The race to demonstrate quantum supremacy, and onward to quantum computers

Abdullah Khalid

Quantum Information Scientist

HUAIC

5th November 2019

Computational Problems

Decision

Search

Optimization

Decision Problems

Multiplication

Input: integers P and Q

Output: integer R = P x Q

Algorithms

Is left most digit 1 in binary?

Sampling Problems

Binomial sampling

Input: n, p

Output: a sample from the binomial probability distribution

A random number generator

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

Chemistry

Biology

Computer science

Computing Machine = Physical System

Computing Machines = Physical Systems

=> Computational complexity is determined by physical laws

Computational Complexity

Multiplication

Factorization

Problem size (n)

Decision Problems Complexity Classes

Factoring

Multiplication

Circuit model of classical computation

Depth/Time = m

Input: Any of 2ⁿ n-bit strings

Output: 1-bit string

Quantum Computers

Quantum Circuits

Text

Text

n-qubits => 2ⁿ outcomes

• Solves same computational problems as classical computer
• Algorithm is different because of architecture difference

Quantum Computers: The transport analogy

Human computer

Super computer

Quantitative

Qualitative

Quantum computer

Solve computational problem = Go from A to B

If this was true, quantum computers could solve NP-complete problems efficiently

But they don't!

Quantum vs Classical Computers

Breaking encryption on Quantum Computer

Text

NP-Complete Problems on Classical/Quantum Computer

Breaking encryption on Classical Computer

Problem size (n)

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

Nature | Vol 574 | 24 OCTOBER 2019

Depth/Time = m

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.

Quantum Random Circuit

Computation problem

Input: Circuit C

Output: a sample from the output probability distribution of C

Easy for quantum computer

Difficult for classical computer

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

1. Collect finite samples x₁, x₂, x₃, ...
2. Calculate probabilities P(x_i) of measuring x_i given circuit C
3. Calculate F_XEB = 2ⁿ Avg(P(x_i)) - 1

F_XEB = 0 => uniform random distribution

F_XEB = 1 => error-free quantum random circuit

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