Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2+1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

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Quantum key distribution (QKD) provides ultimate cryptographic security based on the laws of quantum mechanics. For point-to-point QKD protocols, the security of the generated key is compromised by detector side channel attacks. This problem can be solved with measurement device independent QKD (mdi-QKD). However, mdi-QKD has shown limited performances in terms of the secret key generation rate, due to post-selection in the Bell measurements. We show that high dimensional (Hi-D) encoding (qudits) improves the performance of current mdi-QKD implementations. The scheme is proven to be unconditionally secure even for weak coherent pulses with decoy states, while the secret key rate is derived in the single photon case. Our analysis includes phase errors, imperfect sources and dark counts to mimic real systems. Compared to the standard bidimensional case, we show an improvement in the key generation rate. * luca.delantonio@nbi.ku.dk † dabac@fotonik.dtu.dk to increase the dimension of the Hilbert space [19-23] for standard QKD. We propose a protocol, where Alice and Bob generate qudits (quantum states in N -dimensions) encoded in different paths or time slots of the photons. These photons then interfere at Charlie's Beam Splitters (BS), as shown in Fig. 1. As discussed below, the measurement projects the qubits into a two dimensional subspace, which can be used for QKD. In the following, we analyse this high dimensional mdi-QKD protocol, considering the main sources of errors, such as, imperfect photon generation, dark counts and (unknown) phase shifts. We prove that high dimensional mdi-QKD is unconditionally secure for coherent states with the decoy state technique [15,24], and analyse the key generation rate for single photon sources. In analogy to a similar result for standard QKD [23], we find that our Hi-D mdi-QKD protocol is advantageous, particularly in the detector saturation regime, where the time between photon clicks at Charlie's detectors is comparable to the detectors' dead time τ d . We study the protocol both for time and space encoding, and analyse the practical constraints that make one encoding better than the other. A different Hi-D mdi-QKD scheme was proposed in Ref. [18], but remains experimentally unfeasible, since discriminating Bell states in high dimensions is impossible by simple means [25,26]. In comparison, our protocol can be implemented without significant increase in the complexity of existing setups. In particular, for weak coherent states and time encoding, no change in the hardware is required. Protocol definitionMost QKD protocols are based on mutually unbiased bases (MUBs). Usually, the computational Z basis ({|0 , |1 } for qubits) is less susceptible to errors than arXiv:1809.04405v1 [quant-ph]

The fields of optomechanics and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to make the detection of the mechanical mode occupation difficult, typically requiring the single-photon strong-coupling regime. Here, we propose and analyse an electromechanical setup, which allows us to overcome this limitation and resolve the energy levels of a mechanical oscillator. We found that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups.

Variational quantum eigensolvers (VQEs) combine classical optimization with efficient cost function evaluations on quantum computers. We propose a new approach to VQEs using the principles of measurement-based quantum computation. This strategy uses entangled resource states and local measurements. We present two measurement-based VQE schemes. The first introduces a new approach for constructing variational families. The second provides a translation of circuit-to measurement-based schemes. Both schemes offer problem-specific advantages in terms of the required resources and coherence times.