A quantum algorithm for model independent searches for new physics - PowerPoint PPT Presentation

A quantum algorithm for model independent searches for new physics Prasanth Shyamsundar University of Florida based on [arXiv:2003.02181] Prof. Konstantin T. Matchev Prasanth Shyamsundar Dr. Jordan Smolinsky Pheno 2020 May 4-6, 2020

Quantum Adiabatic Optimization — D-Wave machine ◮ T ask: Find the ground state of an Ising lattice + + − + + + + − + + � � H = − h i s i − J ij s i s j s i ∈ {− 1 , + 1 } − + − + + i i , j + − − − + + + + − − ◮ 2 N possible states, where N is the number of spin sites. ◮ For general h i and J ij , finding the exact ground state using a classical computer takes O � 2 N � time. Intractable for N > ∼ 40 Adiabatic Quantum Optimization (AQO): ◮ Choose a Hamiltonian H 0 which doesn’t commute with H . Initialize the system in the ground state of H 0 . ◮ Adiabatically (slowly) evolve the Hamiltonian of the system from H 0 to H . 1 − t H 0 + t � � H ( t ) = T H T ◮ System stays in the ground state of H ( t ) . At time t = T , measure the state of the system. Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 1/11 Go to end

Quantum Adiabatic Optimization — D-Wave machine Takeaway: Find an Ising Hamiltonian whose ground state describes the solution to the problem of interest. Solve using AQO. ◮ D-wave systems implement AQO. D-Wave 2000Q has 2048 qubits. Pegasus (2020) will have 5640 qubits. ◮ Approximate ground states can be found using heuristic algorithms like simulated annealing on classical computers. ◮ Note: AQO is different from Universal Gate Quantum Computing. Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 2/11 Go to end

The physics problem Search for unmodeled new physics in collider data Hypothesis tests: ◮ Ingredients: 1. Data D 2. Null hypothesis: H 0 (say Standard Model) 3. Alternative hypothesis: H 1 (say SM + new physics) (no free parameter in either hypothesis for simplicity) ◮ T est statistic TS to perform the hypothesis test with: ◮ Function of data D ◮ Inspired by H 0 and H 1 ◮ Examples: Likelihood ratio test, χ 2 difference test LR = ln P( D ; H 1 ) χ 2 d = χ 2 H 0 − χ 2 H 1 P( D ; H 0 ) What if we don’t have an alternative hypothesis? Alternative hypothesis becomes “not H 0 ”. Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 3/11 Go to end

The physics problem Search for unmodeled new physics in collider data Hypothesis tests Goodness-of-fit tests: ◮ Ingredients: 1. Data D 2. Null hypothesis: H 0 (say Standard Model) 3. Alternative hypothesis: H 1 (say SM + new physics) (no free parameter in either hypothesis for simplicity) ◮ T est statistic TS to perform the hypothesis test with: ◮ Function of data D ◮ Inspired by H 0 and H 1 ◮ Examples: Likelihood ratio test, χ 2 difference test LR = ln P( D ; H 1 ) χ 2 d = χ 2 H 0 − χ 2 H 1 P( D ; H 0 ) What if we don’t have an alternative hypothesis? Alternative hypothesis becomes “not H 0 ”. Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 3/11 Go to end

The difficulty: Look-elsewhere effect ◮ p -value depends on: ◮ The data and H 0 (doesn’t depend on H 1 , even when available) ◮ Test statistic TS The more types of deviations a test is sensitive to ↓ The easier it is for statistical fluctuations to mimic a given value of TS or higher. Higgs search Fully specified for known m H model Sensitivity Sensitivity Sensitivity Simplified model Higgs search for unknown m H No model Specificity Specificity Specificity Specificity (sensitivity) takes a hit when we lose the alternative hypothesis in the design of TS . Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 4/11 Go to end

Look-elsewhere effect in an N binned χ 2 test e i is the expected count under H 0 . N N ( o i − e i ) 2 � � χ 2 = ∆ 2 o i -s are Poisson distributed. = i e i ∆ i = o i − e i i = 1 i = 1 (normalized residual) √ e i ∆ i -s are mutually independent, and follow a standard normal distribution under H 0 . i 10 2 = 146.0 3 4 9 2 8 2 7 1 6 T op row: Background only 0 0 i 5 1 4 2 Bottom row: Background + signal 3 2 4 2 r = 49 3 1 1 20 40 60 80 100 1 2 3 4 5 6 7 8 9 10 Bin i In these cases, data from the two i 10 3 hypotheses have the same χ 2 value. 9 2 = 145.7 2 4 8 7 1 2 6 0 5 0 i 1 4 Yet, the “eye-ball test” can 3 2 2 2 3 distinguish between them. 4 1 r = 50 1 2 3 4 5 6 7 8 9 10 1 20 40 60 80 100 Bin i χ 2 = 129 . 7 Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 5/11 Go to end

