Compilation-informed probabilistic logical-error cancellation

arXiv:2508.20174 · quant-ph · Submitted 2025-08-27 · Read on arXiv

Listen

Transcript

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

Kai: Today's paper: "Compilation-informed probabilistic logical-error cancellation".

Mira: The gist The scheme introduces compilation-informed probabilistic error cancellation (CIPEC), a logical error mitigation scheme that simultaneously removes biases from compilation errors and logical-gate errors in expectation-value estimates,

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

Paper summary: Mira: So to wrap up this discussion on "Compilation-informed probabilistic logical-error cancellation," the authors are proposing a method that tackles errors from both the compilation process and the physical gates themselves.

Kai: The thesis is that by using information about gate compilations, they can get an unbiased estimate of expectation values with overheads that don't scale with target precision.

Lev: What this means for us in terms of actual hardware implementation is that we might be able to achieve lower logical circuit depths than what pure QEC or PEC would require for high-precision tasks.

Mira: The paper demonstrates this by showing that circuit depth and the required QEC codedistance are both independent of epsilon, which is a key finding because it decouples those two factors.

Kai: So, in simple terms, this approach gives us a way to solve bigger problems with lower overhead when we're aiming for high precision, provided we can characterize the gates well enough initially.

Lev: The authors mention that they need characterization to diamond-norm precision epsilon/(2LO) for stability, which is a specific requirement for running this on real systems <ref:2508.20174#pg1>.

Mira: Ultimately, this work offers a practical pathway toward fault-tolerant quantum computation with overheads that are stable against the precision we demand.

Conclusion: Kai: So we've looked at how this scheme works, and now we need to wrap up what "Compilation-informed probabilistic logical-error cancellation" actually means for us on a hardware level.

Mira: It’s about taking those errors that come from writing the program and the errors from the gates themselves, and trying to get rid of them at the same time.

Kai: Exactly. The authors are saying you can do this without needing super-high precision in your target results, which is a big deal for scaling up these computations.

Lev: From my side, I’m looking at how much characterization you actually need to do upfront to make this whole thing stable. It seems like they're getting pretty specific about that characterization error bound.

Mira: Yeah, because if the setup takes way too long just to figure out what the gate errors are, then we haven't really solved anything practical yet.

Kai: So when you put it all together, this is about making logical circuits shorter than we thought was possible with just running QEC alone.

Lev: It looks like they’re showing a way to reduce the required circuit depth down to something that depends only on the circuit size, not how demanding your precision target is.

Mira: That's the core of it, I think. If you fix your code distance, you can run deeper circuits with less overhead than traditional methods allow for high precision.

Kai: It shifts the focus from just brute-force error correction to something more informed about how the compilation process is introducing noise.

Lev: And that means we need to look at how this affects the practical timeline for building these machines, not just the theoretical speedup.

Mira: Right, because if we can reduce that overhead dependence on precision, it opens up a whole new area for fault tolerance research.

Quantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE · Department of Mathematical Sciences, University of Copenhagen

quant-ph

Submitted: 2025-08-27

Updated: 2026-10-07

Comments: Version accepted for publication in npj Quantum Information

Code: https://github.com/giancamilo/CIPEC

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 88/100

The gist: The gist The scheme introduces compilation-informed probabilistic error cancellation (CIPEC), a logical error mitigation scheme that simultaneously removes biases from compilation errors and

Key concepts

Compilation-informed probabilistic error cancellation (CIPEC): A logical error mitigation scheme that simultaneously removes biases caused by compilation errors and errors from logical gates in expectation-value calculations. It uses a probabilistic approach to cancel these errors, making the required overhead dependent only on the circuit size rather than how precise you need your final result to be.
Quasiprobability Decomposition: This technique treats unitary quantum gates as affine combinations of ideal gates mixed with noisy operations from a native gate set. This decomposition is performed at the level of logical qubits relative to a Quantum Error Correction (QEC) code, allowing the scheme to exploit the structure of the noise in a controlled way.
Precision-independent Overhead: A key finding showing that for a fixed circuit and QEC code distance, the overhead required by CIPEC does not increase as you demand higher target precision (lower epsilon). This is achieved because the scheme's performance scales with circuit size rather than the inverse of the error tolerance.

