Logical qubit behavior model and fast simulation for surface code

Abstract

AbstractThis study proposes a logical qubit behavior model (LQBM) that calculates the state of the logical qubit based on a surface code after a logical qubit operation. LQBM can simulate the surface code whose distance exceeds 5, which is impossible with conventional quantum simulators. A complex error syndrome measurement must not be executed in this model. LQBM works at the mixed level of a logical and physical qubit. Probability amplitudes and the number of state vectors are designed at the physical qubit level. The state vectors of physical qubits constituting a logical qubit are abstracted to the value of the logical qubit level. LQBM converts all logical qubit operations, which include an initialization, a state injection, universal gates, and lattice surgery operations (e.g., a merge and a split) to simple calculations. LQBM provides a better computational complexity of O(log(distance)) than O(distance$$^2$$ 2 ). Through simulation experiments, it was found that LQBM performs logical qubit operations up to 24 million times faster than existing quantum simulators in the case of distance = 5.