Thermodynamic irreversibility is well characterized by the entropy production arising from non-equilibrium quantum processes. We show that the entropy production of a quantum system undergoing open-system dynamics can be formally split into a term that only depends on population unbalances, and one that is underpinned by quantum coherences. This allows us to identify a genuine quantum contribution to the entropy production in non-equilibrium quantum processes. We discuss how these features emerge both in Lindblad-Davies differential maps and finite maps subject to the constraints of thermal operations. We also show how this separation naturally leads to two independent entropic conservation laws for the global system-environment dynamics, one referring to the redistribution of populations between system and environment and the other describing how the coherence initially present in the system is distributed into local coherences in the environment and non-local coherences in the system-environment state. Finally, we discuss how the processing of quantum coherences and the incompatibility of non-commuting measurements leads to fundamental limitations in the description of quantum trajectories and fluctuation theorems.

Landauer’s bound relates changes in the entropy of a system with the inevitable dissipation of heat to the environment. The bound, however, becomes trivial in the limit of zero temperature. Here we show that it is possible to derive a tighter bound which remains nontrivial even as $T\to 0$. As in the original case, the only assumption we make is that the environment is in a thermal state. Nothing is said about the state of the system or the kind of system-environment interaction. Our bound is valid for all temperatures and is always tighter than the original one, tending to it in the limit of high temperatures.

Quantifying the degree of irreversibility of an open system dynamics represents a problem of both fundamental and applied relevance. Even though a well-known framework exists for thermal baths, the results give diverging results in the limit of zero temperature and are also not readily extended to nonequilibrium reservoirs, such as dephasing baths. Aimed at filling this gap, in this paper we introduce a phase-space-entropy production framework for quantifying the irreversibility of spin systems undergoing Lindblad dynamics. The theory is based on the spin Husimi-Q function and its corresponding phase-space entropy, known as Wehrl entropy. Unlike the von Neumann entropy production rate, we show that in our framework, the Wehrl entropy production rate remains valid at any temperature and is also readily extended to arbitrary nonequilibrium baths. As an application, we discuss the irreversibility associated with the interaction of a two-level system with a single-photon pulse, a problem which cannot be treated using the conventional approach.

Quantum Error Mitigation (QEM) enables the extraction of high-quality results from the presently-available noisy quantum computers. In this approach, the effect of the noise on observables of interest can be mitigated using multiple measurements without additional hardware overhead. Unfortunately, current QEM techniques are limited to weak noise or lack scalability. In this work, we introduce a QEM method termed ‘Adaptive KIK’ that adapts to the noise level of the target device, and therefore, can handle moderate-to-strong noise. The implementation of the method is experimentally simple — it does not involve any tomographic information or machine-learning stage, and the number of different quantum circuits to be implemented is independent of the size of the system. Furthermore, we have shown that it can be successfully integrated with randomized compiling for handling both incoherent as well as coherent noise. Our method handles spatially correlated and time-dependent noise which enables us to run shots over the scale of days or more despite the fact that noise and calibrations change in time. Finally, we discuss and demonstrate why our results suggest that gate calibration protocols should be revised when using QEM. We demonstrate our findings in the IBM quantum computers and through numerical simulations.

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the joint probability distribution that heat $Q_1$ is exchanged with ancilla 1, heat $Q_2$ is exchanged with ancilla 2, and so on. This allows us to address questions concerning the correlations between the collisional events. For instance, if in a given realization a large amount of heat is exchanged with the first ancilla, then there is a natural tendency for the second exchange to be smaller. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski–Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated.

The conventional circuit paradigm, utilizing a small set of gates to construct arbitrary quantum circuits, is hindered by significant noise. In the quantum Fourier transform, for instance, the standard gate paradigm employs two CNOT gates for the partial CPhase. In contrast, some quantum computers can directly implement such operations using their native interaction, resulting in less noisy gates. Unfortunately, coherent errors degrade the performance of these gates. In Clifford gates such as the CNOT, these errors can be addressed through randomized compiling (RC). However, RC does not apply to the non-Clifford multi-qubit native implementations described above. The present work introduces and experimentally demonstrates a technique called ‘Pseudo Twirling’ (PST) to address coherent errors. We demonstrate experimentally that integrating PST with the ‘Adaptive KIK’ quantum error mitigation method enables the simultaneous mitigation of noise and coherent errors in multi-qubit non-Clifford gates.