Terminology

Accuracy — 5× in this paper · explained in 1 episode
Quantum Circuits — 4× in this paper · explained in 2 episodes
Sample Complexity — 4× in this paper · explained in 15 episodes
Core — 3× in this paper · explained in 2 episodes
Trace — 3× in this paper · explained in 2 episodes
BQP — 2× in this paper · explained in 2 episodes
BQP-complete — 2× in this paper · explained in 2 episodes
Benchmarking — 1× in this paper · explained in 3 episodes
Distillation — 1× in this paper · explained in 2 episodes
Fidelity — 1× in this paper · explained in 2 episodes
No-Go Theorem — 1× in this paper · explained in 2 episodes
Process tomography — 1× in this paper · explained in 2 episodes

Summary

The gist The scheme introduces compilation-informed probabilistic error cancellation (CIPEC), a logical error mitigation scheme that simultaneously removes biases from compilation errors and logical-gate errors in expectation-value estimates, offering fault-tolerance overheads that depend only on circuit size rather than target precision<ref:2508.20174#pg2>

Motivation and Context

Quantum computers face challenges due to scaling limitations and high error rates, necessitating techniques like quantum error correction (QEC) combined with quantum error mitigation (QEM)<ref:2508.20174#pg4> Early applications will likely rely on QEC combined with QEM against both compilation errors and logical-gate noise<ref:2508.20174#pg2> While QEC and compilation overheads are modest, in practice, such overheads can cause years of delay for implementations<ref:2508.20174#pg4> The goal of QEM is to reduce the impact of noise on expectation values without actually correcting the errors by running noisy quantum circuits multiple times and classically post-processing the outcomes<ref:2508.20174#pg4>

CIPEC Scheme Overview

CIPEC is a logical error mitigation scheme that removes biases from compilation errors epsilonc and logical-gate errors epsilonQ in expectation-value estimates<ref:2508.20174#pg2> The scheme requires the characterization of noisy logical gates up to an accuracy proportional to the target one, but is agnostic to circuit, basis, compiler, and QEC code<ref:2508.20174#pg4> It exploits a quasiprobability decomposition similar to the compensation method of PEC where unitary gates are represented as affine combinations of gate sequences drawn from the noisy native set at the level of logical qubits relative to a QEC code instead of physical ones<ref:2508.20174#pg4>

Mechanism and Performance

The core mechanism involves a hybrid classical/quantum procedure based on randomly sampling j in Be according to its importance in the quasi-probability distribution for each gate<ref:2508.20174#pg4> The algorithm decomposes each unitary Ui into a sum involving ideal gates from the universal set V and noisy operations from the basis Be, solved via an optimization problem (Eq. 2)<ref:2508.20174#pg4> This decomposition is used to estimate expectation values statistically by Monte-Carlo sampling noisy circuits from the distribution defined by them<ref:2508.20174#pg4> The key result is that each circuit’s depth and the required QEC codedistance are both independent of epsilon<ref:2508.20174#pg4> Specifically, for a fixed code distance and a circuit, the overhead depends only on the circuit size, not the target precision<ref:2508.20174#pg4> The total negativity of U is bounded by gamma <= e lambda with lambda:= P i∈[G] c∗ (epsilonc,i + Li epsilonQ)<ref:2508.20174#pg4>

Key Results and Applications

The main theorem states that if the total logical gate length L is less than Lmax:= log(omega2)/(2c∗epsilonQ), Algorithm 5 solves Problem 1 on Q for any target precision 1/epsilon with constant sample overhead gamma squared This allows for solving problem instances orders of magnitude larger than those achievable using only QEC<ref:2508.20174#pg4> For Jones polynomial estimation, CIPEC B1 (any) and B2 allow solving the problem for any target precision 1/epsilon with constant sample overhead gamma squared ≈ 2.46<ref:2508.20174#pg4> The stability analysis shows that CIPEC is stable against characterization errors, requiring characterization to diamond-norm precision epsilon/(2LO)<ref:2508.20174#pg4>

Conclusion

CIPEC offers a practical route towards fault-tolerant quantum computation with precision-independent overheads for fixed circuit complexity and code distance<ref:2508.20174#pg2> It enables logical circuit depth reduction, where L = O(G polylog(G)) is epsilon-independent while QEC and PEC require O(G polylog(G/epsilon)) depth<ref:2508.20174#pg4> This makes CIPEC advantageous in high-precision regimes where QEC alone fails to guarantee correctness even with infinite samples<ref:2508.20174#pg4> The findings offer a practical route towards fault-tolerant quantum computation with precision-independent overheads<ref:2508.20174#pg2>

Appendix Details

The characterization of implementable operations can be done using standard gate set tomography (GST) methods, requiring O(1/epsilon squared char) uses to estimate a two-qubit channel up to diamond norm error epsilonchar<ref:2508.20174#pg4> Long-sequence GST can improve this scaling to Tchar = O(tau L log(L)/epsilon 2)<ref:2508.20174#pg4> The analysis shows that CIPEC is stable with respect to imperfect characterization, requiring characterizing the error channels to diamond norm precision epsilon/(2LO)<ref:2508.20174#pg4> The compilation error in Step 1(a) is shown to be O(1/G) independent of epsilon<ref:2508.20174#pg4> The total number of samples required for estimation is SCIPEC:= gamma squared O squared log(2/delta)/(2epsilon 2)<ref:2508.20174#pg4>

