deMarti-iOlius, A. (Antonio)

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    Multiqubit time-varying quantum channels for NISQ-era superconducting quantum processors
    (2023) deMarti-iOlius, A. (Antonio); NO USAR Fuentes, P. (Patricio); Rodriguez, J. (Javier); Etxezarreta-Martínez, J. (Josu); García-Frías, J. (Javier); Crespo, P.M. (Pedro M.)
    Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (T1) and dephasing times (T2). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of T1 and T2 are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.
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    Multiqubit time-varying quantum channels for NISQ-era superconducting quantum processors.
    (2023) Etxezarreta-Martínez, J. (Josu); Fuentes-Ugartemendia, P. (Patricio); deMarti-iOlius, A. (Antonio); García-Frías, J. (Javier); Rodríguez-Fonollosa, J. (Javier); Crespo-Bofill, P. (Pedro)
    Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (T1) and dephasing times (T2). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of T1 and T2 are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.
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    Performance of surface codes in realistic quantum hardware.
    (2022) deMarti-iOlius, A. (Antonio); Etxezarreta-Martínez, J. (Josu); NO USAR Fuentes, P. (Patricio); Crespo-Bofill, P. (Pedro); García-Frías, J. (Javier)
    Surface codes are generally studied based on the assumption that each of the qubits that make up the surface code lattice suffers noise that is independent and identically distributed (i.i.d.). However, real benchmarks of the individual relaxation (T1) and dephasing (T2) times of the constituent qubits of state-of-the-art quantum processors have recently shown that the decoherence effects suffered by each particular qubit actually vary in intensity. In consequence, in this paper we introduce the independent nonidentically distributed (i.n.i.d.) noise model, a decoherence model that accounts for the nonuniform behavior of the decoherence parameters of qubits. Additionally, we use the i.n.i.d. model to study how it affects the performance of a specific family of quantum error correction codes known as planar codes. For this purpose we employ data from four state-of-the-art superconducting processors: ibmq_brooklyn, ibm_washington, Zuchongzhi, and Rigetti Aspen-M-1. Our results show that the i.i.d. noise assumption overestimates the performance of surface codes, which can suffer up to 95% performance decrements in terms of the code pseudothreshold when they are subjected to the i.n.i.d. noise model. Furthermore, we consider and describe two methods which enhance the performance of planar codes under i.n.i.d. noise. The first method involves a so-called reweighting process of the conventional minimum weight perfect matching (MWPM) decoder, while the second one exploits the relationship that exists between code performance and qubit arrangement in the surface code lattice. The optimum qubit configuration derived through the combination of the previous two methods can yield planar code pseudothreshold values that are up to 650% higher than for the traditional MWPM decoder under i.n.i.d. noise.
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    Decoding algorithms for surface codes
    (2024) deMarti-iOlius, A. (Antonio); Fuentes-Ugartemendia, P. (Patricio); Orús, R. (Román); Crespo, P.M. (Pedro M.); Etxezarreta-Martínez, J. (Josu)
    Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build near term error corrected qubits given their two-dimensional architecture, the requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that they can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art decoding algorithms for surface codes is provided. The target audience of this work are both readers with an introductory understanding of the field as well as those seeking to further their knowledge of the decoding paradigm of surface codes. We describe the core principles of these decoding methods as well as existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface codes decoding is also provided.
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    Performance enhancement of surface codes via recursive minimum-weight perfect-match decoding.
    (Amer. Physical Soc., 2023) deMarti-iOlius, A. (Antonio); Etxezarreta-Martínez, J. (Josu); Fuentes-Ugartemendia, P. (Patricio); Crespo-Bofill, P. (Pedro)
    The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or nonidentical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the nonuniformities, and the relationship between X, Y, and Z errors of the constituent qubits of a given surface code. Our modified approach, which we refer to as the recursive MWPM decoder, obtains an 18% improvement in the probability threshold p(th) under depolarizing noise. We also obtain significant performance improvements when considering biased noise and independent nonidentically distributed (i.ni.d.) error models derived from measurements performed on state-of-the-art quantum processors. In fact, when subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance improvement of 105.5% over the conventional MWPM strategy, and in some cases, it even surpasses the performance obtained over the well-known depolarizing channel.