  As the quantum computing ecosystem grows in popularity and utility it is
important to identify and address the security and privacy vulnerabilities
before they can be widely exploited. One major concern is the involvement of
third party tools and hardware. Usage of untrusted hardware could present the
risk of intellectual property (IP) theft. For example the hybrid quantum
classical algorithms like QAOA encodes the graph properties e.g. number of
nodes edges and connectivity in the parameterized quantum circuit to solve a
graph maxcut problem. QAOA employs a classical computer which optimizes the
parameters of a parametric quantum circuit (which encodes graph structure)
iteratively by executing the circuit on a quantum hardware and measuring the
output. The graph properties can be readily retrieved by analyzing the QAOA
circuit by the untrusted quantum hardware provider. To mitigate this risk, we
propose an edge pruning obfuscation method for QAOA along with a split
iteration methodology. The basic idea is to (i) create two flavors of QAOA
circuit each with few distinct edges eliminated from the problem graph for
obfuscation (ii) iterate the circuits alternately during optimization process
to uphold the optimization quality and (iii) send the circuits to two different
untrusted hardware provider so that the adversary has access to partial graph
protecting the IP. We demonstrate that combining edge pruning obfuscation with
split iteration on two different hardware secures the IP and increases the
difficulty of reconstruction while limiting performance degradation to a
maximum of 10 percent (approximately 5 percent on average) and maintaining low
overhead costs (less than 0.5X for QAOA with single layer implementation).
