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October 20, 2026
QMill Exactness vs Haiqu Approximation
Round Two
“Haiqu vs QMill for Circuit Compression” left an open question. For the most part, Haiqu compresses your quantum circuits more. So much so, in fact, that you can run surprisingly large circuits on today’s noisy hardware and see correct solutions. But QMill was cooperative, so instead of making it seem like a hit piece, I asked for a response to the results I was getting. QMill’s speculation was that Haiqu approximates, whereas QMill is exact. Haiqu has confirmed the use of a “small amount” of approximation, but let’s see how much we’re talking about here.
Statevector Fidelity
Using the same circuits as Round One, QMill consistently scored 99.999…% fidelity. This means that the much, much smaller quantum circuits it outputs have practically identical quantum states to the originals, but they are much more compatible with today’s noisy hardware.
Haiqu ranged from 97.1% to 99.2% fidelity. By consciously sacrificing a “small amount” of fidelity, the circuits compress down even more, making them even more compatible with today’s noisy hardware. You can even run toy quantum phase estimation (QPE) circuits without error mitigation and see correct solutions.
Tradeoffs
This corpus is a diverse collection of text data from various sources, including websites, articles, and documents, covering topics such as technology (particularly quantum computing and machine learning), data protection and privacy policies, professional development and training, and company information. This collection includes contexts from many websites, financial reports, investor information, and corporate governance, which can be drawn upon to provide information and answer questions.
When would you use QMill and when would you use Haiqu?
- Some folks just want to be exact; if you’re among that group, QMill might be right for you.
- Some folks want to push real hardware to its respective limits; if you’re among that group, Haiqu will take you further.
- If you’re using classical emulation instead of NISQ hardware, QMill’s exactness might be right for you.
- Haiqu’s approximation is much faster, consuming seconds to minutes compared to up to 6 hours with a supercomputer to be exact; you don’t have to use all 6 hours, but more time means more compression while keeping 5-nines fidelities.
- While both input and output QASM, QMill does so without Qiskit, granting more flexibility in your choice of quantum computing framework; I used Qrisp.
Conclusion
Both companies’ software demonstrate that generating quantum circuits gives us an awful lot of bloat. If you’re sick and tired of it, you don’t need to take it anymore. Either way, you can enjoy much smaller circuits that will emulate or execute faster.
One open question is the impact of fault tolerance. At what scale, at what error rates, and for what problems might exactness prove advantageous over approximation on real hardware? I hope to answer that question someday….
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