#quantumapproximateoptimizationalgorithms

VQC Variable Quantum Circuits

Introduced BVQC, a new backdoor-style watermarking mechanism to protect IP stored in Variational Quantum Circuits (VQCs), advancing quantum computing security. This novel approach addresses major flaws in previous watermarking methods to maintain the VQCs' original performance during regular operation while ensuring that the watermark is detectable and resistant to optimisation procedures like circuit re-compilation.

Variational Quantum Circuits (VQCs) are a powerful quantum computation paradigm because they can scale difficulties beyond traditional computers. These circuits encode solutions using a task loss function to minimise loss across a training dataset. VQCs are used in VQD, QAOA, and VQE.

Building VQCs involves expertise in robust encoding, hardware calibration, parameter tuning, and circuit ansatz, which is rare outside of quantum computing businesses. Leading quantum computing businesses sell their VQCs as valuable intellectual property in a growing industry due to their promise. A reliable watermarking solution is needed to validate VQC IP ownership since criminals may make and distribute unauthorised copies due to its commercial importance.

Current quantum circuit watermarking methods have two fundamental concerns. When circuits were recompiled, watermarks were removed. Many earlier techniques used suboptimal gate decomposition, qubit mapping, or gate scheduling as watermarks. Quantum compilers increase circuit fidelity and execution performance, hence unoptimised signature blocks should be removed during recompilation.

Approximation compilation eliminated several approaches, including random gates and rotation. Second, these techniques' lengthy inserted watermarks increased work loss, which reduced circuit accuracy, especially on noisy intermediate-scale quantum (NISQ) computers.

After re-compilation with state-of-the-art watermarking, Probabilistic Proof of Authorship (PPA) rose from Kolkata values, implying watermark removal. The Ground Truth Distance (GTD) for watermarked VQCs (using earlier techniques) increased from 0.036 to 0.107 on Kolkata and from 0.063 to 0.182 on Cairo, indicating accuracy degradation.

BVQC tackles these issues.

BVQC confronts these difficulties. The peculiarity is its backdoor-style embedding, which raises the loss to a specified amount during watermark extraction while keeping the original loss in normal execution circumstances. This is achieved by making BVQC a multi-task learning objective. The VQC learns to achieve high accuracy utilising base inputs and measurements for standard execution and to generate a predetermined watermark loss for a set of given inputs and measurements under watermark extraction conditions.

Predefined inputs, measurements, and losses are needed to develop a watermarked model. These elements are intentionally deviated from the basic input/measurement by modifying amplitude, phase, measurement bases, or weights.

Optimisation of the circuit to achieve the watermark set's loss and minimise base task loss.

Privacy for the preset set and public access to the well-trained VQC with the base set.

To prove ownership, the owner gives a third party the private input, measurement, and loss. Ownership is confirmed if the VQC delivers a loss equal to the predetermined (as opposed to typical circuit behaviour) under these settings.

The grouping algorithm in BVQC minimises watermark task interference to maximise base job accuracy. The system carefully selects inputs, measurements, and watermark losses by measuring the impact of gradient updates from the watermark work on the base job aim. In particular, it looks for setups where watermark gradient changes do not increase base task loss.

By aligning the two activities' optimisation routes, this cautious selection prevents performance deterioration. Without this categorisation, the base task GTD may differ significantly. The basic task's GTD value in BVQC, which averages 0.016 over 50 sample groups, shows the grouping algorithm's accuracy.

BVQC outperforms previous watermarking approaches.

BVQC reduces Probabilistic Proof of Authorship (PPA) changes, making it resistant to recompilation. BVQC-taught VQCs preserve watermarks, unlike other methods that raised PPA dramatically after re-compilation. BVQC uses parameter optimisation to put the watermark directly into the VQC's unitary matrix, which is mostly unaffected by compiler optimisations that focus on structural alterations.

Keep Accuracy: BVQC reduces Ground Truth Distance (GTD) by 0.089 compared to other watermarking approaches. BVQC yields lower task GTD than previous methods. The GTD of BVQC is similar to that of unwatermarked VQCs, implying that loss changes are modest. This shows that BVQC passes security criteria to maintain accuracy and prevent watermarking interference with VQC jobs. Preset inputs and measurements keep the average watermark GTD low, simplifying watermark extraction and distinguishing watermarked circuits from unwatermarked ones.

The study has made considerable strides, but the scientists recognise that strategies like fine-tuning the model with locally selected datasets are still needed to resist modern attacks. Current parameter smoothing methods reduce fine-tuning while retaining watermark persistence. Future study could increase the scheme's resistance to changing threats and investigate its application with more quantum computations.