Tensor Products​

Kronecker product

• a way to multiply vectors and matrices to generate bigger vectors and matrices

$|\psi\rangle \otimes |\phi\rangle = \begin{pmatrix} \psi_0 \\ \psi_1 \end{pmatrix} \otimes \begin{pmatrix} \phi_0 \\ \phi_1 \end{pmatrix} = \begin{pmatrix} \psi_0 \begin{pmatrix} \phi_0 \\ \phi_1 \end{pmatrix} \\ \\ \psi_1 \begin{pmatrix} \phi_0 \\ \phi_1 \end{pmatrix} \end{pmatrix} = \begin{pmatrix} \psi_0 \phi_0 \\ \psi_0 \phi_1 \\ \psi_1 \phi_0 \\ \psi_1 \phi_1 \end{pmatrix}$

$|\psi\rangle \otimes |\phi\rangle \equiv |\psi\rangle |\phi\rangle \equiv|\psi\phi\rangle$

Tensor product of Matrices​

$A \otimes B = \begin{pmatrix} a_{00}B & a_{01}B \\ a_{10}B & a_{11}B \end{pmatrix}$

• The tensor product $|0\rangle \langle1| \otimes |1\rangle \langle0|$ is:

$|0\rangle \langle 1| \otimes |1\rangle \langle 0| = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix} \otimes \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}$

$|0\rangle \langle 1| \otimes |1\rangle \langle 0| = \begin{pmatrix} 0 \cdot \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix} & 1 \cdot \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix} \\ 0 \cdot \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix} & 0 \cdot \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix} \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}$

• To short hand this, we can write:

$|0\rangle \langle 1| \otimes |1\rangle \langle 0| \equiv |0\rangle|1\rangle \langle 1| \langle 0| \equiv |01\rangle \langle 10|$

• $(|a\rangle \langle b|) \otimes (|c\rangle \langle d|) = (|a\rangle |c\rangle)(\langle b| \langle d|) = |ac\rangle \langle bd|$

Bases​

• The basis for a single qubit is $\{|0\rangle, |1\rangle\}$
• It is given by taking the tensor product of the basis for each qubit:
  • $\{|0\rangle \otimes |0\rangle, |0\rangle \otimes |1\rangle, |1\rangle \otimes |0\rangle, |1\rangle \otimes |1\rangle\}$
  • For short hand, we write $\{|00\rangle, |01\rangle, |10\rangle, |11\rangle\}$
• The computational basis for two qubits is $\{|00\rangle, |01\rangle, |10\rangle, |11\rangle\}$
• For three qubits $\{|000\rangle, |001\rangle, |010\rangle, |011\rangle, |100\rangle, |101\rangle, |110\rangle, |111\rangle\}$

Matrices​

$\{|0\rangle\langle0|,\; |0\rangle\langle1|,\; |1\rangle\langle0|,\; |1\rangle\langle1|\}$

• forms a basis for the space of $2 \times 2$ matrices
• operator basis: a set of matrices that can be used to express any matrix as a linear combination of the basis matrices

$\begin{pmatrix} a & b \\ c & d \end{pmatrix} = a |0\rangle\langle0| + b |0\rangle\langle1| + c |1\rangle\langle0| + d |1\rangle\langle1|$

• One of the basis elements is: $|0\rangle\langle0| \otimes |0\rangle\langle0| = |00\rangle\langle00|$
• Similarly $|0\rangle\langle0| \otimes |0\rangle\langle1| = |00\rangle\langle01|$
• In total, the tensor products yields $4 \times 4 = 16$ basis elements for the space of $4 \times 4$ matrices: $\{|00\rangle\langle00|,\; |00\rangle\langle01|,\; |00\rangle\langle10|,\; |00\rangle\langle11|,\; |01\rangle\langle00|,\; |01\rangle\langle01|,\; \ldots,\; |11\rangle\langle11|\}.$

The Golden Rule of Tensor Products​

What starts on the left of the tensor product says on the left

$(A \otimes B)(|\psi\rangle \otimes |\phi\rangle) = (A|\psi\rangle) \otimes (B|\phi\rangle)$

