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Aritra Sarkar - Search and Optimisation Algorithms for Genomics on Quantum Accelerators
- 1. QuantumForce.eu Search and optimisation algorithms for genomics on quantum accelerators 04th Apr, 2019 Aritra Sarkar PhD candidate, Quantum Computer Architecture lab QuTech (Faculty of Applied Sciences) Dept. of Q&CE (Faculty of Electrical Engineering, Mathematics and Computer Sciences) Delft University of Technology Genomics Machine Learning Quantum Computing Application Platform Method access the presentation here
- 3. QuantumForce.eu 3 NISQ acceleration NISQ FTQC QEC ClassicalSimulationLimit number of qubits errorrate https://arxiv.org/abs/1801.00862 - John Preskill, Quantum Computing in the NISQ era and beyond NISQ: Noisy Intermediate-Scale Quantum map problem to quantum: do: run Q Algorithm assess answer while (result not satisfactory) save measurement result/statistics interpret classical answer HostCPU Graphics Processing Unit Field-Programmable Gate Array Digital Signal Processor Neural Processing Unit QuantumAccelerator
- 4. 4QuantumForce.eu Genomical exa-scale data 2-40 EB/year Genomical Big Data
- 6. QuantumForce.eu 6 Whole Genome Sequencing pipeline https://software.broadinstitute.org/gatk/best-practices/
- 7. QuantumForce.eu 7 • Map-to-reference vs. Variant calling – Multiple solutions evaluated in superposition, but cannot access results for every state • Superposition is doesn’t have a classical logic equivalent (e.g. AND/OR) • Generalization of probability theory for complex amplitudes – Useful when used to explore large solution space but requires only the min/max/mean answer Superposition vs. ParallelismIndexedbase-pairs Ref. Genome Target Genome Differences Variants embarrassingly parallel no interaction need all answers Not suitable for Q-Acceleration Ref. Genome Splices Short Reads Differences Index of min-diff. Indexedsplices parallel evolution global/local interactions statistical answer
- 9. 9QuantumForce.eu NP Searching solutions 𝑦𝑠 = 𝑓(𝑥 𝑠) 𝑦𝑠 = 𝑓(𝑥 𝑠) 𝑦𝑠 = 𝑓(𝑥 𝑠) 𝑥 𝑠 = 𝑓−1 (𝑦𝑠) 𝑦0 = 𝑓 𝑥0 𝑦1 = 𝑓 𝑥1 𝑦2 = 𝑓 𝑥2 = 𝑦𝑠 𝑦3 = 𝑓 𝑥3 ⋮ Function Evaluation Inductive Logic, GP, ANN, …Function Inversion Quantum Superposition P Bounded Quantum Polynomial
- 10. QuantumForce.eu 10 Sub-sequence index search RG: Reference Genome (3 × 108 𝑏𝑝) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 SR: Short Read (50𝑏𝑝) 0 1 2 4 3 21 21 22 23 24 25 0 1 2 4 3 𝑄𝑡𝑎𝑔 𝑄 𝑑𝑎𝑡𝑎
- 11. QuantumForce.eu 11 Ab initio alignment Naïve Method • Substring(/subsequence) matching problem Exact match Boyer-Moore + Improvements Knuth-Morris-Pratt + Improvements Suffix Trees + Improvements Exact match (wildcards) Needleman-Wunsch Global Alignment Smith-Waterman Local Alignment Simple Edit Transcript using memoization of Levenshtein Distance + Improvements(alphabet/operation weights) Approximate match BYP/CL/Myers/hybrid-dynamic methods Alignment with arbitrary (k bounded) gaps Approximate match Approximate match Burrows-Wheeler-Transform + Smith-Waterman (BWT-SW) All local hits Burrows-Wheeler-Aligner + super-Maximal Exact Match (BWA-MEM) Heuristics
- 12. 12QuantumForce.eu Dissecting a quantum algorithm Superpose Soln. Space Encode Function Clever Process Measure Initialize |0⟩⊗n Classical Output Classical Input 1. Prepare all-zero state for n-qubits (not so trivial experimentally as it sounds) 2. Full superposition in computational basis (H-gate on all qubits) – OR, superposition of classical input space 3. Transform superposition to evaluate the function (using 1 & 2 qubit gates) – OR, evaluate function based on classical input space 4. Somehow* increase the amplitude of the solution space 5. Measure out the state 6. Repeat Steps 1-5 to access the modal classical output * the quantum magic of interference
- 13. 13QuantumForce.eu Evolution Tight bounds on quantum searching … arbitrary initial amplitude distribution Quantum Pattern Matching Grover Search one solution full, uniform database known Oracle for solution in database optimal iterations multiple (un)known solutions full, uniform database known Oracle for solution in database optimal iterations multiple known solutions arbitrary database known Oracle for solution in database optimal iterations multiple unknown solutions sliding index database alphabet based Oracles optimal iterations one solution sub-string phonebook 0 Hamming Distance Oracle optimal iterations … Quantum Bioinformatics Quantum Associative Memory multiple known solutions arbitrary database known Oracle for solution in database higher Pmax iteration … associative memory with distributed queries multiple known solutions arbitrary database Binomial Oracle optimal iterations … improved distributed queries multiple unknown solutions arbitrary database Binomial Oracle higher Pmax iteration Gen 1 (tested) QUS Gen 2 (tested) QPM Gen 3 (tested) QNN Q Walk / Graph SearchQ Unstructured Search Q Structured Search HSP (abelian/dihedral)
