Enigma: Privacy-Preserving Execution of QAOA on Untrusted Quantum
  Computers
Quantum computers can solve problems that are beyond the capabilities of
conventional computers. As quantum computers are expensive and hard to
maintain, the typical model for performing quantum computation is to send the
circuit to a quantum cloud provider. This leads to privacy concerns for
commercial entities as an untrusted server can learn protected information from
the provided circuit. Current proposals for Secure Quantum Computing (SQC)
either rely on emerging technologies (such as quantum networks) or incur
prohibitive overheads (for Quantum Homomorphic Encryption). The goal of our
paper is to enable low-cost privacy-preserving quantum computation that can be
used with current systems.
  We propose Enigma, a suite of privacy-preserving schemes specifically
designed for the Quantum Approximate Optimization Algorithm (QAOA). Unlike
previous SQC techniques that obfuscate quantum circuits, Enigma transforms the
input problem of QAOA, such that the resulting circuit and the outcomes are
unintelligible to the server. We introduce three variants of Enigma. Enigma-I
protects the coefficients of QAOA using random phase flipping and fudging of
values. Enigma-II protects the nodes of the graph by introducing decoy qubits,
which are indistinguishable from primary ones. Enigma-III protects the edge
information of the graph by modifying the graph such that each node has an
identical number of connections. For all variants of Enigma, we demonstrate
that we can still obtain the solution for the original problem. We evaluate
Enigma using IBM quantum devices and show that the privacy improvements of
Enigma come at only a small reduction in fidelity (1%-13%).
Ramin Ayanzadeh Ahmad Mousavi Narges Alavisamani Moinuddin Qureshi