  Quantum data locking is a quantum communication primitive that allows the use
of a short secret key to encrypt a much longer message. It guarantees
information-theoretical security against an adversary with limited quantum
memory. Here we present a quantum data locking protocol that employs
pseudo-random circuits consisting of Clifford gates only, which are much easier
to implement fault tolerantly than universal gates. We show that information
can be encrypted into $n$-qubit code words using order $n -
H_\mathrm{min}(\mathsf{X})$ secret bits, where $H_\mathrm{min}(\mathsf{X})$ is
the min-entropy of the plain text, and a min-entropy smaller than $n$ accounts
for information leakage to the adversary. As an application, we discuss an
efficient method for encrypting the output of a quantum computer.