- 14. 14QuantumForce.eu QiMAM-dq • Quantum indexed multi-associative memory (MSc thesis) – Grover’s Search + Quantum Neural Networks + Content Addressable Storage
- 16. 16QuantumForce.eu Purebreds • a.k.a. Coherent Protocols – e.g. Shor’s factorisation, Shor’s discrete-log, QFT, Quantum Phase Estimation, Harrow-Hassidim-Lloyd, Matrix inversion ... – Most studied/popular quantum algorithms so far • Exponential speedup – Caveats • Noise tolerance – Number of qubits for FT • Circuit depth • Quantum I/O – Classical Input: State preparation – Classical Output: State tomography – QRAM O ( f(experimental) x g(no-cloning) x h(algorithm) )
- 17. 17QuantumForce.eu Workhorses • Peter Shor estimates 2048-RSA requires ~5k qubits (times 102-103 physical qubits) & ~107 gates • Near-term Quantum Algorithms – low depth circuits without extensive QEC (small-codes) – enough qubits to just store the problem (hard to do better) – still solve useful problems with local constraints – Adaptable optimization algorithms (easy to map to problem) • Genetic Algorithm / Evolutionary Programs • Deep Learning – Quantum Approximate Optimization Algorithm • NP-Hard combinatorial optimisation problems in Quantum Machine Learning • Polynomial-time solution for every instance with guaranteed approximation quality bound • Interesting because of its potential to exhibit near-term quantum supremacy • Gate-based implementation inspired by Adiabatic QC and Q Annealing https://www.bcg.com/en-ca/publications/2018/next-decade-quantum-computing-how-play.aspx
- 19. 19QuantumForce.eu De novo assembly • Eulerian path/cycle [De Bruijn Graph] – Eulerian path is a trail in a finite graph which visits every edge exactly once. – Eulerian cycle is an Eulerian trail which starts and ends on the same vertex. • Hamiltonian path/cycle [Overlap-Layout-Consensus] – Hamiltonian path is a graph path between two vertices of a graph that visits each vertex exactly once. – Hamiltonian cycle is a path which starts from one node and ends at the same node covering all the nodes of that graph. – If a Hamiltonian path exists whose endpoints are adjacent, then the resulting graph cycle is called a Hamiltonian cycle. • Decision version vs. Function version • Travelling Salesman Problem – A cycle that visits all nodes of the graph and such that the sum of the edge weights is minimum. – Find a Hamiltonian cycle of minimum weight. • Using Quantum Approximate Optimisation Algorithm + “Easy” to solve - Error-prone - Bad for super-sampled reads - Bad for long reads - NP-Hard to solve
- 20. 20QuantumForce.eu QAOA Genomics optimisation Bitflip (X) mixers VQE Controlled-bit-flip (Λf(X)) mixers XY mixers Controlled-XY mixers Permutation mixers Maximum cut Maximum-L-SAT Minimum-L-SAT Set Splitting MaxE3LIN2 Maximum Independent Set Maximum Clique Minimum Vertex Cover Maximum Set Packing Minimum Set Cover Maximum-K-Colorable Subgraph Graph Partitioning (Minimum Bisection) Maximum Bisection Maximum Vertex K-Cover Maximum-K-Colorable Induced Subgraph Minimum Graph Coloring Minimum Clique Cover Traveling Salesperson Problem = minimum cost Hamiltonian Cycle SMS, minimizing total weighted squared tardiness SMS, minimizing total weighted tardiness SMS, with release dates DNA Sequence Reconstruction by De novo Assembly
- 21. 21QuantumForce.eu QAOA • Quantum/classical Hybrid algorithm – Parameterised quantum subroutine is run within a classical optimization loop – Prepare the quantum state | 𝜓 𝜃 , often called the ansatz – Measure the expectation value 𝜓 𝜃 ℋ 𝜓 𝜃 • By Variational theorem, expectation value ℋ ⟩|𝑎𝑛𝑠𝑎𝑡𝑧 ≥ λ1 (smallest eigenvalue; lowest energy; ground-state) – Find an optimal choice of real-valued parameters 𝜃 such that the expectation value is minimised – Implementation based on Variational Quantum Eigensolver primitive • Challenges – Heuristic - no general recipe of Ansatz definition works universally – Optimiser choice – Initial Parameter selection is arbitrary – Convergence not always guaranteed – High number of Iteration
