Watermarking of Quantum Circuits

TL;DR

Two lightweight watermarking techniques to prove ownership in the event of an adversary cloning the circuit design are presented and compared against the state-of-the-art.

Abstract

Quantum circuits constitute Intellectual Property (IP) of the quantum developers and users, which needs to be protected from theft by adversarial agents, e.g., the quantum cloud provider or a rogue adversary present in the cloud. This necessitates the exploration of low-overhead techniques applicable to near-term quantum devices, to trace the quantum circuits/algorithms\textquotesingle{} IP and their output. We present two such lightweight watermarking techniques to prove ownership in the event of an adversary cloning the circuit design. For the first technique, a rotation gate is placed on ancilla qubits combined with other gate(s) at the output of the circuit. For the second method, a set of random gates are inserted in the middle of the circuit followed by its inverse, separated from the circuit by a barrier. These models are combined and applied on benchmark circuits, and the circuit depth, 2-qubit gate count, probability of successful trials (PST), and probabilistic proof of authorship (PPA) are compared against the state-of-the-art. The PST is reduced by a minuscule 0.53\% against the non-watermarked benchmarks and is up to 22.69\% higher compared to existing techniques. The circuit depth has been reduced by up to 27.7\% as against the state-of-the-art. The PPA is astronomically smaller than existing watermarks.

Figures (6)

• Figure 1: (a) Random gate based watermarking applied on a Miller circuit, (b) rotation gate based watermarking applied on 4gt5 circuit. Q4 is the functional qubit while the others are ancillary. We choose Q1 & Q2 to place our watermark. Other qubits can also be used for watermarking.
• Figure 2: Time needed to extract the watermark.
• Figure 3: (a) Baseline circuit transpiled on FakeValencia and (b) watermarked circuit transpiled on FakeLagos.
• Figure 4: TVD measured on ancillary qubits for rotation gate (Ry) based watermarking in 4gt4 on (a) FakeValencia (same as base), (b) FakeBogota, (c) FakeKolkata and (d) FakeSherbrooke backends with respect to original 4gt4 circuit on FakeValencia.
• Figure 5: TVD measured (a) on ancillary qubits for rotation based watermarking for all possible inputs, (b) for rotation & CNOT based watermarking, (c) on functional qubits for random-gate-set watermarked circuits for all possible inputs.