@article {2933, title = {Surface code compilation via edge-disjoint paths}, year = {2021}, month = {10/21/2021}, abstract = {

We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a 2D grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit\&$\#$39;s qubits in surface codes can result in long-range two-qubit operations across the grid. We show how to prepare many long-range Bell pairs on qubits connected by edge-disjoint paths of ancillas in constant depth which can be used to perform these long-range operations. This forms one core part of our Edge-Disjoint Paths Compilation (EDPC) algorithm, by easily performing parallel long-range Clifford operations in constant depth. It also allows us to establish a connection between surface code compilation and several well-studied edge-disjoint paths problems. Similar techniques allow us to perform non-Clifford single-qubit rotations far from magic state distillation factories. In this case, we can easily find the maximum set of paths by a max-flow reduction, which forms the other major part of our EDPC algorithm. We compare EDPC to other compilation approaches including a SWAP-based algorithm, and find significantly improved performance for circuits built from parallel CNOTs, and for circuits which implement the multi-controlled X gate.

}, url = {https://arxiv.org/abs/2110.11493}, author = {Michael Beverland and Vadym Kliuchnikov and Eddie Schoute} } @article {1832, title = {Practical Approximation of Single-Qubit Unitaries by Single-Qubit Quantum Clifford and T Circuits}, journal = {IEEE Transactions on Computers}, volume = {65}, year = {2016}, month = {2016/01/01}, pages = {161 - 172}, abstract = {

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation down to size 10-15, resulting in the optimal single-qubit circuit designs required for implementation of scalable quantum algorithms. Our implementation along with the experimental results are available in the public domain.

}, issn = {0018-9340}, doi = {10.1109/TC.2015.2409842}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7056491http://xplorestaging.ieee.org/ielx7/12/7350319/7056491.pdf?arnumber=7056491}, author = {Vadym Kliuchnikov and Dmitri Maslov and Michele Mosca} }