Error Mitigation and Quantum-Assisted Simulation in the Error Corrected Regime.

A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of "magic" quantum states. In this context, we develop a general framework to discuss the value of the available, nonideal magic resources, relative to those ideally required. We single out a quantity, the quantum-assisted robustness of magic (QROM), which measures the overhead of simulating the ideal resource with the nonideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally developed for noisy intermediate-scale quantum devices, to the case where qubits are logically encoded. The QROM shows how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit and enables the construction of explicit protocols, interpolating between classical simulation and an ideal quantum computer.

Gaussian Thermal Operations and The Limits of Algorithmic Cooling.

The study of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results typically do not apply to continuous variable systems and do not take into account that, in many practically relevant settings, system-environment interactions are effectively bilinear. Here we tackle these issues by focusing on Gaussian quantum states and channels. We provide a complete characterization of the most general Gaussian thermal operation acting on an arbitrary number of bosonic modes, which turn out to be all embeddable in a Markovian dynamics, and derive necessary and sufficient conditions for state transformations under such operations in the single-mode case, encompassing states with nonzero coherence in the energy eigenbasis (i.e., squeezed states). Our analysis leads to a no-go result for the technologically relevant task of algorithmic cooling: We show that it is impossible to reduce the entropy of a system coupled to a Gaussian environment below its own or the environmental temperature, by means of a sequence of Gaussian thermal operations interspersed by arbitrary (even non-Gaussian) unitaries. These findings establish fundamental constraints on the usefulness of Gaussian resources for quantum thermodynamic processes.