This book set introduces multiple-valued quantum-DNA computing and multiple-valued DNA-quantum computing, a noble combination of quantum physics and molecular biology. Multiple-Valued Computing in Quantum Molecular Biology, Two Volume Set, is a blend of quantum physics and theoretical computer science that allows it to be more unique and faster than current silicon-based multiple-valued computing systems. Multiple-valued Quantum computing is an exciting topic for multiple-valued computing systems since it addresses many problematic multiple-valued traditional computer concerns. Volume one, Multiple-Valued Computing in Quantum Molecular Biology: Arithmetic and Combinational Circuits, introduces Multiple-Valued Quantum Computing and DNA Computing. It contains the basic understandings of Multiple-Valued Quantum Computing, Multiple-Valued DNA Computing. Part two reviews heat calculation, speed calculation, heat transfer, data conversion and data management in multivalued quantum, DNA, quantum-DNA and DNA-quantum computing. Part three discusses multiple-valued logic operations in quantum and DNA computing such as ternary AND, NAND, OR, NOR, XOR, XNOR, multiple-valued arithmetic operations such as adder, multiplier, and divider. Part four explains multiple-valued quantum and DNA combinational circuits such as multiple-valued DNA-quantum and quantum-DNA multiplexer, demultiplexer, encoder, and decoder. Volume two, Multiple-Valued Computing in Quantum Molecular Biology: Sequential Circuits, Memory Devices, Programmable Logic Devices, and Nano Processors, discusses multiple-valued quantum and DNA sequential circuits such as D flip-flop, SR latch, SR flip-flop, JK flip-flop, T flip-flop, shift register, ripple counter, synchronous counter are described with the applications and working procedures. Part two discusses the architecture and design procedure of memory devices such as Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read Only memory (PROM) in multiple-valued quantum, DNA, quantum-DNA, and DNA-quantum computing. Part three examines programmable logic devices such as Programmable Logic Array (PLA), Programmable Array Logic (PAL), Field Programmable Gate Array (FPGA), and Complex Programmable Logic Device (CPLD) in multiple-valued quantum, DNA, quantum-DNA and DNA-quantum computing are described with their architectures and working principles. Part four explores the designs and algorithms of Multiple-valued quantum, DNA, quantum-DNA and DNA-quantum nano processors. This book set will be of interest to those working in Quantum Computing, DNA Computing, Quantum-DNA Computing and DNA-Quantum Computing researchers, as well as graduate level students.