$(|0\rangle\langle0| \otimes |1\rangle\langle1|)(|00\rangle) \\ = (|0\rangle\langle 0| \otimes |1\rangle\langle1|)(|0\rangle \otimes |0\rangle) \\ \\ = (|0\rangle\langle0||0\rangle) \otimes (|1\rangle\langle1||0\rangle) \\ = |0\rangle \otimes 0 \\ = 0$

• $|\psi\rangle \otimes |\phi\rangle \equiv |\psi\rangle|\phi\rangle \equiv |\psi\phi\rangle$
• $(|\psi\rangle \otimes |\phi\rangle)^\dagger = \langle\psi| \otimes \langle\phi|$
• $(\alpha|\psi\rangle + \beta|\phi\rangle) \otimes |\omega\rangle = \alpha|\psi\rangle \otimes |\omega\rangle + \beta|\phi\rangle \otimes |\omega\rangle$
• $((\langle\psi| \otimes \langle\phi|)(|\omega\rangle \otimes |\eta\rangle)) = \langle\psi|\omega\rangle \langle\phi|\eta\rangle$
• $(A + B) \otimes C = A \otimes C + B \otimes C$
• $A \otimes (B + C) = A \otimes B + A \otimes C$
• $(A \otimes B)(C \otimes D) = AC \otimes BD$
• $(A \otimes B)^\dagger = A^\dagger \otimes B^\dagger$

Entanglement​

• Single-qubit state is a two dimensional vector: $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$
• where $\alpha$ and $\beta$ are complex numbers such that $\||\psi\rangle\|^2 = |\alpha|^2 + |\beta|^2 = 1$
• Two qubits $\psi_1\rangle$ and $\psi_2\rangle$ can be combined to form a four-dimensional vector: $|\psi_{12}\rangle = |\psi_1\rangle \otimes |\psi_2\rangle \equiv |\psi_1\rangle|\psi_2\rangle \equiv |\psi_1\psi_2\rangle$
• Separable States: can be written as a tensor product of single-qubit states
  • $|\Psi\rangle = \alpha_{00} |00\rangle + \alpha_{01} |01\rangle + \alpha_{10} |10\rangle + \alpha_{11} |11\rangle \\ = |\psi_1\rangle| \otimes \psi_2\rangle$
• if the state is not separable, it is called entangled.
  • entangled: $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$
• if $ad = 0$ and $bc = 0$, then $ac$ or $bd$ must also vanish.
  • separable: $\frac{1}{2}(|00\rangle + |01\rangle) = |0\rangle \otimes \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$

Two-Qubit Gates​

• Two-qubit gates are $4 \times 4$ unitary matrices that act on two-qubit states.

CNOT Gate​

Controlled NOT gate

• flips target if control is $|1\rangle$

$\text{CNOT} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix} = |0\rangle\langle0| \otimes \mathbb I + |1\rangle\langle1| \otimes X$

SWAP Gate​

• Exchanges the two qubits.

$\text{SWAP} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}$

CZ Gate​

Controlled Z gate

• Applies $Z$ to target if control is $|1\rangle$

$\text{CZ} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix}$

Building Multi-Qubit Gates​

• Two qubits $|\psi_1\rangle$ and $|\psi_2\rangle$ can be combined to form a four-dimensional vector:
  • if $U_1$ and $U_2$ are single-qubit gates, then $U_1 \otimes U_2$ is a two-qubit gate that acts on the combined state $|\psi_1\rangle \otimes |\psi_2\rangle$.
  • $(U_1 \otimes U_2)(|\psi_1\rangle \otimes |\psi_2\rangle) = (U_1|\psi_1\rangle) \otimes (U_2|\psi_2\rangle)$
  • For shorthand, $U_1 U_2|\psi_1\psi_2\rangle$

Order of Operations​

• When gates act independently, it doesn't matter the order in which they are apply with the understanding that if only a single gate is applied, identity acts on the other qubits.

