  Generation of logical zero states encoded with a quantum error-correcting
code is the first step for fault-tolerant quantum computation, but requires
considerably large resource overheads in general. To reduce such overheads, we
propose an efficient encoding method for the distance-three, nine-qubit surface
code and show its fault tolerance. This method needs no measurement, unlike
other fault-tolerant encoding methods. Moreover, this is applicable to a
one-dimensional qubit array. Observing these facts, we experimentally
demonstrate the logical zero-state encoding of the surface code using a
superconducting quantum computer on the cloud. We also experimentally
demonstrate the suppression of fast dephasing due to intrinsic residual
interactions in this machine by a dynamical decoupling technique dedicated for
the qubit array. To extend this method to larger codes, we also investigate the
concatenation of the surface code with itself, resulting in a distance-nine,
81-qubit code. We numerically show that fault-tolerant encoding of this large
code can be achieved by appropriate error detection. Thus, the proposed
encoding method will provide a new way to low-overhead fault-tolerant quantum
computation.
