Time-Space Complexity Advantages for Quantum Computing

Preliminary Results of Applying Modified MSA Algorithm on Quantum Annealers (MAQ)

“…That is, standard classical computers have bit values restricted to either 0 and 1, or True and False, and therefore are only able to represent one state at a time [12]. Quantum computers -which make use of parallel processing and quantum mechanical properties to bypass these restrictions -have emerged as new contenders for finding alignments [13].…”

“…While the absolute supremacy of quantum computers over their classical counterparts is yet unproven [14], they have two key properties whose partnership make computation on quantum systems especially advantageous: one, parallel processing and, two, entanglement. The parallel processing capabilities come from the ability for the quantum bits to be in a probabilistic suspension between the bit values, or in a superimposed state [13]. This phenomenon allows for an exponential number of solutions to be simultaneously represented [12].…”

“…[35]. Quantum computers -which make use of parallel processing and quantum mechanical properties to bypass these restrictionshave emerged as new contenders for finding alignments [44].…”

A Quantum Finite Automata Approach to Modeling the Chemical Reactions

“…Initially, Kondacs and Watrous [8], and Moore and Crutchfield [9] proposed the concept of quantum automata separately. Since then, a variety of quantum automata models have been studied and demonstrated in various directions, such as QFAs, Latvian QFA, 1.5-way QFA, two-way QFA (2QFA), quantum sequential machine, quantum pushdown automata, quantum Turing machine, quantum multicounter machines, quantum queue automata [10], quantum multihead finite automata, QFAs with classical states (2QCFA) [11,12], state succinctness of two-way probabilistic finite automata (2PFA), QFA, 2QFA, and 2QCFA [13][14][15], interactive proof systems with QFAs [16,17], quantum finite state machines of matrix product state [18], promise problems recognition by QFA [19][20][21][22], quantum-omega automata [23] and semi-quantum two-way finite automata [24][25][26], time complexity advantages of QFA [27], nonuniform classes of polynomial size QFA [28,29], QFA and linear temporal logic relationship [30], and many more since the past 2 decades [31][32][33][34]. These models are effective in determining the boundaries of various computational features and expressive power [35][36][37].…”