Since Claude Shannon's seminal work on information, there has been progress relating information theory to thermodynamics. The Shannon entropy, and its relationship to the thermodynamic entropy, is at the core of this. Given the connections between information theory and thermodynamics, one can ask: do there exist decompositions of thermodynamic observables into information-theoretic quantities? My work provides an answer by demonstrating information-theoretic decompositions of thermodynamic observables that track the reversible exchange of entropy between a system and its environment, the irreversible internal production of entropy within a system, and the total change of entropy from these two contributions. My resulting decomposition is entirely in terms of information-theoretic quantities known as finite-time entropy rates. This connection between information theory and thermodynamics holds arbitrarily far from equilibrium and even in the presence of external forces.

Since my work focuses on the irreversible production of entropy, it is naturally related to the second law of thermodynamics. I have shown that this irreversible component of the entropy can be seen as a (pre)-measure of time-reversal asymmetry even in the case of discrete-time. I have also illustrated how this decomposition sheds light on ensemble averages versus experimental realizations by building on previous work regarding the (information) typicality of particular paths.

Stochastic Thermodynamics in Python (STP)

STP is a Python library meant to construct random quantities and track their information-theoretic properties. These objects include continuous-time rate matrices, discrete-time transition matrices, and matrices representing 3-state self assembly models. STP also facilitates calculating information-theoretic quantities such as path entropies, entropy rates, the entropy production, and even typical sets from samplings of path spaces.

STP is available at PyPi, documentation is available at ReadTheDocs. The code is also available directly from my GitHub.

You can learn more about this research and the Green research group on information theory and stochastic thermodynamics at UMass Boston by going to Jason Green's research page.

On quantum computation

The advent of quantum computing places us on the forefront of a revolution in computational power and capability. Quantum computation will have direct impacts on cryptography and cyber-security, the development of pharmaceutical drugs, sustainable energy, novel quantum materials, meteorological forecasting, and more. The greatest obstacle for the construction and use of quantum computers lies in system decoherence–environmental noise and interactions challenge our ability to construct quantum systems with many qubits (> 40). A quantum computer can be built within a circuit model by having access to a minimal “universal” set of gates. Scalable universal quantum computation hinges on the possibility of keeping the error rate of such gates below a certain threshold that is currently hard to achieve. In contrast, Clifford gates are elements of a group of quantum gates that can be implemented with arbitrarily high precision. Not surprisingly, they do not allow for universal quantum computation. Moreover, Clifford circuits can be efficiently simulated on a classical computer, showing that quantum advantage lies outside the Clifford gate model. Since Clifford gates are not universal by themselves, understanding in which ways they fail to be is paramount to understanding to what extent non-Clifford gates are needed.

Haar Versus Clifford

Universal and Clifford circuits exhibit remarkably different behavior. Universal circuits show chaotic behavior and their outputs are random states in a Hilbert space. Instead, Clifford circuits fail to be ergodic and their outputs cover a tiny (finite) portion of the Hilbert space. The chaotic/non-chaotic behavior can be revealed by several properties: Entanglement Spectrum Statistics (ESS), response to disentangling algorithms, or the adherence to moments of the probability distribution over the Haar measure. My work aims to understand the transition between outputs of universal circuits and Clifford circuits by studying how statistics on random quantum circuits affect these figures of merit as functions of the impurity of Clifford circuits through strategic doping of universal gates. I want to improve the understanding on the number and placement of universal gates needed in a quantum circuit to improve resource management and reduce the overall impact of decoherence.

A better understanding of this transition has both long-term theoretical significance and immediate practical significance. Chaotic behavior from quantum systems is known to emerge from this transition of Clifford to universal circuits, and a better understanding of this phenomenon will shed light on irreversibility at the quantum level. This goal of this work was also improve our understanding of intelligent circuit design and resource management of the, otherwise difficult to implement, universal gates, while improving stability against decoherence for our quantum computers.

Random Quantum Circuits (RandQC)

Random Quantum Circuits (RandQC) is a Python library meant to make use of pseudo-random number generators to facilitate generating random quantum circuits, random quantum states, and track quantities of interest. It also handles input and output for these objects. This way saving and storing them can be automated, easing data gathering and access for analysis. The code is available directly from my .