quantum computing in the nisq era - alba cervera-lierta
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Quantum Computing in the NISQ era
Alba Cervera-Lierta
University of Toronto
UCL Quantum Technologies Winter School 2020
The MatterLab
Alán Aspuru-Guzik
https://www.matter.toronto.edu/
Our MissionTo 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
https://www.matter.toronto.edu/
Postdocs
PhD students
+ visitors and undergrad
Brief introduction to quantum computing
NISQ vs Fault-Tolerant QC
Variational Quantum Algorithms
A tool for NISQ: Tequila
A NISQ example: Meta-VQE
Comments and Remarks
Outlook
Slides will be availableat
albacl.github.io/talk/
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
Prenatal
1900-1930
Infancy
1930-1950
Childhood
1950-1980
Adolescence
1980-2000
Youth
2000-
First applications:e.g. nuclear energy,…
Quantum theorybirth (1900)Postulates (1926)
Transistor (1947), Solar Cells (1954), GPS (1955), Laser (1960), MRI (1971), …
First Quantum chips (2005), Quantum teleportation withsatellites (2017),Quantum advantage (2019)
Q Turing Machine, Quantum simulation (1980), Shor algorithm(1994), CNOT (1995), Bose-Einstein condensate (1997)
Quantum 1.0 Quantum 2.0
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Quantum 2.0
Ap
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ati
on
sT
he
ore
tic
al
fra
me
wo
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Quantum Information
Quantum Communication
sQuantum Cryptography
Quantum Computing
Quantum Sensing
Quantum Mechanics
Information Theory
Quantum Simulation
Quantum Metrology
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
What is a quantum computer
HARDWARE
Qubits
SOFTWARE
Instructions
Result
QuantumClassic
A device capable of processing data in a quantum mechanical form.A device that uses the properties of quantum mechanics to process data.
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Why do we need a quantum computer
Quantum
Quantum
Quantum Not Quantum
Powerful, but NotQuantum
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
“Quantum supremacy using a programmable superconducting processor”, Nature 574, 505–510(2019)
“Quantum computational advantage using photons”, Science eabe8770 (2020)
Less time… and less energy!
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
How does it work
0 1
Bit
𝝍
Qubit
|𝜓 = 𝛼 |0 + 𝛽 |1
|𝜓 = 𝛼 |00 + 𝛽 |01 + 𝛾 |10 + 𝛿 |11
entanglement
|𝜓 ≠ |𝜓 1⨂ |𝜓 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.
CNOT
|𝒙
|𝒚
|𝒙
|𝒙 ⊕ 𝒚
𝒙 𝒚 𝒙⨁𝒚
0 0 0
0 1 1
1 0 1
1 1 0
|𝜓0 = 𝛼 |00 + 𝛽 |01 + 𝛾 |10 + 𝛿 |11
𝐶𝑁𝑂𝑇|𝜓0 = 𝛼 |00 + 𝛽 |01 + 𝛾 |11 + 𝛿 |10
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
Groundstate
|0 |1
Excitedstate
Qubit: physical system that 1) is quantum and 2) have two well-defined states
Example: atomic orbitals Example: superconducting circuit(transmon qubit)
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Who is building a quantum computer
More information: https://quantumcomputingreport.com/… and many more!
Software
NISQ vs Fault-Tolerant
NISQ = Noisy Intermediate Scale Quantum
Experimental challenges
• Scalability: how to design and construct milion-qubit chips
• Qubits are not perfect, they are “noisy”
Whichtechnology?
- Superconducting circuits- Ion traps- Photons- NV- centers- …
Quantum error correction codes
Noise-resistant algoritms(variational algorithms)
“Fault-tolerant” quantum computation
Noisy Intermediate Scale quantum computation (NISQ)
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
NISQ vs Fault-Tolerant
Image: “Quantum computing: near- and far-term opportunities”, Ewan Munro, Medium @quantum_wa
Who lives in the Fortress?
- Factorization algorithm- Grover search algorithm- …
Who lives in the Plains?
- Variational Quantum Eigensolver- QAOA- …
Noisy
Qubits
Logical
Qubits
~1000 noisy qubits/logical qubit
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Noisy Intermediate Scale Quantum computation
A few qubits(~100)
Noise
Decoherence
Classicaloptimizers
Different qubitsarchitectures
Something useful:
Quantum advantage
Quantum McGyver carrying a quantum advantage experiment
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Variational Quantum Algorithms
Hybrid Quantum-ClassicalAlgorithms
A.K.A.
Variational Quantum Eigensolver
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)
Bond dissociation curve of the He–H+ molecule.
