Quantum Computing in the NISQ era - Alba Cervera-Lierta

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/

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

plic

ati

on

sT

he

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tic

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fra

me

wo

rk

Quantum Information

Quantum Communication

sQuantum Cryptography

Quantum Computing

Quantum Sensing

Quantum Mechanics

Information Theory

Quantum Simulation

Quantum Metrology


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.


Why do we need a quantum computer

Quantum

Quantum

Quantum Not Quantum

Powerful, but NotQuantum

MareNostrum supercomputer (BSC)



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 supremacy using a programmable superconducting processor”, Nature 574, 505–510(2019)

“Quantum computational advantage using photons”, Science eabe8770 (2020)

Less time… and less energy!


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


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!


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)


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)


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


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


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


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


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).


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


…and quantum software tools…

Qibo

And manymore…

Mitiq

And manymore…



…and quantum software tools…

…plus classical tools for the NISQ era

Qibo

And manymore…

Mitiq

And manymore…

And manymore…


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


Unification, standarization, acceleration

A quantum language to simplify andaccelerate implementation of new ideas forquantum algorithms.


Code


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.

NISQ software players

Quantum backends

Real (experiments) Simulators

Classical tools

OptimizersGradient methods

CompChem…

Abstractmanipulation

WavefunctionsQuantum gate

definitionNoise models

…


Tequila API


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?


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


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.


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)


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)


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


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?


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 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.


Thanks!Questions?

Alba Cervera-Lierta

University of TorontoSlides: albacl.github.io/talk/

@albaclierta

Quantum Computing in the NISQ era - Alba Cervera-Lierta

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