Preparing quantum states for simulations demands increasingly complex circuits but is hampered by noise affecting today’s processors. For preparing ground states of a tight-binding chain, a common problem in materials science and chemistry, adiabatic evolution outperforms standard methods like the Fermionic Fourier Transform (FFT) when systems exceed approximately twenty qubits. Prioritising precision is not always beneficial given current technological limitations when preparing quantum systems simulating materials or chemicals.

Beyond approximately twenty qubits, the slower technique called adiabatic evolution outperforms the faster Fermionic Fourier Transform (FFT) because it spreads errors more slowly through the calculation; both methods require similar computational effort. This suggests focusing on strong performance against imperfections in near-term quantum computers may be preferable to minimising steps within an algorithm. When simulating complex quantum systems, such as those found in materials science and chemistry, prioritising algorithmic precision isn’t always optimal given current limitations of quantum processors.

The team focused on preparing ‘ground states’, representing the lowest energy configuration of electrons within a material; imagine beads connected by springs describing how these electrons move. They compared two methods for achieving this: an approach called adiabatic evolution and the Fermionic Fourier Transform (FFT), which is akin to analysing sound using an extremely sensitive microphone, capturing even unwanted noise. This suggests that building strong performance against imperfections may be preferable to minimising steps in an algorithm; but will this trade-off continue as hardware improves.

Adiabatic evolution exceeds Fermionic Fourier Transform performance beyond twenty qubits on trapped ions

Beyond twenty qubits, ground state energy achieved using adiabatic evolution surpasses that obtained via Fermionic Fourier Transform (FFT) on Quantinuum’s System Model H2; this represents a shift considering previous limitations where FFT consistently outperformed other methods at smaller system sizes. Both approaches utilise comparable numbers of gates and circuit depths, demonstrating prioritising noise reduction can yield better results than simply minimising computational steps.

The slower error propagation inherent in adiabatic evolution’s local circuits, compared with the long-range couplings required by FFT’s high momentum resolution, accounts for this success because finer precision demands more susceptibility to errors within current hardware constraints.

Analysis revealed ground states prepared from tight-binding chains, models used to understand material properties, exhibited demonstrably lower energy levels using adiabatic evolution beyond twenty qubits on Quantinuum computers compared to those obtained via FFT on their System Model H2 computer. Despite similar algorithmic complexity between both methods, these findings highlight noise sensitivity as a key performance factor. Furthermore, an alternative momentum measurement scheme proved less noisy and more effective than FFT when performing spectral function measurements on Quantinuum hardware.

Strong durability to precision trade-offs define scalable ground state preparation limits

A counterintuitive principle in quantum computation has been demonstrated by scientists at Quantinuum: prioritising durability over precision can yield superior results when preparing ground states for complex systems modelling materials science and chemistry. This advantage isn’t universal however; the team discovered that beyond a specific system size their adiabatic evolution technique consistently outperformed the conventional Fermionic Fourier Transform (FFT) method, a threshold not easily predicted by traditional metrics such as gate count or circuit depth. Such findings highlight a subtle nuance in quantum algorithm design, where minimising computational steps doesn’t guarantee optimal performance given present noise levels.

Superior ground state preparation for tight-binding chains involved trading high momentum resolution, the ability to finely distinguish between energy states, for reduced sensitivity to errors, an approach proving particularly effective as system size increased beyond twenty qubits. Acknowledging inherent limitations within today’s processors suggests algorithms should be designed to withstand imperfections instead of striving for unattainable precision. Prioritising robustness against errors can prove more beneficial for applications like materials modelling and chemistry simulations where precise calculations aren’t always essential; optimising solely on gate count overlooks the impact of noise.

The research demonstrated that prioritising error resilience over absolute precision improves ground state preparation on Quantinuum System Model H2 quantum computers. Beyond a system size of twenty qubits, adiabatic evolution consistently achieved lower energies than the Fermionic Fourier Transform method despite having similar computational complexity. This result indicates that reducing an algorithm’s sensitivity to noise is important alongside minimising circuit depth or gate count. The authors also developed a less noisy momentum measurement scheme which performed better than FFT for spectral function measurements on their hardware.

👉 More information
🗞 Less precise but less noisy: local circuits for momentum-space state preparation and measurement
✍️ Etienne Granet and Henrik Dreyer (Affiliation: Quantinuum)
🧠 ArXiv: https://arxiv.org/abs/2610.01704

More like this