Entropy Flow in Near-Critical Quantum Circuits

Near-critical quantum circuits close to equilibrium are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from microscopic environmental fluctuations by the renormalization group. Entropy flows in near-critical quantum circuits near equilibrium as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. These “Kirchhoff laws” for entropy flow are the fundamental design constraints for asymptotically large-scale quantum computers. A quantum circuit made from a near-critical system (of conventional type) is described by a relativistic 1+1 dimensional relativistic quantum field theory on the circuit. The quantum entropy current near equilibrium is just the energy current divided by the temperature. The universal properties of the energy–momentum tensor constrain the entropy flow characteristics of the circuit components: the entropic conductivity of the quantum wires and the entropic admittance of the quantum circuit junctions. For example, near-critical quantum wires are always resistanceless inductors for entropy. A universal formula is derived for the entropic conductivity: σS(ω) = iv2S/ωT , where ω is the frequency, T the temperature, S the equilibrium entropy density and v the velocity of “light”. The thermal conductivity is Re(TσS(ω)) = πv2S δ(ω). The thermal Drude weight is, universally, v2S. This gives a way to measure the entropy density directly.