Integrated photonic traveling salesman problem probabilistic solver with polynomial calculation time complexity

駿 矢島, Shun Yajima, 雄哉 庄司 +1 more

Craig Alan Feinstein

In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer.

Richard H. Warren

The D_Wave quantum computer is an analog device that approximates optimal solutions to optimization problems. The traveling salesman problems in the TSP Library are too large to process on the D_Wave quantum computer DW_2000Q_6. We report favorable approximations for solving the smallest, symmetric traveling salesman problems in the TSP Library by two D_Wave hybrid solvers, Kerberos and LeapHybridSampler. This is useful work about results from new quantum tools on problems that have been studied. It is expected to show a quantum way forward with larger problems when the hardware is upgraded. Also this work demonstrates that the TSP Library is a source of benchmarks for quantum processing of combinatorial problems. The hybrid solvers combine quantum and classical methods in a manner that is D_Wave proprietary information. The results from Kerberos were closer to optimal than the results from LeapHybridSampler. We show that the error percent from optimal increases as the problem size increases, which is consistent with results on D-Wave_s quantum computer for other optimization problems. An appendix contains outcomes from the two hybrid solvers for two asymmetric traveling salesman problems that are in the TSP Library. Again, the Kerberos results were closer to optimal than those from LeapHybridSampler, which indicates that Kerberos is superior to LeapHybridSampler on traveling salesman problems.

Florian Klug

Alessio Baldazzi, Stefano Azzini, Lorenzo Pavesi

We present a new variational quantum algorithm to solve the travelling salesman problem and its experimental validation for four-cities problems using a silicon photonics circuit with integrated photon-pair sources.

Satoshi Iriyama, Masanori Ohya