This paper presents a theoretical framework for constructing decoherence-protected quantum states in one-dimensional systems, known as "quantum wires," by utilizing unpaired Majorana fermions. The key idea is that certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses two ground states with an energy difference proportional to exp(-L/l₀) and different fermionic parities. These systems can be used as qubits since they are intrinsically immune to decoherence. The presence of boundary Majorana fermions is determined by a condition on the bulk electron spectrum. This condition is satisfied in the presence of an arbitrary small energy gap induced by proximity to a 3D p-wave superconductor, provided the normal spectrum has an odd number of Fermi points in each half of the Brillouin zone. The paper describes a toy model of a quantum wire on the surface of a 3D superconductor, where the Hamiltonian is analyzed to show the emergence of unpaired Majorana fermions at the ends of the wire. The model demonstrates that when the superconducting gap is non-zero, Majorana fermions can appear at the ends of the wire. The analysis shows that the ground state parity depends on the system's parameters and that the Majorana number, a topological invariant, determines the existence of unpaired Majorana fermions. The paper also discusses the physical realization of such systems, noting that achieving M = -1 quantum wires is challenging due to spin degeneracy. However, scenarios involving charge density waves and magnetic fields could potentially lift this degeneracy. The paper concludes with speculations about experimental tests, such as using a quantum wire bridge between superconducting leads to observe Majorana fermions and their effects on Josephson currents.This paper presents a theoretical framework for constructing decoherence-protected quantum states in one-dimensional systems, known as "quantum wires," by utilizing unpaired Majorana fermions. The key idea is that certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses two ground states with an energy difference proportional to exp(-L/l₀) and different fermionic parities. These systems can be used as qubits since they are intrinsically immune to decoherence. The presence of boundary Majorana fermions is determined by a condition on the bulk electron spectrum. This condition is satisfied in the presence of an arbitrary small energy gap induced by proximity to a 3D p-wave superconductor, provided the normal spectrum has an odd number of Fermi points in each half of the Brillouin zone. The paper describes a toy model of a quantum wire on the surface of a 3D superconductor, where the Hamiltonian is analyzed to show the emergence of unpaired Majorana fermions at the ends of the wire. The model demonstrates that when the superconducting gap is non-zero, Majorana fermions can appear at the ends of the wire. The analysis shows that the ground state parity depends on the system's parameters and that the Majorana number, a topological invariant, determines the existence of unpaired Majorana fermions. The paper also discusses the physical realization of such systems, noting that achieving M = -1 quantum wires is challenging due to spin degeneracy. However, scenarios involving charge density waves and magnetic fields could potentially lift this degeneracy. The paper concludes with speculations about experimental tests, such as using a quantum wire bridge between superconducting leads to observe Majorana fermions and their effects on Josephson currents.