$(U_1 \otimes U_2) = (\mathbb I \otimes U_2)(U_1 \otimes \mathbb I) = (U_1 \otimes \mathbb I)(\mathbb I \otimes U_2)$

• Example: Apply $X$ to qubit 1 and $H$ to qubit 2, starting with $|00\rangle$:
• $(X \otimes \mathbb I)|00\rangle = |10\rangle$
• $(\mathbb I \otimes H)|10\rangle \\ = (\mathbb I \otimes H)(|1\rangle \otimes |0\rangle) \\ = |1\rangle \otimes H|0\rangle \\ = |1\rangle \otimes \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle) \\ = \frac{1}{\sqrt{2}}(|1\rangle \otimes |0\rangle + |1\rangle \otimes |1\rangle) \\ = \frac{1}{\sqrt{2}}(|10\rangle + |11\rangle)$

Quantum Circuits​

• A quantum program is a sequance of gates applied to qubits, which are typically assumed to be initialized in the state $|0\rangle$.
• Two qubits start in the state $|0\rangle \otimes |0\rangle = |00\rangle$

$CNOT(H \otimes \mathbb I)|00\rangle = CNOT\left(\frac{1}{\sqrt{2}}(|00\rangle + |10\rangle)\right) = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$

Name	Gates	Matrix
Pauli-X	$X$ or $\oplus$	$\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
Pauli-Y	$Y$	$\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$
Pauli-Z	$Z$	$\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$
Rotation-X	$R_x(\theta)$	$\begin{pmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}$
Rotation-Y	$R_y(\theta)$	$\begin{pmatrix} \cos\frac{\theta}{2} & \sin\frac{\theta}{2} \\ -\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{pmatrix}$
Rotation-Z	$R_z(\theta)$	$\begin{pmatrix} e^{i\theta/2} & 0 \\ 0 & e^{-i\theta/2} \end{pmatrix}$
Phase Shift	$Ph(\delta)$	$\begin{pmatrix} 1 & 0 \\ 0 & e^{i\delta} \end{pmatrix}$
Hadamard	$H$	$\frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$
Phase	$S$	$\begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix}$
T	$T$	$\begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix}$

• $S = Ph(\pi/2)$
• $T = Ph(\pi/4)$
• $Z = Ph(\pi)$

Multi-Qubit Gates​

Name	Gates	Matrix
CNOT		$\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix}$
CZ		$\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix}$
SWAP		$\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}$
Toffoli		$\begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix}$

• CNOT gate can be $|0\rangle\langle0| \otimes \mathbb I + |1\rangle\langle1| \otimes X$
  • $|0\rangle \text{state} \rightarrow \mathbb I$ (do nothing)
  • $|1\rangle \text{state} \rightarrow X$ (flip the target)
• Larger gates can be built from smaller ones
• Toffoli gate (CCNOT): flips the target if both controls are $|1\rangle$.
• $\text{Toffoli} = |00\rangle\langle00| \otimes \mathbb I_4 + |11\rangle\langle11| \otimes X$
  • two control qubits and one target qubit
  • if both control qubits are $|1\rangle$, then apply $X$
  • $|110\rangle \rightarrow |111\rangle$
  • $|111\rangle \rightarrow |110\rangle$
• Can be generalized to $n$-qubits: $C^{n-1}NOT$ gate, which flips the target if all $n-1$ control qubits are $|1\rangle$.
  • CNOT: $|10\rangle \rightarrow |11\rangle$ and $|11\rangle \rightarrow |10\rangle$
  • Toffoli: $|110\rangle \rightarrow |111\rangle$ and $|111\rangle \rightarrow |110\rangle$
  • 3-control gate: $|1110\rangle \rightarrow |1111\rangle$ and $|1111\rangle \rightarrow |1110\rangle$

$(\mathbb I - |111\ldots\rangle\langle 111\ldots|)\otimes \mathbb I + |111\ldots\rangle\langle 111\ldots|\otimes U$

The Rules of Quantum Computing​

Initialization​

• An $n$-qubit computation starts in the all-zero state:

$|phi\rangle = |0\rangle \otimes |0\rangle \otimes \ldots \otimes |0\rangle = |00\ldots0\rangle$

Algorithm​

• Apply a sequence of unitary gates to obtain the final state:

$U = U_1U_2\ldots U_m \implies U|\psi\rangle$

Measurement​

The Born Rule

• Reading $n$ qubits producs $n$ classical bits.
• The probability of outcome $b_1b_2\ldots b_n$:

