Phase-Tunable Thermal Logic: Computation with Heat

Boolean algebra, the branch of mathematics in which variables can assume only true or false values, is the theoretical basis of classical computation. The analogy between Boolean operations and electronic switching circuits, highlighted by Shannon in 1938, paved the way for modern computation based on electronic devices. The growth in the computational power of such devices, after an exciting exponential—Moore’s trend—is nowadays blocked by heat dissipation due to computational tasks, which are very demanding due to the miniaturization of chips. Heat is often a detrimental form of energy which increases the system’s entropy, decreasing the efficiency of logic operations. Here, we propose a physical system that is able to perform thermal-logic operations by reversing the old heat-disorder epitome into a heat-order paradigm. We lay the foundations of heat computation by encoding logic state variables in temperature and introducing the thermal counterparts of electronic logic gates. Exploiting quantum effects in thermally biased Josephson junctions (JJs), we propound a possible realization of a functionally complete logic. Our architecture ensures high operational stability and robustness, with switching frequencies reaching the GHz range.

Figure 1

Thermal-logic gates. (a) The distinctive shapes and logic truth tables of not, and, and or thermal-logic gates (“cold” is the logic state 0, while “hot” is the logic state 1) are depicted. (b) A schematic representation of a generic thermal-logic gate. The device consists of two inputs (at temperature $T_A$ and $T_B$, respectively) controlling the heat flow between the power supply (at temperature $T_P$) and the output (at temperature $T_C$) through a valve (red hourglass) by means of an actuator (blue half-circumference). The output (${\dot{Q}}_{\mathrm{OUT}}$) and loss (${\dot{Q}}_{\mathrm{loss}}$) heat currents are shown.

Figure 2

The not logic gate. (a) A thermal schematic: an actuator (blue half-circumference) at input temperature $T_A$ controls, through an normally open valve (red hourglass), the heat flow from the power supply (at temperature $T_{\mathrm{hot}}$) to the output (at temperature $T_C$). The output (${\dot{Q}}_{\mathrm{OUT}}$) and loss (${\dot{Q}}_{\mathrm{loss}}$) thermal currents are shown. (b) A schematic of the coherent caloritronic realization: the thermoelectric elements are constituted of a metal (orange), a ferromagnetic insulator (gray), and a superconductor (blue). The blue spirals depict the superconducting coils $L_A$ and $L_O$. The SQUIPT is composed of a superconductor ring, kept at temperature $T_{\mathrm{hot}}$ (red), interrupted by a metal wire (orange) tunnel-coupled to a metal probe (green) through a thin insulator (gray). (c) The output temperature $T_C$ and output logic state $C$ versus the logic input configuration for $T_{\mathrm{cold}}=T_{\mathrm{bath}}=100\mathrm{mK}$ and $T_{\mathrm{hot}}=150\mathrm{mK}$. The output temperature $T_C$ for optimum (squares) and fluctuating (lines) input is shown.

Figure 3

The and logic gate. (a) A thermal schematic: two actuators (blue half-circumferences) at input temperature $T_A$ and $T_B$ control, through a valve (red hourglass), the heat flow between the power supply (at temperature $T_{\mathrm{hot}}$) and the output (at temperature $T_C$). The output (${\dot{Q}}_{\mathrm{OUT}}$) and loss (${\dot{Q}}_{\mathrm{loss}}$) thermal currents are shown. (b) A schematic of the coherent caloritronic realization: the thermoelectric elements are constituted of a metal (orange), a ferromagnetic insulator (gray), and a superconductor (blue). The blue spirals depict the superconducting coils $L_A$ and $L_B$. The SQUIPT is composed of a superconductor ring, kept at temperature $T_{\mathrm{hot}}$ (red), interrupted by a metal wire (orange) tunnel-coupled to a metal probe (green) through a thin insulator (gray). (c) The output temperature $T_C$ and output logic state $C$ versus the logic input configuration for $T_{\mathrm{cold}}=T_{\mathrm{bath}}=100\mathrm{mK}$ and $T_{\mathrm{hot}}=150\mathrm{mK}$. The output temperature $T_C$ for optimum (squares) and fluctuating (lines) input is shown.

Figure 4

The or logic gate. (a) A thermal schematic: two actuators (blue half-circumferences) at input temperature $T_A$ and $T_B$ control, through two valves (red hourglasses), the heat flow from the power supply (at temperature $T_{\mathrm{hot}}$) to the output (at temperature $T_C$). The output (${\dot{Q}}_{\mathrm{OUT}}$) and loss (${\dot{Q}}_{\mathrm{loss}}$) thermal currents are shown. (b) A schematic of the coherent caloritronic realization: the thermoelectric elements are constituted of a metal (orange), a ferromagnetic insulator (gray), and a superconductor (blue). The blue spirals depict the superconducting coils $L_A$ and $L_B$. The SQUIPTs are composed of a superconductor ring, kept at temperature $T_{\mathrm{hot}}$(red), interrupted by a metal wire (orange) tunnel-coupled to a metal probe (green) through a thin insulator (gray). (c) The output temperature $T_C$ and output logic state $C$ versus the logic input configuration for $T_{\mathrm{cold}}=T_{\mathrm{bath}}=100\mathrm{mK}$ and $T_{\mathrm{hot}}=150\mathrm{mK}$. The output temperature $T_C$ for optimum (squares) and fluctuating (lines) input is shown.

Figure 5

The temperature dependence of the logic architecture. (a) The maximum operating frequency as a function of the bath temperature $T_{\mathrm{bath}}$. Inset: the fan-out as a function of the phonon temperature $T_{\mathrm{bath}}$. (b) The output temperature $T_C$ versus the input configuration $(A,B)$ of an and logic gate for $T_{\mathrm{bath}}=0.5,1,2\mathrm{K}$. The output signals for optimum (squares) and fluctuating (lines) inputs are shown.