BosonSampling with Lost Photons

BosonSampling is an intermediate model of quantum computation where linear-optical networks are used to solve sampling problems expected to be hard for classical computers. Since these devices are not expected to be universal for quantum computation, it remains an open question of whether any error-correction techniques can be applied to them, and thus it is important to investigate how robust the model is under natural experimental imperfections, such as losses and imperfect control of parameters. Here we investigate the complexity of BosonSampling under photon losses---more specifically, the case where an unknown subset of the photons are randomly lost at the sources. We show that, if $k$ out of $n$ photons are lost, then we cannot sample classically from a distribution that is $1/n^{\Theta(k)}$-close (in total variation distance) to the ideal distribution, unless a $\text{BPP}^{\text{NP}}$ machine can estimate the permanents of Gaussian matrices in $n^{O(k)}$ time. In particular, if $k$ is constant, this implies that simulating lossy BosonSampling is hard for a classical computer, under exactly the same complexity assumption used for the original lossless case.Comment: 12 pages. v2: extended concluding sectio

The Computational Power of Non-interacting Particles

Shortened abstract: In this thesis, I study two restricted models of quantum computing related to free identical particles. Free fermions correspond to a set of two-qubit gates known as matchgates. Matchgates are classically simulable when acting on nearest neighbors on a path, but universal for quantum computing when acting on distant qubits or when SWAP gates are available. I generalize these results in two ways. First, I show that SWAP is only one in a large family of gates that uplift matchgates to quantum universality. In fact, I show that the set of all matchgates plus any nonmatchgate parity-preserving two-qubit gate is universal, and interpret this fact in terms of local invariants of two-qubit gates. Second, I investigate the power of matchgates in arbitrary connectivity graphs, showing they are universal on any connected graph other than a path or a cycle, and classically simulable on a cycle. I also prove the same dichotomy for the XY interaction. Free bosons give rise to a model known as BosonSampling. BosonSampling consists of (i) preparing a Fock state of n photons, (ii) interfering these photons in an m-mode linear interferometer, and (iii) measuring the output in the Fock basis. Sampling approximately from the resulting distribution should be classically hard, under reasonable complexity assumptions. Here I show that exact BosonSampling remains hard even if the linear-optical circuit has constant depth. I also report several experiments where three-photon interference was observed in integrated interferometers of various sizes, providing some of the first implementations of BosonSampling in this regime. The experiments also focus on the bosonic bunching behavior and on validation of BosonSampling devices. This thesis contains descriptions of the numerical analyses done on the experimental data, omitted from the corresponding publications.Comment: PhD Thesis, defended at Universidade Federal Fluminense on March 2014. Final version, 208 pages. New results in Chapter 5 correspond to arXiv:1106.1863, arXiv:1207.2126, and arXiv:1308.1463. New results in Chapter 6 correspond to arXiv:1212.2783, arXiv:1305.3188, arXiv:1311.1622 and arXiv:1412.678

Regimes of classical simulability for noisy Gaussian boson sampling

As a promising candidate for exhibiting quantum computational supremacy, Gaussian Boson Sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS --- in the form of an inequality between the input squeezing parameter, the overall transmission rate and the quality of photon detectors. Our result serves as a non-classicality test that must be passed by any quantum computationalsupremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.Comment: 13 pages, 4 figures, final version accepted for publication in Physical Review Letter

Dominant two-loop electroweak corrections to the hadroproduction of a pseudoscalar Higgs boson and its photonic decay

We present the dominant two-loop electroweak corrections to the partial decay widths to gluon jets and prompt photons of the neutral CP-odd Higgs boson A^0, with mass M_{A^0} < 2 M_W, in the two-Higgs-doublet model for low to intermediate values of the ratio tan(beta) = v_2/v_1 of the vacuum expectation values. They apply as they stand to the production cross sections in hadronic and two-photon collisions, at the Tevatron, the LHC, and a future photon collider. The appearance of three gamma_5 matrices in closed fermion loops requires special care in the dimensional regularization of ultraviolet divergences. The corrections are negative and amount to several percent, so that they fully compensate or partly screen the enhancement due to QCD corrections.Comment: 9 pages, 3 figure