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Paper 1
Fault Tolerant Quantum Error Mitigation
Alvin Gonzales, Anjala M Babu, Ji Liu, Zain Saleem, Mark Byrd
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2308.05403
- arXiv
- 2308.05403
Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based error mitigation techniques. We also demonstrate that similar to results in fault tolerant quantum computing, code concatenation in fault-tolerant quantum error mitigation (FTQEM) can exponentially suppress the errors to arbitrary levels. For a family of circuits, we provide analytical error thresholds for FTQEM with the repetition code. These circuits include a set of quantum circuits that can generate all of reversible classical computing. The post-selection rate in FTQEM can also be increased by correcting some of the outcomes. Our threshold results can also be viewed from the perspective of quantifying the number of gate operations we can delay checking the stabilizers in a concatenated code before errors overwhelm the encoding. The benefits of FTQEM are demonstrated with numerical simulations and hardware demonstrations.
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Simulation of quantum computation with magic states via Jordan-Wigner transformations
Michael Zurel, Lawrence Z. Cohen, Robert Raussendorf
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2307.16034
- arXiv
- 2307.16034
Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the magic state model. It is based on generalized Jordan-Wigner transformations, and it has a close connection to the probability representation of universal quantum computation based on the $Λ$ polytopes. For each number of qubits, it defines a polytope contained in the $Λ$ polytope with some shared vertices. It leads to an efficient classical simulation algorithm for magic state quantum circuits for which the input state is positively represented, and it outperforms previous representations in terms of the states that can be positively represented.
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