- 23. 23QuantumForce.eu Quantum HLL • OpenQL (inspired by OpenCL) • Programs (Kernels (Operations)) – Decompose: Toffoli, Control, Unitary, Rotation, CX-CZ – Optimize: Cancel UU† – Scheduling: ASAP, ALAP, Balanced – Mapping: Surface-17 connectivity routing – QASM: cQASM, eQASM (topology, resource constraints) • Other features: – Conjugate uncompute – Classical logical/comparative operations – Language features • Recursion, loops, functions • Libraries like NumPy, Matplotlib Configure Platform Create Program Create Kernels Populate each Kernel Add Kernels to Program Compile Program
- 24. 24QuantumForce.eu Testing 1. Shortest superstring (Σ,M) – (4,3) = AAATTTGTTCTTATGGTGCTGATCGTCCTCATAGTACTAAGGGCGGAGCCGCAGACGAACCCACAA – (2,2) = 00110 – (4,2) = AATTGTCTAGGCGACCA 2. Random String – Chargaff's Parity rules • %A = %T • %C = %G – %GC : %AT (40:60) – Other entropic measures 3. Real Data Segment (GenBank, wgsim) – part of HBB (hemoglobin subunit beta) • Chromosome 11 (region p15.4) of Homo sapiens – Sickle cell anemia • ATG-GTG-CAT-CTG-ACT-CCT-GAG • ATG-GTG-CAC-CTG-ACT-CCT-GTG 4. Minimal entropy – tandem repeats
- 25. 25QuantumForce.eu Platforms • Quantum Infinity – DiCarlo lab (QuTech) – Simulator (QX and QuantumSim) – Superconducting qubits – Cloud access • Quantum Inspire – QuTech (TU Delft + TNO) – ~ 37 qubits simulator on Cartesius supercomputer with SURFsara – Semiconducting qubits • Quantum Learning Machine – AtoS BullSequana • Digital Annealers – Fujitsu
- 26. 26QuantumForce.eu Related applications DNA Fingerprinting Motif FindingAmino-acid Sequencing Pattern based Trading Object Recognition Speech Recognition 18x18 px 17 qubits ~ 50k gates Exact matching Traffic OptimisationWarehousing
- 27. 27QuantumForce.eu QuantumForce.eu Experimental Q Chip (Decoherence and Gate errors) Superconducting/Semiconducting qubits Industrial/Societal Q Chip (no decoherence, no gate errors) Classical Q simulators QuTech Perfect Qubits Realistic Qubits QuantumForce Industry/Society App. Physical Platform QCA lab
- 29. 29QuantumForce.eu QuantumForce.eu • Big Data Analytics • Industry 4.0 • Cyber-Physical Systems • Artificial Intelligence and Machine Learning ..... and other applications Contacts for collaboration: • Koen Bertels, CEO koen@QuantumForce.eu • Zaid Al-Ars, CTO zaid@QuantumForce.eu
- 30. 30QuantumForce.eu Koen Bertels Carmen G. Almudever Razvan Nane Imran Ashraf Nader Khammassi Hans van Someren Leo DiCarlo Jeroen van Straten LingLing Lao Savvas Varsamopoulos Matthijs Brobbel Aritra Sarkar Abid Moueddene Xiang Fu Leon Riesebos Daniel Moreno Miguel Serrao Amitabh Yadav Alejandro Morais Anneriet Krol Yaoling Yang Mengyu Zhang Bas van Wee Diogo Valada
- 31. Search and optimisation algorithms for genomics on quantum accelerators Aritra Sarkar Quantum Computer Architecture Lab QuTech and Department of Quantum & Computer Engineering Delft University of Technology
Editor's Notes
- Near-term? Accelerators? Genomics? https://t2m.io/1anKYnJu images wider abb. wider
- add stack
- What’s the big challenge? We all know about the Moore’s Law of transistor scaling – more and more transistors are getting integrated into chips, but we are no longer making better processors – power, memory and frequency walls One the other hand – the amount of data generated from genomics are also increasing exponentially – enabled by the lower cost of sequencing Within the next decade, the amount of data generated per year would be 2-40 exabytes – which is huge! Our computing clusters are not equipped to handle this kind of data volume – a driver for us to turn to the exascale computing promise of quantum systems
- sorry if this is not the latest version of the ever-evolving stack diagram
- Putting this project in a bigger perspective – let’s have a look at the Whole Genome Sequencing pipeline Extract DNA from human, crops or microorganisms Sequence the DNA in a wet lab – i.e. read the base pairs of the DNA – problem: it is too long (3 billion bp) and tangled to be read in one go Oversample the DNA (make many copies), cut it off in smaller pieces (shotgun sequencing) and the sequencing machine gives back a bucket of short reads Stitch them back together (like solving a jigsaw puzzle) Use the reconstructed DNA for further analysis like disease diagnosis (personalized medicine) or GM crops We focus on the Data analysis part of this pipeline It too consists of a bunch of algorithmic steps as shown in the GATK best practices from Broad Institute – these are for example, reference mapping, indel alignment, variant calling We are going to focus only on the reference mapping (solving the jigsaw puzzle) as it is one of the most computation intensive part
