Quantum computing for simulating high energy collisions Sarah Alam Malik Imperial College London
Outline • Intro to quantum computers • Review of quantum computers in HEP • Quantum algorithm for helicity amplitudes • Quantum algorithm for parton showers • Future outlook for quantum computers 2
Evolution of classical computer Classical computers have come a long way since 1950s - size of machines (current size of transistor O(nm)) and complexity of computers Quantum computing at a similar stage of development as classical computers in 1950s 3
Bit vs qubit | 0 i ! 0 0 • | 1 i ! 1 1 quantum bit classical bit 2-qubit system 4 basis states → | 00 ⟩ | 01 ⟩ | 10 ⟩ | 11 ⟩ N qubits 2 N dimensional Hilbert space → Power of quantum computing: this exponential increase in size of Hilbert space 4
Quantum computing: Two classes/paradigms Quantum Annealing Quantum Gate Circuit measurement Find ground state of Hamiltonian through Apply unitary transformations to qubits continuous-time adiabatic process through discrete set of gates • Large number of ‘noisy’ qubits • Small number of qubits but universal quantum computer • Good for solving specific problems; for instance optimisation, machine learning. • Google, IBM, Microsoft, Rigetti focused on gate-based quantum computing • D-Wave specialises in quantum annealers 5
Gate-based quantum computers 6
Quantum gates: Hadamard Hadamard gate - One of the most frequently used and important gates in quantum computing - Has no classical equivalent. - It puts a qubit initialised in the or state into a superposition of states. | 0 ⟩ | 1 ⟩ 1 1 � � � � p p H | 0 i = | 0 i + | 1 i , H | 1 i = | 0 i � | 1 i . 2 2 Circuit representation Matrix representation H 7
Quantum gates: CNOT and Toffoli CNOT CNOT | 00 i = | 00 i , CNOT | 01 i = | 01 i , - One of the most important gates in QC CNOT | 10 i = | 11 i , CNOT | 11 i = | 10 i . - 2-qubit operation that flips the state of a target qubit based on state of a control qubit. Circuit representation Matrix representation - This is used to create entangled qubits. To ff oli (CCNOT) CCNOT | 000 i = | 000 i , CCNOT | 001 i = | 001 i , CCNOT | 100 i = | 100 i , CCNOT | 010 i = | 010 i , - 3-qubit operation, an extension of CNOT gate but on CCNOT | 110 i = | 111 i , CCNOT | 111 i = | 110 i . 3 qubits Circuit representation Matrix representation - Flips the state of a target qubit based on state of the 2 other control qubits 8
Quantum supremacy? Nature volume 574 • Google claimed quantum supremacy with 54- qubit quantum computer - performed a random sampling calculation in 3 mins, 20 sec. • They claimed the this would take 10,000 years to do on classical machine. • IBM counterclaim : can be done on classical machine in 2.5 days Layout of processor Sycamore chip 9
Quantum computing in High Energy Physics 10
Track reconstruction at HL-LHC • One of the key challenges at HL-LHC : track reconstruction in a very busy, high pileup environment (140 - 200 overlapping pp collisions) • Much more CPU and storage needed • Can quantum computers help? ATLAS 11
Track reconstruction at HL-LHC arXiv:1902.08324 https://hep-qpr.lbl.gov • Express problem of pattern recognition as that of finding the global minimum of an objective function (QUBO) • Use D-Wave quantum annealer as minimiser (D-Wave 2X (1152 qubits)) • Use triplets (set of 3 hits); which triplets belong to the trajectory of a charged particle. Minimise function O : equivalent to finding the ground state of the Hamiltonian tive function to minimize becomes: N N N ∑ ∑ ∑ O ( a , b , T ) = a i T i + b ij T i T j T i , T j ∈ { 0, 1 } (4) i = 1 i j < i ATLAS weights quality of individual encodes relationship between triplets based on physics triplets properties Minimising O = selecting the best triplets to form track candidates. 12
Track reconstruction at HL-LHC arXiv:1902.08324 https://hep-qpr.lbl.gov e ffi ciency • Use dataset representative of HL-LHC • Study performance of algorithm as a function of purity particle multiplicity • Similar purity and efficiency as current algorithms • Execution time of algorithm not expected to scale with track multiplicity e ffi ciency purity Overall timing still needs to be measured and studied, but physics performance of tracking algorithm similar to classical 13
Nature volume 550: 375–379(2017) Higgs optimisation using D-Wave • Precise measurement of Higgs boson properties requires selecting large and high purity sample of signal events over a large background • Use quantum and classical annealing to solve a Higgs signal over background machine learning optimisation problem • Map the optimization problem to that of finding the ground state of a corresponding Ising spin model. Signal 10 5 Higgs signal 10 4 Background 10 4 10 3 10 3 10 2 10 2 10 1 10 1 10 0 10 0 0 2 4 6 1 2 3 p 1 p 2 T / m �� T / m �� 10 5 10 4 10 4 10 3 10 3 10 2 10 2 Background 10 1 10 1 Number of events 10 0 10 0 1 2 3 4 0 2 4 6 8 p �� Δ R T / m �� 10 5 10 5 10 4 10 4 s e 10 3 10 3 n. 10 2 10 2 r 10 1 10 1 e 10 0 10 0 e, 2 4 6 8 0 1 2 3 4 5 d ( p 1 T + p 2 ( p 1 T – p 2 T ) /m �� T ) /m �� 10 4 ic or 10 3 Build a set of weak classifiers from kinematic 10 3 ) 10 2 r- 10 2 observables of a decay, use these to H → γγ n 10 1 10 1 construct a strong classifier e 10 0 10 0 - 0 1 2 3 0 2 4 6 8 10 in Δ � | � �� | - 14
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