The race to demonstrate quantum supremacy, and onward to quantum computers
Abdullah Khalid
Quantum Information Scientist
HUAIC
5th November 2019
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Computational Problems
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Decision
Search
Optimization
Decision Problems
Multiplication
Input: integers P and Q
Output: integer R = P x Q
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6607109/grade-school-example-5.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6607128/multiplication.png)
Algorithms
Is left most digit 1 in binary?
Decision Problems
Factorization
Input: integer R
Ouput: prime numbers P and Q
such that R = P x Q
Algorithms
R = 21
digits = 2
R = 498556150811
digits = 12
- Dixon's algorithm
- Continued fraction factorization
- Quadratic sieve
- Rational sieve
- General number field sieve
- Shanks's square forms factorization
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6607206/1808Q.png)
Is left most digit of bigger prime 1 in binary?
Cryptography
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"Top secret info"
"Top secret info"
"hf72h18v82ja9"
You
You
Military
Bank
Email provider
Military
Sampling Problems
Binomial sampling
Input: n, p
Output: a sample from the binomial probability distribution
A random number generator
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6734049/binomial.jpeg)
Extended Church-Turing Thesis [1]
Any algorithmic process can be simulated efficiently using a probabilistic Turing machine.
Church-Turing Thesis
Any algorithmic process can be computed using a Turing machine.
[1] They didn't actually say it.
Physicist's Extended Church-Turing Thesis
Every finitely realizable physical system can be perfectly simulated by a universal computing machine operating by finite means - Deutsch 1985
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Chemistry
Biology
Computer science
Computing Machine = Physical System
Computing Machines = Physical Systems
=> Computational complexity is determined by physical laws
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Computational Complexity
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Multiplication
Factorization
Resources
Problem size (n)
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Decision Problems Complexity Classes
Factoring
Multiplication
Circuit model of classical computation
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6734106/booleancircuit.png)
Width/Space = n
Depth/Time = m
Input: Any of 2n n-bit strings
Output: 1-bit string
Quantum Computers
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6610825/quant-ed.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6734130/quantumcircuit.jpeg)
Quantum Circuits
Text
Text
n-qubits => 2n outcomes
- Solves same computational problems as classical computer
- Algorithm is different because of architecture difference
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Quantum Computers: The transport analogy
Human computer
Super computer
Quantitative
Qualitative
Quantum computer
Solve computational problem = Go from A to B
Quantum computers CANNOT
do industrial optimization
predict the stock market
optimize airline schedules
predict the stock market
optimize airline schedules
NP-Complete problems
exponentially faster than classical computers.
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If this was true, quantum computers could solve NP-complete problems efficiently
But they don't!
Quantum computers can
simulate atoms, molecules and materials,
exponentially faster than classical computers.
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6608939/Comparison_solar_cell_poly-Si_vs_mono-Si.png)
Quantum computers can
maybe do machine learning and optimization
exponentially faster than classical computers.
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6610866/20170919-New-progress-in-Quantum-Machine-Learning-featured.png)
Quantum computers can
break all currently used asymmetric encryption protocols
exponentially faster than classical computers.
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6610897/170208_encryption.jpg)
Quantum vs Classical Computers
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Breaking encryption on Quantum Computer
Text
NP-Complete Problems on Classical/Quantum Computer
Breaking encryption on Classical Computer
Resources
Problem size (n)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6734075/777px-BQP_complexity_class_diagram.svg.png)
Decision Problems Complexity Classes
BQP (bounded-error quantum polynomial time )
= set of problems efficiently solvable by a quantum computer
Quantum computers difficult to build due to engineering challenges
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Nature | Vol 574 | 24 OCTOBER 2019
Quantum Supremacy | Quantum Advantage | |
---|---|---|
A devices that: | Solves any problem faster than classical | Solves useful problems faster than classical |
Requires | Non-universal quantum computational device | Universal Quantum Computer |
Quantum error correction | ||
Analogies | Fission experiments | Nuclear power stations |
Wright brothers flight | Commercial/military airplanes |
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Depth/Time = m
Width/Space = n
Quantum Random Circuit
Outputs = 2n Output strings, each with different probability
Form a random circuit using √ X , √ Y , √ W , and a combination of iSWAP and C-Z.
,![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6733958/randomcircuit.png)
Quantum Random Circuit
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6734190/qrcdistribution.png)
Computation problem
Input: Circuit C
Output: a sample from the output probability distribution of C
Easy for quantum computer
Difficult for classical computer
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6734202/superconductingchip.png)
Google's superconducting chip
53+1 qubits, depth = 20
How to verify a device which you claim can't even be classically simulated?
Linear cross-entropy benchmarking fidelity
- Collect finite samples x1, x2, x3, ...
- Calculate probabilities P(xi) of measuring xi given circuit C
- Calculate FXEB = 2n Avg(P(xi)) - 1
FXEB = 0 => uniform random distribution
FXEB = 1 => error-free quantum random circuit
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1144553/images/6734241/verification.jpg)
Verification that device works
Is quantum supreme?
Google's claim: 10,000 years on a state of the art supercomputer, using the best classical algorithm they could think of.
IBM's claim: Sorry, 2.5 days only using our better classical algorithm!
Quantum device performance: 600 seconds to sample 3 million times
The race to demonstrate quantum supremacy, and onward to quantum computers
By abdullahkhalids
The race to demonstrate quantum supremacy, and onward to quantum computers
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