Hamiltonian that can be written with Pauli strings
Quantum circuit that generates the ground stateof that Hamiltonian
Outputs of thequantum computer
e.g. Hartree-Fock
Unitary operation, e.g. Cluster operator
GOAL: find |𝝍that minimizes
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Variational Quantum Algorithm
Example: VQE, QAOA, …
Quantum circuitthat depend on
𝜽
Expectedvalue
𝜓 𝐻 𝜓
𝐦𝐢𝐧𝜽𝑬 𝜽New 𝜃
Output
|𝜓
Obs. Operator𝐻
Firstapproximationto the quantum state solution
|𝜓0
𝑬𝟎 + 𝝐
Variational principle: E = 𝜓 𝐻 𝜓 ≥ 𝐸0Classical part
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.
𝐻 = 2𝑛 × 2𝑛 matrix 𝐻 = 𝑃𝑜𝑙𝑦(𝑛) expectation values
To compute those expectation values, we need to first prepare the ground state |𝜓
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
HARDWARE
Qubits
SOFTWARE
Instructions
Result
QuantumClassic
The golden era of quantum languages…
Qibo
And manymore…
https://github.com/aspuru-guzik-group/tequila
The golden era of quantum languages…
…and quantum software tools…
Qibo
And manymore…
Mitiq
And manymore…
https://github.com/aspuru-guzik-group/tequila
The golden era of quantum languages…
…and quantum software tools…
…plus classical tools for the NISQ era
Qibo
And manymore…
Mitiq
And manymore…
And manymore…
https://github.com/aspuru-guzik-group/tequila
Which language should I use?
What if I want to run the same code in
different quantum computers?
What if the language doesn’t contain
the features that I need?
Qibo
Mitiq
https://github.com/aspuru-guzik-group/tequila
Unification, standarization, acceleration
A quantum language to simplify andaccelerate implementation of new ideas forquantum algorithms.
https://github.com/aspuru-guzik-group/tequila
Code
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
https://github.com/aspuru-guzik-group/tequila
Many quantum computers in development; need to benchmark, compare and test.
NISQ software players
Quantum backends
Real (experiments) Simulators
Classical tools
OptimizersGradient methods
CompChem…
Abstractmanipulation
WavefunctionsQuantum gate
definitionNoise models
…
https://github.com/aspuru-guzik-group/tequila
Tequila API
https://github.com/aspuru-guzik-group/tequila
Objective function
f E Θ
Hamiltonian H
Operator
Quantum Circuit
𝑈 Θ
State
Ansatz
Expectation values
E Θ = 𝐻 𝑈 Θ
Pauli strings
- Wave-function- Draw circuit- Define gates
from Hermitianoperators
Options
- Noise- Sampling
Options
Molecule
Quantum backend(simulator or real)
Optimizer
- Method- Method options- Gradient- Initial values- …
NISQ algorithm example:the Meta-VQE
Variational Quantum Eigensolver
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)
Bond dissociation curve of the He–H+ molecule.
GOAL: find |𝝍that minimizes
Find the atomicseparation that
minimizes the energy
min 𝐻(𝑅)
Pros and cons VQA
To obtain this you need to scan from 0
to 300.
Each blue point is a VQE, that is, youhave to prepare, run and optimize thequantum circuit.
Can we avoid to compute theseuninteresting points?
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Parameterized Hamiltonian 𝐻 𝜆
Training points: 𝜆𝑖 for 𝑖 = 1,… ,𝑀
Loss function with all 𝐻( 𝜆𝑖)
ACL, J. S. Kottmann and A. Aspuru-Guzik, arXiv:2009.13545 [quant-ph] (2020)
The Meta-VQE
See also: K. Mitarai, T. Yan, K. Fujii, Phys. Rev. Applied 11, 044087 (2019)
Output: 𝜱𝒐𝒑𝒕 and 𝜣𝒐𝒑𝒕
Option 1: run the circuit with test 𝜆 and obtain the g.s. energy profile.
Option 2: use Φ𝑜𝑝𝑡 and Θ𝑜𝑝𝑡 as starting point of a standard VQE optimization (opt-meta-VQE)
The Meta-VQE
ACL, J. S. Kottmann and A. Aspuru-Guzik, arXiv:2009.13545 [quant-ph] (2020)
1D XXZ spin chain
14 qubits simulation, 𝜆 = 0.75
Linear encoding: 𝑅𝑧(𝑤1𝜟 + 𝜙1)𝑅𝑦(𝑤2𝜟+ 𝜙2)⨂
Processing layer: 𝑅𝑧(𝜃1)𝑅𝑦(𝜃2)⨂
Results 2 encoding + 2 processing layers
AlternatingCNOT
Meta-VQE: encoding & processing layers. Loss function with test points.GA-VQE: standard VQE (only procesinglayers) with test points lossfunction.Opt-meta-VQE: VQE optimization with opt. meta-VQE parameters as starting point. Single minimization per parameter.Opt-GA-VQE: standard VQE optimizationwith opt. GA-VQE parametersas starting point. Single minimization per parameter.
