Quantum Computing in the NISQ era Alba Cervera-Lierta University of Toronto UCL Quantum Technologies Winter School 2020 The MatterLab https://www.matter.toronto.edu/ Alán Aspuru-Guzik Our Mission To accelerate the discovery of new chemicals and materials that are useful to society by means of new technologies such as quantum computing, machine learning, and automation. The Quantum MatterLab Postdocs PhD students + visitors and undergrad https://www.matter.toronto.edu/ Outlook Brief introduction to quantum computing NISQ vs Fault-Tolerant QC Variational Quantum Algorithms Slides will be available at A tool for NISQ: Tequila albacl.github.io/talk/ A NISQ example: Meta-VQE Comments and Remarks Brief story of Quantum Computing The “Quantum Bible”: “Quantum Computation and Quantum Information”, Michael A. Nielsen & Isaac L. Chuang Practical approach: Qiskit and Pennylane quantum algorithm tutorials More learning resources (books, blogs, courses, …): https://qosf.org/learn_quantum/ Brief history of quantum mechanics Quantum 1.0 Quantum 2.0 1900-1930 1930-1950 1950-1980 1980-2000 2000- Prenatal Infancy Childhood Adolescence Youth Quantum theory First applications: Transistor (1947), Q Turing Machine, First Quantum birth (1900) e.g. nuclear Solar Cells (1954), Quantum chips (2005), Postulates (1926) energy,… GPS (1955), Laser simulation (1980), Quantum (1960), MRI (1971), Shor algorithm teleportation with … (1994), CNOT satellites (2017), (1995), Bose- Quantum Einstein advantage (2019) condensate (1997) Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Quantum 2.0 Quantum Quantum Quantum Communication Computing Sensing Quantums Quantum Quantum Metrology Applications Cryptography Simulation Quantum Information Information Theory framework Theoretical Theoretical Quantum Mechanics Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. What is a quantum computer A device capable of processing data in a quantum mechanical form. A device that uses the properties of quantum mechanics to process data. Instructions SOFTWARE HARDWARE Qubits Result Classic Quantum Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Why do we need a quantum computer Quantum Quantum Not Quantum Powerful, but Not Quantum Quantum MareNostrum supercomputer (BSC) Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Why do we need a quantum computer I therefore believe it’s true that with a suitable class of quantum machines you could imitate any quantum system, including the physical world. –Richard P. Feynman, “Simulating physics with computers”, 1982. Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Why do we need a quantum computer Less time… and less energy! “Quantum supremacy using a programmable superconducting “Quantum computational advantage using processor”, Nature 574, 505–510(2019) photons”, Science eabe8770 (2020) Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. How does it work Bit Qubit 0 1 흍 |휓 = 훼|00 + 훽|01 + 훾|10 + 훿|11 |휓 = 훼|0 + 훽|1 entanglement |휓 ≠ |휓 1⨂|휓 2 Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. A new paradigm in computation A single operation (logic gate) affects all posible qubit states. |풙 |풙 CNOT |풚 |풙 ⊕ 풚 풙 풚 풙⨁풚 0 0 0 |휓0 = 훼|00 + 훽|01 + 훾|10 + 훿|11 0 1 1 퐶푁푂푇|휓0 = 훼|00 + 훽|01 + 훾|11 + 훿|10 1 0 1 1 1 0 4 “sums” with a single physical operation! Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. How does it work Qubit: physical system that 1) is quantum and 2) have two well-defined states Example: atomic orbitals Example: superconducting circuit (transmon qubit) Ground Excited state state |0 |1 Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Who is building a quantum computer Software … and many more! More information: https://quantumcomputingreport.com/ NISQ vs Fault-Tolerant NISQ = Noisy Intermediate Scale Quantum Experimental challenges • Scalability: how to design and construct milion-qubit chips - Superconducting circuits Which - Ion traps technology? - Photons - NV- centers - … • Qubits are not perfect, they are “noisy” “Fault-tolerant” quantum Quantum error correction codes computation Noise-resistant algoritms Noisy Intermediate Scale quantum (variational algorithms) computation (NISQ) Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. NISQ vs Fault-Tolerant Who lives in the Fortress? - Factorization algorithm Logical - Grover search algorithm Qubits - … Who lives in the Plains? - Variational Quantum Eigensolver - QAOA - … Noisy Qubits ~1000 noisy qubits/logical qubit Image: “Quantum computing: near- and far-term opportunities”, Ewan Munro, Medium @quantum_wa Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Noisy Intermediate Scale Quantum computation Different qubits architectures A few qubits (~100) Noise Something useful: Quantum Decoherence advantage Classical Quantum McGyver carrying a optimizers quantum advantage experiment Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Variational Quantum Algorithms A.K.A. Hybrid Quantum-Classical Algorithms Variational Quantum Eigensolver Bond dissociation curve of the He–H+ molecule. Hamiltonian that can be written with Pauli strings Outputs of the quantum computer Quantum circuit that generates the ground state of that Hamiltonian e.g. Hartree-Fock Unitary operation, e.g. Cluster operator A. Peruzzo, J. McClean, P. Shadbolt, M.