Quantum Computing vs. Coherent Computing

In this review article, we compare the performance of two computing systems: quantum computing and coherent computing. A layered architecture for circuit-model quantum computing, employing surface code quantum error correction, has been recently discussed. Using this concrete hardware platform, it is possible to provide resource analysis for executing the fault-tolerent quantum computing for prime number factoring and molecular eigen-energy calculation that cannot be solved by the present day computing systems. A particular quantum computing system could solve such problems on the time scale of 1-10 days by using 10(8) - 10(9) physical qubits. We discuss an alternative computing system based on an injection-locked laser network wnicn is called a coherent computing system here. A three-dimensional Ising model is mapped onto the mutually injection-locked slave laser network, while the independent injection signal from a master laser implements a Zeeman Hamiltonian. In this computing system, an Ising spin taking either up or down state is represented by the polarization degrees of freedom, right or left circular polarizations, of the lasing photons in each slave laser. A spin-spin coupling coefficient is implemented by simple linear polarization optics connecting the two slave lasers. We numerically study the scaling law of the proposed machine against the anti-ferromagnetic Ising model with varying problem size M. A transient time to reach a steady state polarization configuration is inversely proportional to the locking bandwidth and does not depend on the problem size strongly up to M=1000.