The quark matter symmetry free energy and the thermodynamical properties of strange quark matter (SQM) in strong magnetic fields and non-zero temperature cases are discussed in this work within Nambu–Jona-Lasinio (NJL) model by considering two kinds of vector interactions. The properties of the proto-quark stars (PQSs) are also studied by introducing a density-dependent magnetic field strength distribution and assuming two ‘extreme’ magnetic orientation cases inside the quark stars (QSs). The results indicate that the strength and orientation distribution of the magnetic fields in the QSs and the heating/cooling process during the star evolution may both influence the star mass of QSs within SU(3) NJL model.

Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication. However, the existing decoders are generally incapable of checking node duplication of belief propagation (BP) on quantum low-density parity check (QLDPC) codes. Based on the probability theory in the machine learning, mathematical statistics and topological structure, a GF(4) (the Galois field is abbreviated as GF) augmented model BP decoder with Tanner graph is designed. The problem of repeated check nodes can be solved by this decoder. In simulation, when the random perturbation strength p=0.0115–0.0116 and number of attempts N = 60–70, the highest decoding efficiency of the augmented model BP decoder is obtained, and the low-loss frame error rate (FER) decreases to 7.1975 ×10−5. Hence, we design a novel augmented model decoder to compare the relationship between GF(2) and GF(4) for quantum code [[450,200]] on the depolarization channel. It can be verified that the proposed decoder provides the widely application range, and the decoding performance is better in QLDPC codes.

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We study the thermodynamic properties of asymmetric quark matter and large mass quark stars within the confined-isospin-density-dependent-quark-mass model. We find that the quark matter symmetry energy should be very large in order to describe the recent discovered heavy compact stars PSR J0348+0432 ($$\text {2.01}\pm \text {0.04}M_{\odot }$$ 2.01 ± 0.04 M ⊙ ), MSP J0740+6620 ($$\text {2.14}\pm ^\text {0.10}_\text {0.09}M_{\odot }$$ 2.14 ± 0.09 0.10 M ⊙ of 68.3$$\%$$ % credibility interval and $$\text {2.14}\pm ^\text {0.20}_\text {0.18}M_{\odot }$$ 2.14 ± 0.18 0.20 M ⊙ of 95.4$$\%$$ % credibility interval) and PSR J2215+5135 (2.27$$\pm ^\text {0.10}_\text {0.09}M_{\odot }$$ ± 0.09 0.10 M ⊙ ) as QSs. The tidal deformability $$\Lambda _{1.4}$$ Λ 1.4 of the QSs is also investigated in this work, and the result indicates that $$\Lambda _{1.4}$$ Λ 1.4 may depend on the isospin effects and the strength / orientation distribution of the magnetic fields inside the quark stars.