Less precise but less noisy: local circuits for momentum-space state preparation and measurement

summary

Video file (mp4)

The gist

The gist: Local circuits for momentum-space state preparation and measurement demonstrate that adiabatic evolution can outperform the Fermionic Fourier Transform (FFT) on noisy hardware beyond a

In short

The study compared two methods for preparing and measuring momentum states: the Fermionic Fourier Transform (FFT) and adiabatic evolution. Findings show that for larger systems, adiabatic evolution outperforms FFT on noisy hardware because its lower momentum resolution leads to less error propagation. The paper also proposes a new measurement scheme called MDLM, which is less precise but significantly reduces noise sensitivity.

Key concepts

Fermionic Fourier Transform (FFT)
The FFT is a high-precision method for determining momentum states, capable of distinguishing momenta by 1/N. However, this high resolution requires long-range couplings in real space, which makes the circuit highly sensitive to noise and error propagation when run on noisy quantum hardware.
Adiabatic Evolution
This method prepares ground states using local circuits that evolve slowly over time. While it has coarser momentum resolution than the FFT, it propagates errors more slowly. This slower error propagation makes adiabatic evolution significantly more robust against noise for larger system sizes.
Momentum Distribution from Local Measurements (MDLM)
MDLM is an alternative measurement scheme that uses local operators to estimate momentum densities. Although less precise than the FFT, this method requires fewer measurements and is less costly and noisier, proving better performance for spectral function measurement on the tested hardware.

Terminology used across episodes

This episode discusses

The paper

Less precise but less noisy: local circuits for momentum-space state preparation and measurement · Read on arXiv

Etienne Granet, * Henrik Dreyer

Quantinuum

Quantum algorithms are usually optimized for gate count or circuit depth. We find on Quantinuum System Model H2 quantum computer that for a tight-binding chain ground state preparation, there is a system size N beyond which the adiabatic evolution reaches significantly lower energies than the Fermionic Fourier Transform (FFT), with the same number of gates, and with the same circuit depth. We attribute this high noise sensitivity of the FFT to its high precision, being able to distinguish momenta by 1/N. This high resolution in momentum space requires long-range couplings in real space, which propagates errors faster. In contrast, although local and physical circuits such as the adiabatic evolution have a coarser momentum resolution, they also propagate errors more slowly. For physical applications, high momentum resolution is rarely required and is often worth trading for low noise sensitivity. We also introduce a momentum measurement scheme that although less precise than FFT, is less costly and less noisy. We show that it achieves better performance than FFT for spectral function measurement on Quantinuum System Model H2 quantum computer. Our work emphasizes the importance of reducing the noise sensitivity of quantum algorithms, beyond the number of gates or circuit depth.

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Less precise but less noisy".

Mira: The gist: Local circuits for momentum-space state preparation and measurement demonstrate that adiabatic evolution can outperform the Fermionic Fourier Transform (FFT) on noisy hardware beyond a certain system size,

Kai: First, who's behind it and why it matters.

Paper summary: Mira: Thinking about the title of this paper, "Less precise but less noisy," it really captures what they're doing here; they are suggesting that sacrificing some detail in momentum space can lead to a more robust algorithm on real hardware.

Kai: And the authors are showing that for preparing ground states of tight-binding chains, when you push past N equals twenty the adiabatic approach wins on noisy systems even though it's less precise > <ref:2610.01704#pg2>

Lev: The implication for us is that we should be careful about how much precision we demand in momentum space if we're running these things on actual quantum hardware where noise is unavoidable >

Kai: So, to wrap up, this paper gives us concrete evidence that the FFT isn't always the best choice because its high resolution forces it to be too sensitive to real-world noise compared to simpler local methods like adiabatic evolution >

Mira: It's a practical finding because it means that for many physical problems, we don't need perfect momentum resolution; we just need an algorithm that doesn't break down easily when you add imperfections >

Conclusion: Kai: So we're looking at this paper, "Less precise but less noisy," and it's about comparing two ways to prepare and measure states in momentum space on a quantum computer: the FFT versus adiabatic evolution.

Mira: Exactly, Kai; they’re showing that you can trade some precision in how well you pinpoint a particle's momentum for way less noise sensitivity when you run the circuit on real hardware.

Lev: I mean, if we think about running this on actual quantum hardware right now, the FFT seems too sensitive because it needs such high resolution in momentum space to work correctly.

Kai: Right, and the authors find that for a certain system size beyond twenty qubits, the adiabatic method actually achieves lower energy errors than the FFT even when you use the same number of gates.

Mira: That makes sense from a theory standpoint; their analysis points to how error dilution works differently for these two types of circuits in this specific context.

Lev: It suggests that for physical applications, that loss of high momentum resolution isn't actually a problem if it means the algorithm runs much more reliably on the noisy machine.

Kai: So, what does this mean for us, like people who are just listening to the show? It tells us that maybe we don't always have to chase perfect precision in these kinds of quantum algorithms.

Mira: It implies that reducing noise sensitivity should be a major factor in circuit design alongside gate count and depth.

Lev: The implication for running experiments is that we should prioritize methods like adiabatic evolution if they can give us better error scaling than something with high resolution, even if it's coarser.

Kai: So, the main point here is that noise sensitivity matters just as much as how many gates or how deep the circuit is.

Mira: And their proposed measurement scheme, MDLM, shows another path forward for getting good momentum information without needing that extremely precise FFT approach.

Lev: That's a big deal because it means we don't have to stick to one specific circuit structure if another one gives us better performance on the actual hardware we have.

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