Abstract: The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode 2(n) position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. Themain idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent 2 x 2-block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error epsilon (in terms of the spectral norm), the depth and size of which scale as O(1/epsilon). A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position).

Abstract: The neutron time-of-flight facility nTOF at CERN is a spallation source dedicated to measurements of neutroninduced reaction cross-sections of interest in nuclear technologies, astrophysics, and other applications. Since 2014, Experimental ARea 2 (EAR2) is operational and delivers a neutron fluence of similar to 4 center dot 10(7) neutrons per nominal proton pulse, which is similar to 50 times higher than the one of Experimental ARea 1 (EAR1) of similar to 8 center dot 10(5) neutrons per pulse. The high neutron flux at EAR2 results in high counting rates in the detectors that challenged the previously existing capture detection systems. For this reason, a Segmented Total Energy Detector (sTED) has been developed to overcome the limitations in the detector's response, by reducing the active volume per module and by using a photo-multiplier (PMT) optimized for high counting rates. This paper presents the main characteristics of the sTED, including energy and time resolution, response to gamma-rays, and provides as well details of the use of the Pulse Height Weighting Technique (PHWT) with this detector. The sTED has been validated to perform neutron-capture cross-section measurements in EAR2 in the neutron energy range from thermal up to at least 400 keV. The detector has already been successfully used in several measurements at nTOF EAR2.