Abstract: The Belle II experiment at the SuperKEKB electron-positron collider aims to collect an unprecedented data set of 50 ab-1 to study CP-violation in the B-meson system and to search for Physics beyond the Standard Model. SuperKEKB is already the world's highest-luminosity collider. In order to collect the planned data set within approximately one decade, the target is to reach a peak luminosity of 6 x 1035 cm-2 s-1by further increasing the beam currents and reducing the beam size at the interaction point by squeezing the betatron function down to betay* = 0.3 mm. To ensure detector longevity and maintain good reconstruction performance, beam backgrounds must remain well controlled. We report on current background rates in Belle II and compare these against simulation. We find that a number of recent refinements have significantly improved the background simulation accuracy. Finally, we estimate the safety margins going forward. We predict that backgrounds should remain high but acceptable until a luminosity of at least 2.8 x 1035 cm-2 s-1is reached for betay* = 0.6 mm. At this point, the most vulnerable Belle II detectors, the Time-of-Propagation (TOP) particle identification system and the Central Drift Chamber (CDC), have predicted background hit rates from single-beam and luminosity backgrounds that add up to approximately half of the maximum acceptable rates.

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).