---
# System prepended metadata

title: Assignment 01
tags: [Quantum Physics II]

---

# Assignment 01
###### tags: `Quantum Physics II`

A Feature Article about QM:
The Second Quantum Revolution with Quantum Computers
## ABSTRACT
> The quantum nature superpostion, entanglement, and measurement are applicable to the quantum information industry (one of tech = quantum computing, abbr. QC)

This article includes 
* the current status of QC and app.
* focused topics of QC within TW
* the importance and possible impact of QC

## INTRODUCTION
* 2 most important cincepts in QM:
1. quantization: the discreteness of a physical quantity
2. superposition:  a quantum state can appear in multiple classically measurable states simultaneously

### Quantum Revolution
1. First Quantum Revolution:  we have built classical devices based on quantum principles
    -  lasers for optical communication, the internet, transistors for computers and cellphones, and nuclear weapons and power plants
2. Second Quantum Revolution: it exploits the fundamental properties of quantum mechanics and lets quantum nature deal with the “quantum problems”
    - quantum information (reaches a radically diff. level)
        - **quantum communication/teleportation**
            - 1997 first demonstrated
            - D. Bouwmeester and J-W Pan
            - polarized photons as individual quanta
            - concept based on **quantum entanglement**, **no-cloning principle**
            - safe: 
                - cannot be eavesdropped without known
                - only receiver can decode
        - **quantum computing**
            - also based on **quantum entanglement**
::: info
* [**Moore’s law**]():  the density of devices on silicon chips doubles approximately every 18 months
* [**Landauer’s principle**](https://en.wikipedia.org/wiki/Landauer%27s_principle): erasing a bit of information has an energy cost of at least $k_BT \ln2%
:::
- Classical computing
    - input info. needs to be erased
    - erasing info. consumes energy
    - irreversible calculation
    - IC+ causes (inevitably) overheating of trad. computer
- Quantum computing
    1. advantage 1 
        - input info. can be retrived.
        - reversible calculation 
        - reduces (substantially) the problem of overheating, energy loss
    2. advantage 2
        - exponentially faster and stronger computing power in calculating certain [**non-deterministic polynomial**](https://en.wikipedia.org/wiki/NP_(complexity)) (NP) problems 
        - **quantum supremacy**: coined by John Preskill, refers to a situation in which QC is predicted to outperform any CC in certain prob., when the [qubit](https://en.wikipedia.org/wiki/Qubit) (error-corrected [logical qubits](https://en.wikipedia.org/wiki/Physical_and_logical_qubits)) number > 50 
        - 
::: info
- **NP problems**:  
    If the dimension of a question is $n$,
    and the steps (or time) required to solve this prob. is $T(n)$,
    then:
    - [**Grover’s Search Algorithm**](https://en.wikipedia.org/wiki/Grover%27s_algorithm)  $\sqrt{n}$ as compared to $n$ in classical algorithm.
    - [**Shor’s integer factoring**](https://en.wikipedia.org/wiki/Shor%27s_algorithm) can gain an $n^2 \log n$ speed-up as compared to $\exp(n^{1/3})$ in classical algorithm.
    - Shor’s algorithm severely challenges the current [**RSA cryptosystem**](https://en.wikipedia.org/wiki/RSA_(cryptosystem)).
:::

### Anticipated applications
- artificial intelligence (AI)
- simulation of molecular interactions and chemical reactions
- synthesis of new materials
- large data analysis
    - the exponential increased DoF of a quantum state by $2^n$ ($n$ the number of qubits) enable QC to store and analyze large amounts of data
    - crucial for
        - machine learning
        - optimization of traffic routes
        - trajectory predictions 
- analysis of sequence  of genes in clinical medicine
- pharmaceutics: whether a type of drug cam improve symptoms or cure diseases
    - trad. analysis: run thru every possinbble -- labor intensive and time consuming 

