Doing quantum computing researches as theoretical physicists

Ninnat Dangniam

The Institute for Fundamental Study (IF), Naresuan University

Asst. Prof. Dr. Sikarin Yoo-kong

Asst. Prof. Narongrit Maneejiraprakarn

Prof. Dr. Salvatore De Vincenzo

Quantum Information Science (QIS) Lab

Dr. Ninnat Dangniam (นินนาท แดงเนียม)

Quantum computing, mathematical structure of quantum theory

Mathematical physics, integrable systems

Mathematical structure of quantum theory, relativistic wave equations

Signals and systems

(ณรงค์ฤทธิ์ มณีจิระปราการ)

(สิขรินทร์ อยู่คง)

Quantum algorithms for ML

Quantum characterization

Architectures for showing quantum advantage

Erik Lucero/Google

Kenneth Rudinger (Sandia), APS March Meeting 2016

Works that I do

PI: Dr. Thiparat Chotibut (ธิปรัชต์ โชติบุตร)

Sornsaeng, ND, Palittapongarnpim, Chotibut, Quantum diffusion map for nonlinear dimensionality reduction, PRA 2021

Outline

Reiher et al., PNAS 2017

\(10^5-10^6\) physical qubits with \(10^{-6}-10^{-9}\) error rates

Quantum simulation of nitrogen fixation

The carbon footprint of a loaf of bread is about 590g (more than that of a one-mile commute), 40% of which is CO2 emitted during fertilizer production

Quantum computing is an interdisciplinary field

Quantum computing is an interdisciplinary field

Outline

The Importance of models

Baconian science: inductive, based on empirical observation

Cartesian science: deductive, based on logical and mathematical reasoning

Ali Rahimi (Google), NIPS 2017

"Machine learning has become alchemy."

Yuri Lazebnik (Cold Spring Harbor Laboratory), Cancer Cell 2002

"Physics was a point of view that the world around us is [...] understandable in a predictive and reasonably quantitative fashion."

John Hopfield

There are also "springs" in quantum computing

Springs and balls

Spring

Brian Skinner, Ribbonfarm

Mattress

Carvalho et al., Nucl. Phys. B 2013

Quantum field theories

"The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction."

Sidney Coleman

Outline

Superposition

100% Head

100% Tail

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50% Head 50% Tail

50% Head 50% Tail

A coin in superposition is neither in the state "head AND tail at the same time" nor "head OR tail"; they constitute a new physical ontology.

 

Why? Interference!

Zach Weinersmith, SMBC comics

Interference

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=

Head

Head

Quantum coin flip

(Hadamard gate)

50/50 to measure Head or Tail

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"The goal in quantum computing is to choreograph things so that [the paths leading to a wrong answer destructively interfere.]"

Scott Aaronson

Entanglement

Superposition of states of multiple particles or independent properties

"I would not call entanglement one but rather the characteristic trait of quantum mechanics"

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A generic state of \(n\) quantum coins is a superposition of \(2^n\) states

2 coins: 4 states

3 coins: 8 states

Naïvely, the resource required to represent the state grows exponentially in the number of coins

 

But we can spend much less for certain restricted forms of entanglement

Outline

Kenneth Rudinger (Sandia), APS March Meeting 2016

Quantum characterization

Quantum state determination

 

  • We cannot learn an unknown quantum state using a single measurement
  • Moreover, any measurement destroys the state
  • A single type of measurement cannot distinguish all states
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Both 50% Head 50% Tail

Curse of dimensionality

Full quantum state determination ("tomography") is done by performing a set of carefully chosen measurements, repeated many times to gather the statistics

The exponential complexity presents a problem of its own

Quantum state certification

In a real experiment, we often have a good idea what our state is being produced, given e.g. calibration of our devices 

Are we asking the right question?

Full quantum state determination seeks to find the true state among all possible states

  • Infeasible for >10 qubits
  • May required simultaneous measurements on all qubits
?

Quantum state certification seeks to find if the true state is close to a given target state \(\rho\)

Hayashi et al., J. Phys. A: Math. Gen. 2006

Pallister et al., PRL 2018

  • Much less resource intensive (possibly independent of the number of qubits)
  • Single-qubit measurements only
\rho
?

At the time, not much was known about an optimal certification of more-than-three qubit states except the \(n\)-qubit GHZ ("cat") state

Li et al., PR Applied 2020

ND, Han and Zhu, Optimal verification of stabilizer states, PRR 2020

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=\begin{pmatrix} 1 & & & \\ & 1& & \huge{0}\\ \huge{0}& & 1 & & \\ & & & -1 \end{pmatrix}

CPHASE gate

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Vertex

Edge

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Graph states

"Spring" of quantum computing

  • Efficient representation of states and transformations as graphs and graph transformations
  • Can be created in one entangled step*
  • Equivalent to doing classical dynamics on a discrete phase space*

Architecture for showing quantum advantage

Erik Lucero/Google

Nature/Google

  • Quantum computational advantage ("supremacy") is the goal of demonstrating that a quantum device  can efficiently perform a task that is intractable on any classical computer
  • The task itself does not have to be useful
  • To achieve this goal, we want to reduce the noise on the quantum hardware as much as possible

Arute et al., Nature 2019

"Fidelity"

n

"Free fermionic" entangling gates native to the superconducting qubit architecture can be performed with much higher fidelity (>90%) than CNOT (~50%)

 

Can we use purely those gates to demonstrate quantum supremacy?

Oszmaniec, ND, Morales, and Zimborás, Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states, arXiv:2012.15825 

Free fermions

Another "spring" of quantum computing

Free fermionic entangling gates can be mapped to non-interacting (free) "fermionic" quantum particles

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  • Efficient representation of states and transformations as non-interacting quantum springs and oscillations
  • However, free fermionic gates alone cannot generate entanglement that is intractable on a classical computer
  • Add another type of spring! The cat state!
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Outline

Conclusion

  • Physics teaches us about building a simple model and adding complexity in a controllable way
  • But be open to learning from other disciplines such as computer science
  • Be curious, and have fun venturing into the unknown!

What are theoretical physicists doing here?