponds to a circuit with the lowest resource requirements in terms of physical qubits and computational time, and prove that the complexity of optimizing a quantum circuit in the lattice surgery model is NP-hard.
UR - http://purl.org/au-research/grants/arc/CE110001013
UR - http://www.scopus.com/inward/record.url?scp=85050005068&partnerID=8YFLogxK
U2 - 10.1038/s41534-017-0035-1
DO - 10.1038/s41534-017-0035-1
M3 - Article
SN - 2056-6387
VL - 3
SP - 1
EP - 5
JO - npj quantum information
JF - npj quantum information
M1 - 35
ER -