Controlling the Look-elsewhere effect ◮ Can’t limit attention to a specific alternative hypotheses (we aren’t given one) . ◮ Instead limit attention to “meaningful deviations”. 2 = 146.0 2 = 145.7 4 4 2 2 0 0 i i 2 2 4 4 r = 49 r = 50 1 20 40 60 80 100 1 20 40 60 80 100 Bin i Bin i How are these two images different? Can we capture the intuition in a test statistic? Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 6/11 Go to end

Ising model to capture spatial correlations in ∆ i -s ◮ Associate an Ising spin site with each bin in the histogram. � N N ( ∆ i + ∆ j ) 2 1 , for nearest neighbors | ∆ i | ∆ i s i 2 − 1 1 + s i s j � � H = − w ij = w ij otherwise 0 , 2 2 4 2 i = 1 i , j = 1 ◮ The first term tries to align spin s i with its corresponding deviation ∆ i . – The greater the value of ∆ i , the greater the reward. ◮ The second term tries to align spin s i with the spins s j of its neighbors. – The greater the value of | ∆ i + ∆ j | , the greater the reward (meaningful deviations). ◮ Use ground state H min of the system as a test statistic — the lower the ground state energy, the greater the deviation from the null hypotheses. – Without the second term, H min = − χ 2 / 4 . – The pull from the second term on a spin could conflict with the pull from the first. – This effect makes the exact computation of the ground state intractable classically. Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 7/11 Go to end

The new test statistic in action 2 = 146.0 min = 71.3 4 1 2 1-dimensional data 0 i s i ◮ Approximate ground state 2 discovered using simulated 4 1 annealing. r = 49 ◮ Note how some spins are 1 20 40 60 80 100 Bin i anti-aligned with their deviations. 2 = 145.7 min = 82.5 ◮ H min effectively distinguishes 4 1 between signal and noise of 2 comparable strength. 0 i s i χ 2 H min 2 Bkg only − 71 . 3 146 . 0 4 1 r = 50 Bkg + Sig 145 . 7 − 82 . 5 1 20 40 60 80 100 Bin i Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 8/11 Go to end

The new test statistic in action i 10 3 9 2 8 7 1 2-dimensional data 6 0 H min = − 129 . 6 5 ◮ Approximate ground state 1 4 discovered using simulated 3 2 2 annealing. 3 1 ◮ Note how some spins are 1 2 3 4 5 6 7 8 9 10 anti-aligned with their deviations. i 10 3 ◮ H min effectively distinguishes 9 2 8 between signal and noise of 7 1 comparable strength. 6 H min = − 168 . 2 0 5 1 χ 2 H min 4 3 2 Bkg only 129 . 7 − 129 . 6 2 Bkg + Sig 129 . 7 − 168 . 2 3 1 1 2 3 4 5 6 7 8 9 10 χ 2 = 129 . 7 Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 9/11 Go to end

ROC curves and p -values ◮ The new test outperforms a number of common tests in our simulations. 1.0 1.0 1 10 1 0.8 0.8 True positive rate True positive rate 2 min 0.6 p -value under 0.6 3 10 3 10 × 10 grid Runs test 0.4 0.4 Regions test 2 test 2 + Runs test 4 2 test 0.2 0.2 2 + Regions test KS test 10 5 min test min test 4 3 2 1 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 10 5 10 3 10 1 0.0 0.2 0.4 0.6 0.8 1.0 False positive rate p -value under 2 +Runs False positive rate Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 10/11 Go to end

Summary and outlook Properties of a good goodness-of-fit test: ◮ Should exploit the typical differences between statistical noise and plausible real effects � – Here we leverage spatial correlations. ◮ Should work with multi-dimensional data � – New physics signals are likely to be hidden in multi-dimensional distributions. ◮ The detected deviations should be interpretable � – Extremely important in the absence of an alternative hypothesis. New physics or background systematics? ◮ Our simulators aren’t perfect, especially parts related to non-perturbative QCD (fragmentation, hadronization), and detector response. ◮ An interpretable test can help understand and remove deficiencies in current generative models and bring down systematic uncertainties — especially important in many HL-LHC analyses expected to be bottlenecked by systematics. Thank you! Questions? Konstantin T. Matchev, Prasanth Shyamsundar , Jordan Smolinsky [arXiv:2003.02181] 11/11 Go to end