### Current status of hardware
A quantum computer consists of atoms and light
The computation relies on the interaction btwn. them
- atom
    - storage unit “[**qubit**]()” in quantum computing language
    - can be a real one or an artificial one
    - possesses 2 discrete energy levels to couple with light
    - controlled by optical laser or not
        - Y: [**optical system**]()
        - N: [**solid-state system**](); but uses microwaves
- **optical system**
    - 2 major candidates (intensely studied): 
        1. **trapped ions** 
        2. **diamond vacancies** 
    - [**trapped ion**]()
        1. proposed by Cirac and Zoller in 1995
        1. process:
            1. confine ions within a trap in a vacuum chamber
            2. cool them by an EM field
        1. :+1: ==long [**coherence time**]()==: 
            - optical qubits: 1 to tens of sec.
            - [hyperfine pubits](): can > 600 sec.
        2. :-1: ==long [**gate operation time**]()==: 1-100 μs
        3. :+1: ratio of coherence time and gate time: very good
            - cf: [superconducting qubit](): 1000
        4. :+1: ==high [**gate fidelity**]()==
            - two-qubit gate fidelity reaching 99.9%
            - single qubit gate fidelity reaching 99.9999%
    - [**diamond vacancy**]()
        1. principle:
            - a nearest-neighbor pair nitrogen atom substitutes for a carbon atom in a diamond
            - this causes a defect -- **nitrogen-vacancy** (NV)
            - the defect and a lattice vancy forms a magnetic moment
            - it can be manipulated and measured by light
        2. :+1: quantum coherence perserves even at RT
        3. :-1: weak interaction btwn. defect and photons --> entanglement of pubits is hard to achieve
    - :-1: space requirement of optical setup --> hard to upscale

- **solid state system**
    - 2 (important and promising) platforms:
        1. **superconducting qubits**
        2. **spin qubits** in **quantum dots** (QDs)
    - **superconducting qubits**
        1. consist of an Al/Al<sub>2</sub>O<sub>3</sub>-based [**Josephson junction**](https://en.wikipedia.org/wiki/Josephson_effect)
            - as an inductor and a [shunted capacitor](https://en.wikipedia.org/wiki/Shunt_(electrical))
            - forms a quantum LC resonator with discrete energy levels.
        3. principle:
            - the qubit is capacitively coupled with a superconducting coplanar wavequide 
            - the coplanar wavequide, as a microwave cavity, stores the microwave photons and interacts with qubit
            - apply microwave and DC bias to control the qubit
            - microwave couples to qubit levels
            - the DC bias  generates magnetic flux threading the loop of [**SQUID**]() to change qubit energy
        6. **coherence time** > 100 μs
        7. **gate operatrion** > 40 ns
        8. achievements (til 2019)
            - entangled qubit state = 18 
            - qubit number = 72 (Google)
    - **quantum dots**
        1. an artificial structure where electrons can be confined within nm
        2. principle:
            - the **charge** and **spin** DoF of such confined electrons can both be used as a qubit
        3. :-1: short **coherence time**: tens of ns (charge qubits suffer from charge noises in the surrounding)
        4. forms of spin qubits
            - **spin-up** & **spin-down** states in a [single QD]()
            - two-electron **singlet** and **triplet states** in a [double QD]()
            - **spin-exchange interaction** in [triple QD]()
        5. Ex. isotopically purified <sup>28</sup>Si QDs:
            - **coherence time**: 30 ms 
            - **gate operation time**: ~100 ns
            - **single qubit gate fidelity** 99%
            - **two-qubit [CROT]() gate fidelity** > 90%
        6. Ex. phosphorous atom in silicon
            -  **coherence time**: 30 s 
            -  **gate fidelity** > 99.99%
        7. :+1: small size (< 100 nm), advantageous for up-sacling
        8. :-1: crosstalk and fan-out issues wheb designing the control wires
    - **topological qubit**
        1. prospective, <font color="red">not yet confirmed to exist</font>
        2. principle:
            - bits of information are encoded through braiding [**non-Abelian anyons**](https://en.wikipedia.org/wiki/Anyon#Non-abelian_anyons)
            - their exchange statistics is **non-commutative** (<font color="red">not yet confirmed so far</font>)
            - particle exchange with different routes will lead to different end states
        3. ==very long **coherence time**== (<font color="red">expected</font>)
        4. potent candidate: [**Majorana fermions**](https://en.wikipedia.org/wiki/Majorana_fermion) (<font color="red">not yet found</font>)
            - exist in 1D or 2D p-wave superconductors
            - experimental signs of progess have been made to reveal its signature

### Three types of quantum computer
- **universal quantum computer**
    -  aims to use gate operators to solve all kinds of problems within a reasonable time
    -  but needs millions of logical pubits
    -  unlikely to be mature within a decade
- **Noisy intermediate-scale quantum computer (NISQ)**
    - since the currently available qubits are not enough to achieve a fault-tolerant quantum computer
    - NISQ now adopted for special app. within a noise environment with *a limited number of qubits*. [news](https://www.ithome.com.tw/news/124665) [paper](https://www.researchgate.net/publication/322243414_Quantum_Computing_in_the_NISQ_era_and_beyond)
- [**quantum annealer**](https://en.wikipedia.org/wiki/Quantum_annealing)
    - already on the market
    - digital annealer: 
        - developed by Fujistu [news](https://www.mem.com.tw/arti.php?sn=1805170003)
        - a digital process inspired by quantum phenomena
    - quantum annealer:
        - used by [D-wave](https://en.wikipedia.org/wiki/D-Wave_Systems)
    - provide a great advantage in optimization problems

