Classical simulators as quantum error mitigators via circuit cutting

arXiv:2212.07335 · quant-ph · Submitted 2022-12-14 · Read on arXiv

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

Kai: We're looking at the paper: "Classical simulators as quantum error mitigators via circuit cutting".

Mira: The gist The Simulated Quantum Error Mitigation (SQEM) framework introduces an error mitigation technique that mitigates errors in a quantum circuit by running error mitigation subcircuits on a classical simulator…

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

Paper summary: Kai: Thinking about what we've seen with "Classical simulators as quantum error mitigators via circuit cutting" and the authors, Ji Liu, Alvin Gonzales, and Zain H. Saleem >

Mira: It seems the main contribution here is showing that you don't have to run all your error mitigation calculations on the limited quantum processor itself >

Lev: They're essentially saying you can offload the heavy lifting of simulating those error correction subcircuits to a classical machine while keeping your main computation on the quantum device >

Kai: And they did this by using circuit cutting, which breaks the circuit up so they can run parts on different computers >

Mira: It’s important because it means we can get results that are very accurate for problems like VQE, but only if we can afford that classical simulation step >

Lev: The limitation they flag is that this approach mitigates qubit by qubit, and while the overhead is polynomial in terms of runs, applying it to protect multiple qubits at the same time might be harder than what they've shown here >

Kai: So, for someone listening who just wants to know what this means for their work on quantum computers, it’s about finding a way to get high-fidelity results without needing massive error correction overhead on the hardware itself >

Mira: They matched the VQE results very closely, which suggests that SQEM is a viable way to approximate noise-free simulation results when you can handle the classical processing pipeline >

Conclusion: Kai: So we're wrapping up this look at "Classical simulators as quantum error mitigators via circuit cutting." Basically, they’re showing you how to use a classical computer to simulate the tricky parts of fixing errors while your main quantum computer does its job.

Mira: It seems the core idea is taking those error-mitigation bits and sending them off to a simulator, while keeping the main quantum computation on that hardware. They call it SQEM.

Lev: And they make it work by cutting up the circuit into pieces, running those mitigation bits classically, and then stitching everything back together for the final result. It’s about separating the noisy parts from the clean parts.

Kai: That qubit-wise approach is key here because they aren't trying to fix everything at once with a massive classical simulation. They are doing it one qubit at a time, which keeps the overhead manageable and polynomial in terms of how many runs you need.

Mira: I see why that matters for the theory; they’re not just throwing more qubits at it. By focusing on mitigating one qubit fragment after another, they can actually get results that are pretty close to what you'd expect from a noiseless simulation, even with a relatively simple setup.

Lev: From an engineering standpoint, it means we don't have to build these huge classical error correction machines for every single quantum operation. We just need the simulator to handle the specific fragments they send over.

Kai: It does mean that if you want super high fidelity across the whole circuit, you’re still going to need a significant classical processing pipeline after getting those bits back together.

Mira: So it’s not a magic fix for every noise problem; it's an approximation that works really well for specific circuit structures, like the VQE ansätze they used.

Lev: Exactly. It’s a scalable way to get good enough answers without needing exponentially more resources on the quantum hardware itself right now.

Kai: The authors are essentially saying we can use this classical simulation trick to get results that are accurate enough for practical applications today, even if it isn't perfect noise-free.

Mira: They’re showing us a way to bridge the gap between what’s possible on current quantum hardware and the high-accuracy results we often only see from perfect simulations.

Lev: It sets a precedent for how we can handle complex error mitigation schemes on real systems by breaking them down into manageable chunks that a classical machine can chew through.

Kai: So, it’s about using classical simulation as a tool to clean up the output of quantum hardware in a way that scales nicely.

Mathematics and Computer Science Division, Argonne National Laboratory · Intelligence Community Postdoctoral Research Fellowship Program

quant-ph

Submitted: 2022-12-14

Updated: 2026-10-19

Comments: 5 pages, 4 figures

Code: https://github.com/revilooliver/cut4mitigation

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 76/100

The gist: The gist The Simulated Quantum Error Mitigation (SQEM) framework introduces an error mitigation technique that mitigates errors in a quantum circuit by running error mitigation subcircuits on a

Key concepts

Simulated Quantum Error Mitigation (SQEM): SQEM is a framework where error mitigation steps are simulated on a classical computer while the primary quantum computation executes on the actual quantum hardware. This allows noisy gates to be effectively handled by classical simulation, leading to high-quality results without needing complex, full-scale error correction on the quantum device.
Quantum Circuit Cutting: This technique involves dividing a large quantum circuit into smaller fragments. In SQEM, the main computation is one fragment run on the quantum device, while the error mitigation subcircuits are treated as other fragments simulated classically. This division allows for parallel processing and targeted error handling.
Pauli Check Sandwiching: This is a specific error mitigation method used in the work where checks (Pauli measurements) are placed around qubits. Instead of increasing the number of checks exponentially, this strategy mitigates errors by focusing on one qubit at a time, keeping the required classical runs manageable with polynomial overhead.
Bayesian Recombination Model: After running error mitigation checks on individual parts of the circuit, their resulting probability distributions are combined using a Bayesian model. This process iteratively refines the combined distribution until it closely matches the desired mitigated distribution, ensuring the final output is accurate despite individual noise.

