The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic-centimeter-sized crystals of the Ising magnet LiHo x Y 1-x F 4 to a heat bath can be used to tune the system between a glassy state dominated by thermal excitations over energy barriers and a state with the hallmarks of a quantum spin liquid. Application of a magnetic field transverse to the Ising axis introduces both random magnetic fields and quantum fluctuations, which can retard and speed the annealing process, respectively, thereby providing a mechanism for continuous tuning between the destination states. The nonlinear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways.quantum magnetism | random fields | quantum annealing | quantum information | adiabatic quantum computing T he coupling of a sample to its environment is both a fundamental theoretical concept and a powerful experimental tool in classical thermodynamics. For quantum systems, contact between the internal degrees of freedom and the external world, often referred to as the "bath," can change the measured outcome completely. Typically, such experiments involve a small number of particles sensitive to subtle changes in the external incoherent environment, such as ultracold atoms confined in precisely controlled optical potentials (1-3). With the search for viable solid-state qubits for quantum computing, the control of bath-induced decoherence in solids also has become an important topic for engineers and condensed-matter physicists. Approaches have centered on the nuclear spin bath (4-6), modifying it either with isotopic substitution (7) or radio frequency pulses (8), and on electrical control of the exchange interaction between electron spins in coupled quantum dots (9). The question of the importance of coupling to an external bath, as provided by a cryostat, has not been researched as intensively. Here, we show that by engineering the thermal boundary conditions for a macroscopic magnetic crystal, it is possible to select distinct low temperature states. Conditions of constant energy, as opposed to constant temperature, yield relatively fewer low energy contributions to the fluctuation spectrum and decouple the spin excitations responsible for that spectrum into separate oscillators. The experiments show the importance of thermal heat sinking for quantum annealing, also referred to as adiabatic quantum computation (10-13), as well as new protocols for generating quantum cluster states (14).The LiHo x Y 1-x F 4 family of insulating magnetic salts provides a physical manifestation of the simplest quantum mechanical spin model, the Ising model in transverse field (15). Pure LiHoF 4 (16, 17) is a ferromagnet with Curie temperature, T C = 1.53 K. External magnetic fields can produce the longitudinal and transverse fields in the model, chemical substitution of Ho 3+ ions by the non...