Center for Theoretical Physics

The design of parametric quantum circuits (PQCs) for efficient use in variational quantum simulations (VQS) is subject to two competing factors. On one hand, the set of states that can be generated by the PQC has to be large enough to contain the solution state. Otherwise, one may at best find the best approximation of the solution restricted to the states generated by the chosen PQC. On the other hand, the PQC should contain as few parametric quantum gates as possible to minimize noise from the quantum device. Thus, when designing a PQC one needs to ensure that there are no redundant parameters. The dimensional expressivity analysis discussed in these proceedings is a means of addressing these counteracting effects. Its main objective is to identify independent and redundant parameters in the PQC. Using this information, superfluous parameters can be removed and the dimension of the space of states that are generated by the PQC can be computed. Knowing the dimension of the physical state space then allows us to deduce whether or not the PQC can reach all physical states. Furthermore, the dimensional expressivity analysis can be implemented efficiently using a hybrid quantum-classical algorithm. This implementation has relatively small overhead costs both for the classical and quantum part of the algorithm and could therefore be used in the future for on-the-fly circuit construction. This would allow for optimized circuits to be used in every loop of a VQS rather than the same PQC for the entire VQS. These proceedings review and extend work in [1, 2].

We study general freeze-out scenarios where an arbitrary number of initial and final dark matter particles participate in the number-changing freeze-out interaction. We consider a simple sector with two particle species undergoing such a thermal freeze-out; one of the relics is stable and gives rise to the dark matter today, while the other one decays to the Standard Model, injecting significant entropy into the thermal bath that dilutes the dark matter abundance. We show that this setup can lead to a stable relic population that reproduces the observed dark matter abundance without requiring weak scale masses or couplings. The final dark matter abundance is estimated analytically. We carry out this calculation for arbitrary temperature dependence in the freeze-out process and identify the viable dark matter mass and cross section ranges that explain the observed dark matter abundance. This setup can be used to open parameter space for both heavy (above the unitarity bound) or light (sub-GeV) dark matter candidates. We point out that the best strategy for probing most parts of our parameter space is to look for signatures of an early matter-dominant epoch.

Estimating the free energy, as well as other thermodynamic observables, is a key task in lattice field theories. Recently, it has been pointed out that deep generative models can be used in this context. Crucially, these models allow for the direct estimation of the free energy at a given point in parameter space. This is in contrast to existing methods based on Markov chains which generically require integration through parameter space. In this contribution, we will review this novel machine-learning-based estimation method. We will in detail discuss the issue of mode collapse and outline mitigation techniques which are particularly suited for applications at finite temperature.

We present an error mitigation scheme which corrects readout errors on Noisy Intermediate-Scale Quantum (NISQ) computers [1,2]. After a short review of applying the method to one qubit, we proceed to discuss the case when correlations between different qubits occur. We demonstrate how the readout error can be mitigated in this case. By performing experiments on IBMQ hardware, we show that such correlations do not have a strong effect on the results, justifying to neglect them.