-H.Yung, X.-Q. Zhou, P. J. Love, GOAL: find |흍 A. Aspuru-Guzik , J. L. O’Brien, Nature Comm. 5, 4213 (2014) that minimizes Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Variational Quantum Algorithm Example: VQE, QAOA, … Obs. Operator 퐻 First approximation Quantum circuit Expected Output to the quantum that depend on value 푬ퟎ + 흐 휓 퐻 휓 state solution 휽 |휓 |휓0 New 휃 퐦퐢퐧 푬 휽 휽 Classical part Variational principle: E = 휓 퐻 휓 ≥ 퐸0 Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. Why Variational Quantum Algorithms? Exponentially big Hamiltonians can be represented with a polynomial number of terms that can be obtained efficiently from a quantum computer. 퐻 = 2푛 × 2푛 matrix 퐻 = 푃표푙푦(푛) expectation values To compute those expectation values, we need to first prepare the ground state |휓 1. Initial state that you know how to prepare and it’s as closer as posible to the solution (e.g. Hartree-Fock state) 2. Design a unitary operation (a.k.a. quantum circuit) that transforms that state into the ground state. a) Use a circuit ansatz that depend on some parameters b) Find the correct parameters by optimizing a Loss function, e.g. the expected value of the Hamiltonian (variational principle). Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. A tool for the NISQ era: Tequila Instructions SOFTWARE HARDWARE Qubits Result Classic Quantum The golden era of quantum languages… Qibo And many more… https://github.com/aspuru-guzik-group/tequila The golden era of quantum languages… …and quantum software tools… Mitiq Qibo And many more… And many more… https://github.com/aspuru-guzik-group/tequila The golden era of quantum languages… …and quantum software tools… …plus classical tools for the NISQ era Mitiq Qibo And many more… And many more… And many more… https://github.com/aspuru-guzik-group/tequila Which language should I use? What if I want to run the same code in Qibo different quantum computers? What if the language doesn’t contain the features that I need? Mitiq https://github.com/aspuru-guzik-group/tequila Unification, standarization, acceleration A quantum language to simplify and accelerate implementation of new ideas for quantum algorithms. Code https://github.com/aspuru-guzik-group/tequila https://github.com/aspuru-guzik-group/tequila Noisy Intermediate Scale Quantum computation What can we do with a few qubits How can we deal with the noise What can we do with a few noisy qubits Hybrid quantum-classical algorithms Variational algorithms Applications: chemistry, QML, etc require the knowledge of the classical techniques to compare and test Many quantum computers in development; need to benchmark, compare and test. https://github.com/aspuru-guzik-group/tequila NISQ software players Abstract Classical tools manipulation Wavefunctions Optimizers Quantum gate Gradient methods definition CompChem Noise models … … Quantum backends Real (experiments) Simulators https://github.com/aspuru-guzik-group/tequila Tequila API Operator State Ansatz Quantum Circuit Molecule Hamiltonian H 푈 Θ Options - Wave-function Pauli - Draw circuit strings Expectation values - Define gates E Θ = 퐻 푈 Θ from Hermitian operators Objective function Options f E Θ - Method - Method options - Noise Optimizer - Gradient - Sampling - Initial values - … Quantum backend (simulator or real) https://github.com/aspuru-guzik-group/tequila NISQ algorithm example: the Meta-VQE Variational Quantum Eigensolver GOAL: find |흍 Bond dissociation curve of the He–H+ molecule. that minimizes Find the atomic separation that minimizes the energy min 퐻(푅) A. Peruzzo, J. McClean, P. Shadbolt, M.-H.Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik , J. L. O’Brien, Nature Comm. 5, 4213 (2014) Pros and cons VQA To obtain this you need to scan from 0 to 300. Each blue point is a VQE, that is, you have to prepare, run and optimize the quantum circuit. Can we avoid to compute these uninteresting points? Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020. The Meta-VQE Parameterized Hamiltonian 퐻 휆 Training points: 휆 푖 for 푖 = 1, … , 푀 Loss function with all 퐻(휆 푖) Output: 휱풐풑풕 and 휣풐풑풕 See also: K. Mitarai, T. Yan, K. Fujii, Phys. Rev. Applied 11, 044087 (2019) ACL, J. S. Kottmann and A. Aspuru-Guzik, arXiv:2009.13545 [quant-ph] (2020) The Meta-VQE Option 1: run the circuit with test 휆 and obtain the g.s.