This week, we will have two talks on Tuesday and one talk on Wednesday.

On Tuesday Simon Cichy will tell us about 'A perturbative gadget for delaying the onset of barren plateaus in variational quantum algorithms' and Marcus Haberland will talk about 'Security of Relativistic Quantum Key Distribution'. These talks will take place at 2pm in HIT E 41.1 or on Zoom https://ethz.zoom.us/j/362994444.

On Wednesday Paul Colomer Saus will tell us about 'Quantum-enhanced estimation of a mode parameter’. This talk will take place at 2pm in HIT H51 or on Zoom https://ethz.zoom.us/j/362994444.

See below for the abstracts.

Title: A perturbative gadget for delaying the onset of barren plateaus in variational quantum algorithms (https://arxiv.org/abs/2210.03099)

Variational quantum algorithms are being explored as a promising approach to finding useful applications for noisy intermediate-scale quantum computers. However, cost functions corresponding to many problems of interest are inherently global, defined by Hamiltonians with many-body interactions. Consequently, the optimization landscape can exhibit exponentially vanishing gradients, so-called barren plateaus, rendering optimal solutions difficult to find. Strategies for mitigating barren plateaus are therefore needed to make variational quantum algorithms trainable and capable of running on larger-scale quantum devices. In this work, we contribute the toolbox of perturbative gadgets to the portfolio of methods being explored in the quest for making noisy intermediate-scale quantum devices useful. Specifically, we introduce a novel perturbative gadget, tailored to variational quantum algorithms, that can be used to avoid barren plateaus. Our perturbative gadget encodes an arbitrary many-body Hamiltonian corresponding to a global cost function into the low-energy subspace of a three-body Hamiltonian. Our construction requires rk additional qubits for a k-body Hamiltonian comprising r terms. We provide rigorous guarantees on the optimization of the local cost function defined by our three-body gadget Hamiltonian with respect to the original cost function, and we prove that this local cost function exhibits non-vanishing gradients, thus delaying the onset of barren plateaus. We then provide numerical demonstrations to show the functioning of our approach.

Title: Security of Relativistic Quantum Key Distribution

In this Master’s Thesis, we prove security for Relativistic Quantum Key Distribution (QKD) by utilizing the fact that any malicious adversary is constrained to respect causality. This can be achieved easily in experiments by granting Alice and Bob access to synchronized clocks in addition to their quantum machines, as they can then time the different steps of their QKD protocol appropriately.

We design three novel QKD protocols, which are based on ideas from [KRKM18]. We utilize the Generalized Entropy Accumulation Theorem from [MR22] to numerically prove finite-size security against general adversarial attacks and compute the key rates for two of them. We explain our reasoning as to why we conjecture the third photonic implementation to be secure as well, based on the idea of squashing from [GBN+14]. We show that by relying solely on causality as a security guarantee in QKD, one can establish high key rates and may achieve the maximum theoretically allowed scaling of the key rate in losses. This has importance for satellite-based and large-scale QKD networks and proves that entropic uncertainty, which grants security for well-established protocols like B92 and BB84, is not the only concept that can be used to prove QKD secure.

[KRKM18] - K. S. Kravtsov, I. V. Radchenko, S. P. Kulik, and S. N. Molotkov. Relativistic quantum key distribution system with one-way quantum communication. Sci Rep, 8(6102), Apr 2018. doi:10.1038/s41598- 018-24533-6.

[MR22] - Tony Metger and Renato Renner. Security of quantum key distribution from generalised entropy accumulation, 2022. doi:10.48550/ARXIV.2203.04993.

[GBN+14] - O. Gittsovich, N. J. Beaudry, V. Narasimhachar, R. Romero Alvarez, T. Moroder, and N. Lütkenhaus. Squashing model for detectors and applications to quantum-key-distribution protocols. Phys. Rev. A, 89:012325, Jan 2014. doi:10.1103/PhysRevA.89.012325.

Title: Quantum-enhanced estimation of a mode parameter.

High-precision experiments in interferometry, spectroscopy, positioning, and timing use light parameters to encode information. Therefore, it is critical to estimate them accurately. Using non-classical states of light, it is possible to enhance the sensitivity on the estimation of light-mode parameters (such as the wavelength or the spatial shape) beyond the standard quantum limit. In the presentation, we will discuss how to estimate with quantum-enhanced sensitivity a radial displacement of a light beam in an arbitrary direction and the wavelength. We will find which light-mode schemes allow quantum-enhanced sensitivities, and which quantum states maximize them.