Efficient verification of anticoncentrated quantum states

Abstract I present a method for estimating the fidelity F ( μ , τ ) between preparable quantum state and classically specified pure target $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = using simple circuits on-the-fly classical calculation (or lookup) of selected amplitudes $$\left|\tau \right\rangle$$ . The is sample efficient anticoncentrated states (including many that are hard to simulate classically), with approximate cost 4 ϵ −2 (1 − d p coll where desired precision estimate, dimension Hilbert space, collision probability distribution. This scaling exponentially better than any based on sampling. also more sophisticated version uses efficiently well-characterized as an importance sampler further reduce number copies needed. Though some challenges remain, this work takes significant step toward scalable verification complex produced by processors.