In this work, we describe a similar duality theory for tensor powers of Clifford unitaries. Is spanned by the permutations of the t tensor factors. At its heart is the statement that the space of operators that commute with the t-fold tensor powers $$U^$$ 100–104 (2009)ĭ. Gottesman, Stabilizer codes and quantum error correction(phd thesis) (1997).AbstractSchur–Weyl duality is a ubiquitous tool in quantum information.
#CLIFFORD GROUP QUANTUM ERROR CORRECTION FULL#
Mirzaee, K. Navi, T. Nikoubin, New high-performance majority function based full adders, in 2009 14th International CSI Computer Conference, pp. P. Selinger, Quantum circuits of \(t\)-depth one. Weinfurter, Elementary gates for quantum computation. 65(9), 2889–2895 (2016)Ī. Chattopadhyay, L. Amarú, M. Soeken, P. Gaillardon, G. De Micheli, Notes on majority boolean algebra, in 2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL), pp. De Micheli, A sound and complete axiomatization of majority- \(n\) logic. Advances in Intelligent Systems and Computing, ed.
#CLIFFORD GROUP QUANTUM ERROR CORRECTION CODE#
Rahaman, clifford+t-based fault-tolerant quantum implementation of code converter circuit, in Soft Computing: Theories and Applications. L. Biswal, K. Mondal, A. Bhattacharjee, H. Rahaman, Fault-tolerant quantum implementation of priority encoder circuit using clifford+t-group, in 2020 International Symposium on Devices, Circuits and Systems (ISDCS), pp. L. Biswal, C. Bandyopadhyay, A. Chattopadhyay, R. Wille, R. Drechsler, H. Rahaman, Nearest-neighbor and fault-tolerant quantum circuit implementation, in 2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL), pp. Rahaman, Quantum domain design of cliffordbased bidirectional barrel shifter, in VLSI Design and Test, ed. L. Biswal, C. Bandyopadhyay, H. Rahaman, Efficient implementation of fault-tolerant 4:1 quantum multiplexer (qmux) using clifford+t-group, in 2019 IEEE International Symposium on Smart Electronic Systems (iSES) (Formerly iNiS), pp. Reichardt, Universal fault-tolerant quantum computation with only transversal gates and error correction. Cleland, Surface codes: towards practical large-scale quantum computation. The physical implementation of quantum computation 48 (2000). Quantum computing’s promise for the brave new world (2019). Grover, Quantum mechanics helps in searching for a needle in a haystack. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. Bennett, Logical reversibility of computation.
Irreversibility and heat generation in the computing process. Moore, Cramming more components onto integrated circuits, reprinted from electronics, volume 38, number 8, Apr. T- count, ancillary cost, and T- depth that connected with the quantum circuit of full adder circuit in fault-tolerant logic. We have also calculated the performance parameters viz. In this work, we focus on the implementation of Majority-based 1-bit and n-bit Full Adder (FA) in the fault-tolerant quantum logic circuits. On the other hand, the majority-based data structure converts a ripple-carry adder into a carry-look ahead adder. Due to the efficient physical implementation of promising QECC on multiple quantum technologies, the Clifford+T group of Quantum operators is nowadays commonly used for the fault-tolerant Quantum circuit realizations.
Literally, quantum states are fragile highly sensitive toward noise which requires regular encoding and decoding of quantum information through quantum error-correcting code (QECC) so as to accomplish fault tolerance. The single most important challenge to that ambitious goal is the handling of noise. The rapid progress in quantum technologies, as well as quantum algorithms, has paved the way for general-purpose, scalable quantum computers.
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