### Quantum algorithms
- quantum amplitude amplification algorithm (QAA)
    - a genuine quantum algorithm
    - used by Fujitsu and D-Wave to solve the optimization problems within the Ising model through het quantum annealing processes
- variational quantum eigensolver (VQE)
    - a hybrid of classical and quantum algorithms
    - can give the ground state of a large matrix
    - can be applied to solve optimization problems in finance, e.g. [portfolio optimization](https://en.wikipedia.org/wiki/Portfolio_optimization)
    - determine a stable structure for predicting molecular chemicals and new drugs
- [quantum approximate optimization algorithm]() (QAOA)
    - a polynomial time algorithm for finding a local solution
    - MaxCut problem
    - similar to VQE, both considered very important milestones in the NISQ era
    
- quantum Fourier transform (QTF)
    - uses only $O(n^2)$ gates
    - exponetially better than classical discrete FT, taking $O(n2^n)$ gates
    - faciliate to solve:
        -  Shor’s algorithm for factoring a problem
        -  quantum phase estimation
        -  hidden subgroup problem
        -  other quantum phase related problems
- the Aram Harrow, Avinatan Hassidim and Seth Lloyd (HHL) algorithm
     - based on the QFT
     - used for finding the inverse transformation of a large dimensional matrix within polynomial time. 
    - deep learning, and scientific and engineering research.  
- Grover’s algorithm
    -  an unstructured N database searching problem
    -  classical needs $O(N)$; Grover’s needs $O(\sqrt{N})$
    -  all kinds of search problems

### Current research in Taiwan
- Ying-Cheng Chen’s group (2018): **quantum memories** and storage efficiency of 92.0% with quantum optical methods
- Chin-Sung Chuu’s group: **quantum photonics**
    - built the optical fiber link between NTHU and NCTU
    - demonstrated Taiwan's fisrt outdoor [**quantum key distribution**]() (QKD)
- Yueh-Nan Chen’s group: **quantum steering
- Ite A. Yu’s group: quantum optics & quantum information
    - determines the [efficient cross-phase modulation]() (XPM) achieved at low-light intensities without requiring cavities or tightly focusing laser beams
- NTU
    - Si-based qubits
    - spintronic and quantum devices
    - quantum computing in ML and AI fields
- CYCU proposed to initiate quantum computation college

### IBM Q Hub at NTU
 NTU and IBM signed a contract that allows NTU and the research groups in Taiwan to use the most advanced superconductor qubit-based IBM Q system (53 qubits in 2019)
- Ching-Ray Chang in charge
- research: quantum materials, quantum finances, a quantum random number generator and the applications of quantum algorithms
- promotion:
    - contact: high-tech companies, local industries& traditional and financial industries
    - held many popular talks
    - Qiskit camps
- education: Quantum Physics education in high school and for undergraduates

---
## Applications
### Annealer and photonics
Quantum annealer and digital annealer are not gate-based universal quantum computers s; rather, they are designed to solve **special optimization problems**
::: spoiler
Using the natural evolution of energy minimization of a physical system, the problems in real life are mapped onto the energy landscape, manipulated by bias and coupler, of the system. The entangled and superposed states then adiabatically evolve to the lowest energy state of the energy landscape constructed from real problems and the solution to the problem is derived from a quantum annealing processes. Since the number of qubits in these kinds of annealers have already reached a few thousand, it is possible to solve combinatory optimization problems in a very efficient way.
:::

- use bosonic statistics, e.g. [molecular vibrational spectrum](https://en.wikipedia.org/wiki/Molecular_vibration)
### Quantum Chemistry 
- the original motif for quantum computer
- more focused theme -- bonding, calculating the wave functions of molecular open-shell electrons
- related disciplines: pharmaceutical and materials science. 
- a more common task -- calculating the ground state energy directly
    - [digital Hamiltonian simulation]() and a classical computer allow dynamics of the system to be mapped to a sequence of quantum gates
    - By VQE alorithm we can derive the ground state energy of small molecules with single digit number of qubits
    - quantum magnet can be done so

### Quantum machine learning
### Quantum finance

---
## Future Prospects
### Semiconductor system integration
### Cryogenic CMOS technology 
### Quantum module 
### Integration and packaging 
### Scientific and industrial development strategy
### Industry wide consensus and standards
### Staged technology goals and associated applications
### Boost from other industries 
### Cloud Service 
### QIS investments 