Legend
Hamiltonianparameter
Product state g.s. (easy to find)
Entangled g.s.
ACL, J. S. Kottmann and A. Aspuru-Guzik, arXiv:2009.13545 [quant-ph] (2020)
AlternatingCNOT
𝐻 =
𝑖=1
𝑛
𝜎𝑖𝑥 𝜎𝑖+1𝑥 + 𝜎𝑖
𝑦𝜎𝑖+1𝑦+ ∆𝜎𝑖
𝑧𝜎𝑖+1𝑧 + 𝜆𝜎𝑖
𝑧
𝐻4 molecule
𝐻4 molecule in 8 spin-orbitals (STO-3G basis set)
Ansatz: k-UpCCGSD (k=2 for these results)
Linear encoding: 𝜃 = 𝛼 + 𝑑𝛽
Non-linear encoding: 𝜃 = 𝛼𝑒𝛽(𝛾−𝑑) + 𝛿 (floating Gaussians)
Meta-VQE: Linear encoding. Loss function withtest points.Opt-meta-VQE: VQE optimization with opt. meta-VQE parameters as starting point. Single minimization per parameter.nl-meta-VQE:non-linear encoding meta-VQE.Opt-nl-meta-VQE:VQE optimization with opt. nl-meta-VQE parameters as starting point.VQE0:standard VQE optimized model starting from the Hartree-Fockconfiguration
Legend
Hamiltonian Parameter(intermolecular distance)
ACL, J. S. Kottmann and A. Aspuru-Guzik, arXiv:2009.13545 [quant-ph] (2020)
Single transmon
Single transmon simulation using QCAD mapping
Ansatz: 1 encoding + 1 processing layers + 1 final layer of 𝑅𝑥𝑅𝑧
Layer: 𝑅𝑥𝑅𝑧+ all connected 𝑋𝑋 gates
Parameters of 𝑋𝑋 gates are the same in all layers (same entanglement gate)
Linear encoding: 𝑅𝑥(𝑤1𝒇 + 𝜙1)𝑅𝑧(𝑤2𝒇 + 𝜙2)
Meta-VQE: Linear encoding. Loss functionwith test points.Opt-meta-VQE: VQE optimization with opt. meta-VQE parameters as starting point. Single minimization per parameter.VQE:Standard VQE. 2 processinglayers. Result of previousminimization as initial point of thenext one.VQE enc:Same as VQE but including anencoding layer.
Legend
Hamiltonian Parameter (flux)
ACL, J. S. Kottmann and A. Aspuru-Guzik, arXiv:2009.13545 [quant-ph] (2020)
Kyaw, Menke, Sim, Sawaya, Oliver, Guerreschi, Aspuru-Guzik, arXiV:2006.03070 (2020)
The Meta-VQE
Some conclusions:
- Meta-VQE can be used to scan over Hamiltonian parameteres to find the energy interestingregions.
- We can use its parameter solution to run a more precise algorithm such as opt-meta-VQE orstandard VQE.
- The encoding strategy in VQE-type algorithms might be useful to guide the optimizationtowards the solution.
- Careful with QPT: the ground state changes so the unitary circuit (the encoding and processing parameters used) will change in the different phase areas.
https://github.com/aspuru-guzik-group/Meta-VQE
Code
ACL, J. S. Kottmann and A. Aspuru-Guzik, arXiv:2009.13545 [quant-ph] (2020)
Comments and Remarks
The end of classical computing?
1. We can’t simulate classically more tan ~50 qubits (not even with a supercomputer!)
2. Simulation of quantum phenomena is exponentially costly for a classical computer.
3. Many interesting physical systems (molecules, phases of matter,…) are quantum.
4. Quantum computers are controlled with classical computers.
5. Pre- and post-processing of quantum data is classical.
6. We don’t have a quantum algorithm for each open problem, but do we need them?
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
The needs in NISQ era
1. What can we do with ~100 noisy qubits?
2. Variational Quantum Algorithms are theoretically resistant to smallamount of noise
3. Rethink and adapt algorithms to VQA
4. We need tools for running those algorithms: error mitigationtechniques, programming languages,…
5. What are the limits in NISQ computers? (e.g. what’s the biggestmolecule that we can simulate?)
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Quantum calling
New quantum algorithms: variational or fault-tolerant.
New applications: chemistry, materials, finance, optimization problems, biology, physics,…
Architectures: superconducting circuits, trapped ions, photons,…
Quantum control: reduce noise, error correction, gate fidelities,…
Quantum-classical interface: programming languages, …
Computational complexity: what kind of problems can we solve and how.
Quantum Computing in the NISQ era, Alba Cervera-Lierta, UCL Quantum Tech Winter School 2020.
Thanks!Questions?
Alba Cervera-Lierta
University of TorontoSlides: albacl.github.io/talk/
@albaclierta