Introduction to Quantum Computing for Research

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Sanjay Padhi, Ph.D
Head of AWS Research, US Education
Amazon Web Services
AWS Research Webinar Series
Introduction to Quantum Computing for Research
https://www.linkedin.com/in/sanjaypadhi/

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10-35 m (Plank scale)
Power of Scales in Nature
Quantum Realm (10-9 m)
Richard Feynman (1960): “There is a plenty of room at the bottom”
10-30 m (Grand Unification)
10-18 m (Electroweak Unification)
10-15 m (Quarks)
10-10 m (Atoms)
10-6 m (Bacteria & Viruses)
100 m (Human Scale)
106 m (Earth radius)
1012 m (Solar System)
1020 m (Milky Way radius)
1022 m (Cluster of Galaxies)
1026 m (Cosmological Scale/Size of Universe)
Higher energies allow us to look deeper into nature (E a 1/size)

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Image credit: NASA / WMAP science team.

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Quantum Realm: Large Hadron Collider
Image credit: CERN / ATLAS experiment
Is this a quantum computer?

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Quantum computers are machines that use the properties of
quantum physics to store information and perform computations.
Image credit: Rigetti

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P(Probe) ⋘ P (System)
Quantum: P(Probe) ≃ P (System)
Properties of Classical and Quantum Systems

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Store Information: Bits and Quantum bits (Qubits)
Classical Bits
Qubits (No phase)
0
1 1
0
Not discussed: Qutrit (Particles with 3 states): |1 >, |2 > and |3 >, Qudit with 4 dimensions, etc.

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Store Information: Bits and Quantum bits (Qubits)
Classical Bits Qubits (With phase rotation)
0
1
0
1
If a quantum system can be in the form of two basic states |0 > or |1 > it can also be in superposition of |0 > and |1 > states

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Quantum Properties
Superposition Interference
Entanglement
Complex mix to store (build states), encode it via entanglement and execute outcomes via Interference

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Principle of Superposition
0 0
1 1

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Principle of Superposition
0 0
1 1
Z
Z Quantum Gate or Pauli-Z equates to rotation around Z-axis of Bloch sphere by 1800
Unlike many classical gates, quantum gates are reversible (Unitarity)

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Superposition of States
Example: A photon can be 0.8 |0 > + 0.6 |1 > state
(64% Horizontal and 36% Vertical polarized)
0.8 on |0 >
0.6 on |1 >
1 on |0 >
0 on |1 >
Horizontal Filter Horizontal Filter

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Principle of Interference
Physical observables are quantized. Examples: Energy, Angular Momentum, etc.
Wave-Particle Duality

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Principle of Interference (Constructive or Destructive)
0 0
11
0

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Principle of Entanglement
0
1
0
1
0
1
0
1
Four qubits each with two states 24 = 16 states
Quantum entanglement is a physical phenomenon that occurs when a pair or group of particles are generated,
interact, or share spatial proximity in a way such that the quantum state of each particle of the pair or group cannot
be described independently of the state of the others, including when the particles are separated by a large distance.
Example: Bell state or EPR (Einstein, Podolsky and Rosen) pair

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Principle of Entanglement
(Moreau et al., Science Advances, 2019)

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Deterministic Computing
No randomness is involved
Always produce the same output for a given initial state
Differential Equations
Deterministic Turing Machines
Algorithms, Circuit Codes
Probabilistic Computing
Randomized algorithms
Deterministic computing with randomization (Coin flip)
(True randomization happened in Quantum)
Output random bits, simulating random phenomena
Monte Carlo Simulations, Random 1000 prime numbers
Computational Efficiency
Examples: Minimum spanning tress in a graph, Test of a prime number (n=1024 bit), etc.
Quantum Mechanics/Computing: is more of a probabilistic computing with a –ve sign
Quantum Computing is expected to give exponential speedup over probabilistic computing

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Quantum Circuit is an unit of computation
Make particle interact through gates in its superposition states
Gates are how we control the circuits
We expect each algorithms or domains will have their own libraries of circuits

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Quantum Circuit is an unit of computation

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Quantum Computing Technologies

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Rigetti: Universal gate-model QPU based on superconducting qubits
• Octagonal topology with 3-fold (2-fold for edges) connectivity
• Qubit Coherence time ~20 micro sec

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Ion-Q: Flexible Ion Trap Technology
Trap atomic qubits (ionized ytterbium atoms) on a silicon chip using EM field
Gates: Two-photon Raman transition using a pair of counter-propagating beams from a mode-locked pulsed laser.
This allows single and two-qubit transitions and all-to-all connectivity

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D-Wave: Quantum Annealer based on superconducting QPUs

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Quantum Computing can be useful for exponentially complex problems
Computational Chemistry Material Science Optimization

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Amazon Quantum Computing

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Quantum Computing using Amazon Braket

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Quantum Computers as more like co-processors
Next generation advancements are expected from a mixture of bits + neurons + qubits

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Quantum Chemistry
https://arxiv.org/pdf/1811.05256.pdf

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Quantum Machine Learning to LHC Physics
ttH (H → 𝜸𝜸) analysis at the LHC
The observation of ttH production by ATLAS and CMS at
the LHC directly confirmed the interaction between the
Higgs boson and the top quark, which is the heaviest
known fundamental particle
H → 𝞵𝞵 analysis at the LHC
Although the coupling between the Higgs boson and 3rd-
generation fermions has been observed, currently the coupling
between the Higgs boson and 2nd-generation fermions is
under intensive investigation. H→ 𝞵𝞵 is the most promising
process to observe such a coupling by ATLAS and CMS at the
LHC
Sau Lan Wu et. al (2020)

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Employing Quantum SVM Kernel method to ttH (H → 𝜸𝜸) analysis with Amazon quantum computer simulator
Sau Lan Wu et. al (2020)

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Employing Quantum SVM Kernel method to ttH (H → 𝜸𝜸) analysis with Amazon quantum computer simulator
Sau Lan Wu et. al (2020)

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https://www.cmu.edu/tepper/news/stories/2020/october/quantum-computing-course.html

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Managed Jupyter Lab environment

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Hosted Circuit Simulators

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Managed execution of hybrid quantum algorithms

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Amazon Quantum Solution Lab

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Amazon Quantum Solution Lab

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AWS Center for Quantum Computing
Near-term applications
Error correction & programming models
Quantum hardware and technologies

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Building quantum expertise with AWS training and enablement program

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Open source community
https://github.com/aws/amazon-braket-examples

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Demo of Amazon Braket

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Home Assignment to watch

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Thank you!
https://www.linkedin.com/in/sanjaypadhi/

47. Q&A