  Optimization of quantum circuits using an efficient compiler is key to its
success for NISQ computers. Several 3rd party compilers are evolving to offer
improved performance for large quantum circuits. These 3rd parties, or just a
certain release of an otherwise trustworthy compiler, may possibly be untrusted
and this could lead to an adversary to Reverse Engineer (RE) the quantum
circuit for extracting sensitive aspects e.g., circuit topology, program, and
its properties. In this paper, we propose obfuscation of quantum circuits to
hide the functionality. Quantum circuits have inherent margin between correct
and incorrect outputs. Therefore, obfuscation (i.e., corruption of
functionality) by inserting dummy gates is nontrivial. We insert dummy SWAP
gates one at a time for maximum corruption of functionality before sending the
quantum circuit to an untrusted compiler. If an untrusted party clones the
design, they get incorrect functionality. The designer removes the dummy SWAP
gate post-compilation to restore the correct functionality. Compared to a
classical counterpart, the quantum chip does not reveal the circuit
functionality. Therefore, an adversary cannot guess the SWAP gate and
location/validate using an oracle model. Evaluation of realistic quantum
circuit with/without SWAP insertion is impossible in classical computers.
Therefore, we propose a metric-based SWAP gate insertion process. The objective
of the metric is to ensure maximum corruption of functionality measured using
Total Variation Distance (TVD). The proposed approach is validated using IBM
default noisy simulation model. Our metric-based approach predicts the SWAP
position to achieve TVD of upto 50%, and performs 7.5% better than average TVD,
and performs within 12.3% of the best obtainable TVD for the benchmarks. We
obtain an overhead of < 5% for the number of gates and circuit depth after SWAP
addition.
