How can I optimize Quantum Circuit Depth for VQE on current NISP hardware?

All answers to this question.

To optimize VQE on NISQ hardware, you must focus on "Circuit Transpilation" and "Error Mitigation." Start by using a hardware-efficient ansatz that matches the connectivity of the IBM Eagle processor to minimize SWAP gates, which are high-error operations. Implementing Zero-Noise Extrapolation (ZNE) is essential; it works by intentionally scaling the noise in your circuit and then extrapolating back to the "zero-noise" limit. Additionally, consider using Probabilistic Error Cancellation (PEC). While PEC has a higher sampling overhead, it provides a more robust way to handle gate-specific noise models, allowing you to reach the "chemical accuracy" threshold for molecules like $LiH$ or $H_{2}O$ even with current decoherence limits.

   Answered 2025-05-16 by Emily Thompson

Have you looked into "Measurement Error Mitigation" (MEM) specifically, as readout errors often contribute more to the total noise than single-qubit gates in these experiments?

   Answered 2025-05-18 by Michael Sullivan

• Michael, you are absolutely right. Readout errors can be as high as 5% per qubit on some NISQ devices. Using a calibration matrix (A-matrix) to invert the readout distortion is a standard first step. However, for 127 qubits, a full matrix inversion is computationally expensive. I suggest using Matrix Product States (MPS) or other tensor network methods to approximate the assignment map. This keeps the classical post-processing overhead manageable while significantly cleaning up the expectation values for your VQE energy landscapes.

     Commented 2025-05-19 by David Miller

Keep the ansatz as lean as possible. I’ve found that "ADAPT-VQE" is much better than static templates because it grows the circuit iteratively, adding only the most impactful operators.

   Answered 2025-05-20 by Jennifer Adams

• I completely agree with Jennifer. ADAPT-VQE is a lifesaver for shallow circuits. It prevents the "Barren Plateau" problem by ensuring you're only walking down the most relevant gradients.

     Commented 2025-05-22 by Sarah Jenkins