  The ability to perform quantum error correction is a significant hurdle for
scalable quantum information processing. A key requirement for multiple-round
quantum error correction is the ability to dynamically extract entropy from
ancilla qubits. Heat-bath algorithmic cooling is a method that uses quantum
logic operations to move entropy from one subsystem to another, and permits
cooling of a spin qubit below the closed system (Shannon) bound.
Gamma-irradiated, $^{13}$C-labeled malonic acid provides up to 5 spin qubits: 1
spin-half electron and 4 spin-half nuclei. The nuclei are strongly hyperfine
coupled to the electron and can be controlled either by exploiting the
anisotropic part of the hyperfine interaction or by using pulsed
electron-nuclear double resonance (ENDOR) techniques. The electron connects the
nuclei to a heat-bath with a much colder effective temperature determined by
the electron's thermal spin polarization. By accurately determining the full
spin Hamiltonian and performing realistic algorithmic simulations, we show that
an experimental demonstration of heat-bath algorithmic cooling beyond the
Shannon bound is feasible in both 3-qubit and 5-qubit variants of this spin
system. Similar techniques could be useful for polarizing nuclei in molecular
or crystalline systems that allow for non-equilibrium optical polarization of
the electron spin.