- Application-Platform-Tools Why Genomics? Why Digital? Why NISQ? Why Accelerators?
- There are 3 basic ways of playing with functions The first is simple function evaluation. We feed in the input, we get back the output. Another way is when we have a set of inputs and their corresponding outputs; we want to infer what is the transformation function. This is called inductive logic and is the basis of machine learning where we train a predictor to approximate the function. The third way of course is when we have the output and the function, and we want to know what input resulted in the particular output. This is function inversion. And we know, if we have an inverse function, we can evaluate it to get back x. But what if such a function does not exist? Like you cannot ask your sibling the pattern lock of their mobile. Of course there is this other possibility where you try out every combinations possible, till you find the solution. Start out with the ninja star if your sibling is in QuTech! Which method should we choose for our problem? For that we need to have a quick look at computation complexity classes. For our interest, there are there 2 important classes, Polynomial complexity (P) or the easy problems, and Non-deterministic Polynomial time (NP), or simply the intractable ones. Where does quantum computers lie in this venn diagram? Well, no one knows for sure, but the quantum equivalent for feasible class, called BQP looks somewhat like this. For example, Shor’s famous algorithm lie in the middle star region. Whereas, we arer trying to solve a problem in the upper star – where even efficient quantum algorithms don’t exist. So we cannot invert. But the good news is that, unlike the stupid idea of trying out every possible pattern lock in a classical system, in quantum we can use the parallelism of superposition states. Which in a way can be reasoned as, trying out all possible paths at the same time.
- So let’s define our problem: sub-sequence index search We have a reference genome, which is 3 billion bp for humans, but for this example, I consider a much shorter one of 32 bp. I have used 4 colours for the 4 DNA alphabet Now take one of the read from the bucket. Again the typical size is much larger, but here, it is a modest 5 character string. Proceeding in a naïve linear search style – we start by matching the read at position 0 and give it a score, then at position 1, and so on What we want from our algorithm is the position where it matches best. Note, it doesn’t completely match – approximate yet optimal Additionally some algorithms also give us back the corrected version of our noisy query
- There are many ways of doing quantum pattern matching
- Application-Platform-Tools Why Genomics? Why Digital? Why NISQ? Why Accelerators?
- Application-Platform-Tools Why Genomics? Why Digital? Why NISQ? Why Accelerators?
- The general exploration on pattern matching explored in this thesis can be extended to other domains. Of course we can do amino-acid sequencing by just extending the alphabet size DNA fingerprinting is comparing two large sequences and we can use the concept of Hamming distance and amplify the mismatches. Motif finding might also be trivial as it involves finding the consensus in a stored memory. There are other related domains where similar pattern matching applications are useful. For example in speech signals, or stock market patterns. And definitely on images. For example, this is an output from the same algorithm that was used on DNA tweeked for 2D black and white images. Finding the template took 17 qubits and some 50k gates. MEST: not far before Q App Dev becomes a buzzword and these developers start tinkering with Q Algos to find a killer app for QC
- Image copyright: Novikov Aleksey
- these are the ones people already tried using
- How much wood could a woodchuck chuck If a woodchuck could chuck wood? As much wood as a woodchuck could chuck, If a woodchuck could chuck wood. “Run a shitty circuit shitload times such that there are on average less shit” - Malay