Clifford circuits are insufficient for universal quantum computation
or creating tt-designs
with t\ge 4t≥4.
While the entanglement entropy is not a telltale of this insufficiency,
the entanglement spectrum of a time evolved random product state is: the
entanglement levels are Poisson-distributed for circuits restricted to
the Clifford gate-set, while the levels follow Wigner-Dyson statistics
when universal gates are used. In this paper we show, using finite-size
scaling analysis of different measures of level spacing statistics, that
in the thermodynamic limit, inserting a single T
(\pi/8)(π/8)
gate in the middle of a random Clifford circuit is sufficient to alter
the entanglement spectrum from a Poisson to a Wigner-Dyson
distribution.
Plasma-based electron and positron wakefield acceleration has made great strides in the past decade. However one major challenge for its applications to coherent light sources and colliders is the relatively large energy spread of the accelerated beams, currently at a few percent level. This energy spread is usually correlated with particle position in the beam arising from the longitudinal chirp of the wakefield amplitude. Therefore a dechirper is highly desirable for reducing this spread down to ∼ 0.1% level, while at the same time for maintaining the emittance of the accelerated beam. Here we propose that a low-density hollow channel plasma can act as a near-ideal dechirper for both electrons and positrons. We demonstrate the concept through large-scale three-dimensional particle-in-cell simulations.We show that the initial positive correlated energy spread (chirp) on the beam exiting a plasma accelerator can be compensated by the nearly linear self-wake induced by the beam in the hollow channel from few percent level down to ≤ 0.1%. Meanwhile, the beam emittance can be preserved due to the negligible transverse field inside the channel. This passive method may significantly improve the beam quality of plasma-based accelerators, paving the way for their applications to future compact free electron lasers and colliders.A plasma wake driven by an intense laser pulse or a charged particle beam can be utilized to accelerate electrons and positrons at extremely large accelerating fields of ≥ 100 GV/m, which are orders of magnitude larger than those in state-of-the-art radio-frequency microwave based accelerators [1,2]. In the past decade, plasma-based wakefield acceleration has achieved many significant milestones, such as multi-GeV electron acceleration in laser driven wakes [3][4][5][6][7][8][9][10], and high-energy, high-efficiency electron/positron acceleration in beam driven wakes [11][12][13][14]. However, for the beams produced by plasma accelerators to be useable for critical applications like X-ray free electron lasers (X-FELs) and linear colliders, many challenges still remain. One of these is the relatively large energy spread of the accelerated electron/positron beams produced by plasma arXiv:1805.07031v2 [physics.acc-ph]
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