Resilience-runtime tradeoff relations for quantum algorithms.

A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer's potential to outperform classical computers.

Estimation of Hamiltonian Parameters from Thermal States.

We upper bound and lower bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/sqrt[n], beating the standard quantum limit.

Erratum: Lower Bounds on Quantum Annealing Times [Phys. Rev. Lett. 130, 140601 (2023)].

This corrects the article DOI: 10.1103/PhysRevLett.130.

Limits on the evolutionary rates of biological traits.

This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These rate limits link the variability in a population to evolutionary rates.

Lower Bounds on Quantum Annealing Times.

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing.

Limits to Perception by Quantum Monitoring with Finite Efficiency.

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent's perception of the system is altered by access to additional information.

García-Pintos, Hamma, and del Campo Reply.

We acknowledge that a derivation reported in Phys. Rev. Lett.

Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries.

We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a "free energy operator," defined by F≡H_{W}+β^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery.

Time Evolution of Correlation Functions in Quantum Many-Body Systems.

We give rigorous analytical results on the temporal behavior of two-point correlation functions-also known as dynamical response functions or Green's functions-in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times ⟨A(t)B⟩_{β}→⟨A⟩_{β}⟨B⟩_{β}, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size.

Spontaneous Symmetry Breaking Induced by Quantum Monitoring.

Spontaneous symmetry breaking (SSB) is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the state of the system. We study SSB due to quantum monitoring of a system via continuous quantum measurements.

Extreme Decoherence and Quantum Chaos.

We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus exceeding the polynomial dependence of systems with fluctuating k-body interactions. Our findings suggest the use of quantum chaotic systems as a natural test bed for spontaneous wave function collapse models.

Nonthermal Quantum Channels as a Thermodynamical Resource.

Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of nonthermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work.

Quantum systems equilibrate rapidly for most observables.

Considering any Hamiltonian, any initial state, and measurements with a small number of possible outcomes compared to the dimension, we show that most measurements are already equilibrated. To investigate nontrivial equilibration, we therefore consider a restricted set of measurements. When the initial state is spread over many energy levels, and we consider the set of observables for which this state is an eigenstate, most observables are initially out of equilibrium yet equilibrate rapidly.