References Cited

[1] A. M. Dalzell, S. McArdle, M. Berta, P. Bienias, C.-F. Chen, A. Gily´en, C. T. Hann, M.-J Kastoryano, E.-T Khabiboulline, A Kubica, G Salton and F G S L Brandao Quantum algorithms: A survey of applications and end-to-end complexities (2023), arXiv:2310.03011 [quant-ph]

[2] M. E. Beverland, P Murali, M Troyer, K M Svore T Hoefler V Kliuchnikov G H Low M Soeken A Sundaram and A Vaschillo Assessing requirements to scale to practical quantum advantage (2022), arXiv:2211.07629 [quant-ph]

[3] D Gottesman An introduction to quantum error correction and fault-tolerant quantum computation (2009), arXiv:0904.2557 [quant-ph]

[4] D Aharonov and M Ben-Or Fault-tolerant quantum computation with constant error rate SIAM Journal on Computing 38, 1207 (2008), https://doi.org/10.1137/S0097539799359385

[5] C M Dawson and M A Nielsen The solovaykitaev algorithm (2005), arXiv:quant-ph/0505030 [quant-ph]

[6] N P Breuckmann and J N Eberhardt Quantum low-density parity-check codes PRX Quantum 2, 10.1103/prxquantum.2.040101 (2021)

[7] Z Cai R Babbush S C Benjamin S Endo W J Huggins Y Li J R McClean and T E O’Brien Quantum error mitigation Reviews of Modern Physics 95, 10.1103/revmodphys.95.045005 (2023)

[8] L Lin and Y Tong Heisenberg-limited ground-state energy estimation for early faulttolerant quantum computers PRX Quantum 3, 10.1103/prxquantum.3.010318 (2022)

[9] K Wan M Berta and E T Campbell Randomized quantum algorithm for statistical phase estimation Phys Rev Lett. 129, 030503 (2022)

[10] A Tosta T de Lima Silva G Camilo and L Aolita Randomized semi-quantum matrix processing npj Quantum Information 10, 10.1038/s41534-024-00883-0 (2024)

[11] S Wang S McArdle and M Berta Qubit-efficient randomized quantum algorithms for linear algebra PRX Quantum 5, 020324 (2024)

[12] Z Zimbor´as B Koczor Z Holmes E.

Improvements for AI systems

textbf Compilation-Informed Probabilistic Error Cancellation (CIPEC) for Precision-Independent Overhead: The improved system can estimate expectation values to arbitrary precision ε incurring a constant sample-complexity overhead, meaning each circuit’s depth and the required QEC codedistance are both independent of ε.
textbf Enhanced Resource Scaling for High-Precision Tasks: The system is capable of solving problem instances orders of magnitude larger than those achievable using only QEC (see Fig. 2), specifically enabling high-precision estimations where standard PEC fails, as evidenced by the Jones polynomial estimation example achieving precision ε=10−2 with a manageable sample overhead.
textbf Stability Against Characterization Errors: The protocol is proven stable against characterization errors, showing that O′−⟨O⟩ ≤ ε + L∥O∥ϵchar, allowing for the use of estimated noise channels without requiring perfect knowledge of the device's error models, as long as the error characterization is within diamond norm precision.
textbf Optimized Logical Circuit Depth Reduction: CIPEC enables a logicalcircuit depth reduction, with L = O(G polylog(G)) being ε-independent while QEC and PEC require O(G polylog(G/ε)) depth, leading to shallower circuits for high-precision estimation tasks.

Abstract

The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction (QEC) offers a clear path towards fault tolerance, overcoming the scalability issues will take time. Early applications will likely rely on QEC combined with quantum error mitigation (QEM). We introduce a QEM scheme against both compilation errors and logical-gate noise that is circuit-, QEC code-, and compiler-agnostic. The scheme builds on quasi-probability methods and uses information about the circuit's gates' compilations to attain an unbiased estimation of noiseless expectation values incurring a constant sample-complexity overhead. Moreover, it features maximal circuit size and code distance both independent of the target precision, in contrast to strategies based on QEC alone. We formulate the mitigation procedure as a linear program, demonstrate its efficacy through numerical simulations, and illustrate it for estimating the Jones polynomials of knots. Our method significantly reduces quantum resource requirements for high-precision estimations, offering a practical route towards fault-tolerant quantum computation with precision-independent overheads for fixed circuit size and code distance.