Model of logical errors in circuit from logical errors of individual operations

Quantum Computing is part of Stack Overflow’s open communities: specialist spaces where curiosity is welcome, knowledge is shared freely, and the best answers rise to the top. Stack Overflow for Teams is now called Stack Internal. Bring the best of human thought and AI automation together at your work. Bring the best of human thought and AI automation together at your work. Learn more Bring the best of human thought and AI automation together at your work. Can I infer logical error rates of circuits from logical error rates of single operations? For this, I want to distinguish between two scenarios of different levels of simplification. Let's say I have a certain QEC code and decoder. I experimentally implemented the state preparation of the logical 0- and +-states and determined the probability of success p(init,0). I also implemented the state preparation + logical operation for a universal set of logical operations, each with 0-state and +-state. For each I determined the probability that the outcome state is the expected one after correction p(gate, state). Can I predict from this information, at least approximately, the probability that a logical circuit will be successful? Assume a circuit consists of state preparation of 0-state, gate A, gate B and readout. I further know that after gate A the state ideally should be the +-state and the readout is noiseless. Can I reasonably approximate for example the fidelity of the output state via 1- ( p(gate A, 0) + p(gate B, +) - p(init, +)), where the last term takes into account that in the circuit I don't need a second state preparation? If this was only about physical qubits and noise, this model approximately works as long as the noise is depolarizing, as it is not changed by any of the following gates and thus the error probabilities just add up. For other types, this would not be true. Thus Let's say I did just determine the probability of success in each of the experiments, but did a full state tomography and have a full model of which errors happen effectively for the two state preparations and the gates. Could I treat the error correction as black-box and simulate: ideal logical effect of gate A - noise from 0-state preparation and gate A - ideal logical effect of gate B - inverse noise of +-state prep - noise from +-state prep and gate B ? This of course still would not be exact as for example ideal + & B - inverse + noise - + & B noise is not the same as ideal + - noise + - ideal B - B noisein the general case. Also, potentially the QEC cycles of the full circuit are not the same as simply appending the cycles for each of the block after eachother for some codes? But are there any insights in how bad the approximation would be? Even if it is for a very specific scenario of hardware, code, decoder and circuit? Thanks for contributing an answer to Quantum Computing Stack Exchange! Use MathJax to format equations. MathJax reference. To learn more, see our tips on writing great answers. By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. This comment attacks a person or group. Learn more in our Abusive behavior policy. This comment is rude or condescending. Learn more in our Code of Conduct. A problem not listed above. Try to be as specific as possible. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Site design / logo © 2026 Stack Exchange Inc; user contributions licensed under CC BY-SA . rev 2026.9.15.