Entropy flow in near-critical quantum circuits

TL;DR

This paper explores how entropy flows in near-critical quantum circuits, revealing universal properties and formulas that could impact the design of reversible quantum computers by linking entropy flow to energy currents and circuit laws.

Contribution

It derives universal formulas for entropy flow and conductivity in near-critical quantum circuits using relativistic quantum field theory, connecting entropy transport to circuit components.

Findings

Entropy flows as a conserved quantum current obeying circuit laws.

Universal formula for entropic conductivity: c_S(\u03c9)=iv^{2}S/c T.

Near-critical quantum wires are resistanceless inductors for entropy.

Abstract

Near-critical quantum circuits are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from the environment. The design of reversible computers is constrained by the laws governing entropy flow within the computer. In near-critical quantum circuits, entropy flows as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. The quantum entropy current is just the energy current divided by the temperature. 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 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: \sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the temperature, S the equilibrium entropy density and v the velocity of `light'. The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega). The thermal Drude weight is, universally, v^{2}S. This gives a way to measure the entropy density directly.