SciPost Submission Page
Fidelity decay and error accumulation in random quantum circuits
by Nadir Samos Sáenz de Buruaga, Rafał Bistroń, Marcin Rudziński, Rodrigo Miguel Chinita Pereira, Karol Życzkowski, Pedro Ribeiro
Submission summary
| Authors (as registered SciPost users): | Nadir Samos |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2404.11444v3 (pdf) |
| Date submitted: | 2024-12-31 19:26 |
| Submitted by: | Samos, Nadir |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We present a comprehensive analysis of fidelity decay and error accumulation in faulty quantum circuit models. Our work devises an analytical bound for the average fidelity between desired and faulty output states, accounting for errors that may arise during the implementation of two-qubit gates and multi-qubit permutations. It is shown that fidelity decays exponentially with both circuit depth and the number of qubits raised to an architecture-dependent power, and determine the decay rates as a function of the two types of errors. Furthermore, we establish a robust linear relationship between fidelity and the heavy output frequency used in Quantum Volume tests to benchmark quantum processors, under the considered errors protocol. These findings pave the way for predicting the behavior of fidelity in the presence of specific errors and offer insights into the best strategies for increasing Quantum Volume.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1.- The writing is clear, with well-structured sections, and the calculations are complete without missing steps. I enjoyed reading the paper.
2.- The authors perform detailed, non-trivial analytical calculations for the fidelity of the solvable model and provide examples for different device architectures. In this sense, the study is very complete.
3.- The techniques and calculations used may be of independent interest.
Weaknesses
1.- The relevance and possible applications of this work are not entirely clear to me. The exponential fidelity decay is expected, and the chosen noise model is just one among many possibilities. Moreover, introducing global Haar random unitaries in the solvable model makes it more arbitrary. There may exist other, possibly simpler, random circuits whose predictions numerically match those of the original circuit.
Report
This paper investigates how noise affects random quantum circuits in quantum computing. The authors focus on two types of random circuits:
1.- The original circuit, composed of layers of random two-qubit gates followed by a random permutation of qubits. These circuits are used in quantum volume benchmarking.
2.- The solvable circuit, composed of layers of random two-qubit gates, followed by a global Haar unitary, a random permutation, and another global Haar unitary.
They study the impact of two main sources of noise on these circuits: faulty two-qubit gates and faulty permutations. To quantify the effects of these errors, the paper analyzes the entanglement fidelity between the target and noisy circuits, averaged over all random instances of these circuits. The authors derive an analytical expression for the fidelity decay in the solvable model, showing its dependence on the number of qubits, the number of circuit layers, and the noise parameters. The results show that even for small systems, the target and noisy circuits can be quite different. Numerical simulations indicate that the analytical predictions for the solvable model closely match the numerical results for the better-motivated original model, suggesting that both circuits exhibit similar fidelity decay trends under noise.
Overall, I believe this study was well-conducted and represents a solid piece of research that deserves publication in SciPost Physics, primarily due to its technical contributions.
Requested changes
1.- The motivation and relevance of this work were not entirely clear to me. While I understand that these circuits are related to quantum volume, this is just one possible noise model for quantum volume circuits, and quantum volume itself is only one of several benchmarking methods for quantum computers. Are there any other possible applications?
2.- How does this work relate to previous research? Have similar studies been conducted before?
3.- Why did you choose this error model? Why did you choose this particular form for the solvable model? The global Haar random unitaries seem to be included purely for convenience. Could a simpler circuit yield the same predictions?
4.- I find the text around equation (B13) unclear.
Recommendation
Ask for minor revision
Strengths
1- Strong mathematical description and proof
2- The intuition to create a solvable model that captures the relevant features of the actual quantum computation.
3- Well written.
Weaknesses
1- I miss clear motivation and prospects (personal opinion)
2- The paper should be more clear on the impact of this research, in particular in the context of existing literature.
Report
See report
Recommendation
Ask for minor revision