Terminology

Quantum Circuits — 1× in this paper · explained in 2 episodes

Summary

The gist The Simulated Quantum Error Mitigation (SQEM) framework introduces an error mitigation technique that mitigates errors in a quantum circuit by running error mitigation subcircuits on a classical simulator while the main circuit runs on quantum hardware, achieving results close to noise-free simulations.

SQEM Framework Overview

Simulated quantum error mitigation (SQEM) transforms the error mitigation components of an input circuit into classical pre and post processing procedures by applying circuit cutting The fragments that perform error mitigation are sent to a classical computer to be simulated and the main circuit is sent to the quantum hardware This procedure enables the gates that comprise the error mitigation scheme to be noiselessly executed, while the original unmitigated quantum computation is run on quantum hardware

Quantum Circuit Cutting

The SQEM framework relies on the quantum circuit cutting also known as “quantum knitting” The quantum circuit cutting techniques allow us to divide large quantum circuits into smaller fragments These fragments can then be run on separate quantum devices and then the output distributions from each of these fragments can be combined to generate the output of the full quantum circuit In our error mitigation framework, we fragment the quantum circuit into two parts: the main/original quantum circuit which is executed on a quantum device and the quantum error mitigation subcircuits which are sent to a classical simulator This allows us to error mitigate almost noise free The state preparation and measurement (SPAM) errors due to circuit cutting is also mitigated by the mitigating circuit

Pauli Check Sandwiching

The error mitigation method used in this work is Pauli check sandwiching but other error mitigation schemes can also be used In PCS, the post selection probability exponentially decreases as the number of pairs of checks increases Our strategy resolves this problem by error mitigating one qubit at a time With our strategy the total overhead in the number of runs required is only a polynomial function of the number of pairs of checks used

Probabilities Recombination

Applying the checks for each individual qubit or a subset of qubits makes our approach scalable However, the mitigated probabilities from each check need to be recombined to mitigate the noise of the system Here we use a Bayesian recombination model to recombine the probability distributions The algorithm stops when the hellinger distance between PR0 and PR is smaller than a threshold After the process, the recombined probability distribution PR has bitwise probabilities close to the mitigated bitwise probabilities

Experimental Results

We apply SQEM to simulate the error mitigation fragment on a classical device The recombined result has energy of-7.8625 It is within the chemical accuracy (an energy error of approximately 0.0016 hartree) of the noiseless ansatz result-7.8634 The results show that SQEM can significantly mitigate the noise on quantum devices and generate results close enough to the results on a noise-free simulator The recombined result energy is-98.5653, which is very close to the noiseless ansatz result-98.5684

Conclusion

We introduce the SQEM framework which removes the added gates and ancillas required by many error mitigation techniques from the quantum hardware execution by applying circuit cutting We demonstrate that this can be performed in a polynomially scalable way for a variety of problems by error mitigating individual qubits with PCS and performing a Bayesian recombination of the probability distributions at the end The SQEM framework matched the results of a full classical simulation of the VQE circuits up to a very high accuracy For future directions we can look at applying SQEM for other problems such as the quantum approximate optimization algorithm [22] investigating the effects of protecting multiple qubits at a time improving the probability recombination algorithm testing larger molecules and trying other error mitigation schemes

Acknowledgments

We thank Mark Byrd Paul Hovland and Gokul Subramanian Ravi for helpful discussions This research was also supported in part by an appointment to the Intelligence Community Postdoctoral Research Fellowship Program at Argonne National Laboratory administered by Oak Ridge Institute for Science and Education through an interagency agreement between the U.S <ref:2212.

Improvements for AI systems

The Simulated Quantum Error Mitigation (SQEM) framework transforms error mitigation components into classical pre and post processing procedures by applying circuit cutting. This allows for the execution of the error mitigation protocol almost noiseless because the error mitigation subcircuits are run on a classical simulator whereas the main circuit runs on a quantum device.
The system can perform high-accuracy ground state energy estimation for molecular systems like LiH, BeH2, and HF by matching results to the noiseless ansatz result to a very high accuracy as shown in Figs. 3a and 3b.
The framework is scalable for error mitigation by avoiding exponential cost; specifically, the strategy of error mitigating one qubit at a time ensures that the total overhead in the number of runs required is only a polynomial function of the number of pairs of checks used.
The AI system can generate results with bitwise probabilities close to the mitigated bitwise probabilities by using a Bayesian recombination model, which iteratively updates the distribution such that it has bitwise probabilities close to the protected bitwise probabilities in each mitigated result.