$Pr(b_1b_2\ldots b_n) = |\langle b_1b_2\ldots b_n|\psi\rangle|^2$

• $|\psi\rangle$: initial state of the system
• $U$: an unitary matrix summing up the gates applied to the system
• $U|\psi\rangle$: final state of the system
• $\langle b_1b_2\ldots b_n|U|\psi\rangle$: the amplitude of the outcome $b_1b_2\ldots b_n$
• $|\text{amplitude}|^2$: The probability of the outcome $b_1b_2\ldots b_n$ being observed when measuring the system
  • if $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$
  • then $Pr(00) = Pr(11) = \frac{1}{2}$

Post-measurement States​

Measurement causes the state to collapse

• Measuring all qubits: outcome $b_1 \ldots b_n$ collapses state to $|b_1 \ldots b_n\rangle$
• Measuring a subset: keep matching terms and renormalize.

$|\psi\rangle = c_{00\ldots0}|00\ldots0\rangle + c_{00\ldots1}|00\ldots1\rangle + \ldots + c_{11\ldots1}|11\ldots1\rangle$

• If we measure all qubits, we get outcome $b_1b_2\ldots b_n$
  • The state will collapse to $|\psi'\rangle = |b_1b_2\ldots b_n\rangle$
  • The probability of this outcome is $Pr(b_1b_2\ldots b_n) = |\langle b_1b_2\ldots b_n|\psi\rangle|^2$

$|\psi\rangle = \alpha|00\rangle + \beta|01\rangle + \gamma|10\rangle + \delta|11\rangle$

• If we measure only the first qubit, and get outcome $0$, the state maintains only terms with $0$ in the first position:
  • $|00\rangle$ and $|01\rangle$
  • The remaining state is $|\psi'\rangle = \alpha|00\rangle + \beta|01\rangle$
  • $|10\rangle$ and $|11\rangle$ are removed from the state
• This gives us the unnormalized state: $|\psi'\rangle_{unnorm} = \alpha|00\rangle + \beta|01\rangle$
• The probability of this outcome is $Pr(0) = |\alpha|^2 + |\beta|^2$
  • $|00\rangle$ and $|01\rangle$ are the only terms that contribute to the probability of outcome $0$ for the first qubit
• After measurement, the state must be $\||\psi\|^2 = 1$, so we need to renormalize the state:

$|\psi'\rangle = \frac{(\alpha|00\rangle + \beta|01\rangle)}{\sqrt{|\alpha|^2 + |\beta|^2}}$

QASM2.0​

Quantum Gate	QASM Equivalent	Description
$R_x(\theta)$	rx	Rotation around X-axis: rx(pi/2) q[0];
$R_y(\theta)$	ry	Rotation around Y-axis: ry(0) q[0];
$R_z(\theta)$	rz	Rotation around Z-axis: rz(pi) q[0];
$X$	x	Pauli-gate bit flip: x q[0];
$Z$	z	Pauli-gate phase flip: z q[0];
$XZ$	y	Pauli-gate bit+phase flip: y q[0];
$H$	h	Hadamard gate: h q[0];
$CNOT$	cx	Controlled NOT gate: cx q[0], q[1];
$SWAP$	swap	Swap two qubit registers: swap q[0], q[1];
$CZ$	cz	Controlled $Z$ gate: cz q[0], q[1];

Image Gradient​

• It is a directional change in the intensity or color in an image.
• can be used to extract valuable information from images.
• commonly used in edge detection.
• ➡️ Change is X-directions, ⬇️ Change is Y-directions.
• Combining both X and Y diretion to estimate if changes are in both directions.

HoG, Histogram of Oriented Gradient​

To find edge and shape of the object in the image

• Computing Image Gradient
  • Use the horizontal and vertical filters to compute gradient values
• Compute the strength/magnitude and direction of gradient
  • Strength/Magnitude(g): $\sqrt{g_x^2 + g_y^2}$
  • Direction($\theta$): $\tan^{-1}(g_y / g_x)$
• Create orientation histogram
  • Divide the image into small connected regions called Cells which is a 8x8 patch
  • Create cell histogram based on gradient direction and magnitude
  • 64 (8x8) gradient vectors are put into a 9-bin histogram.
  • The bins are the gradient directions ($\theta$) quantized into 9-bins
• Block Normalization
  • 16x16 pixels blocks or 22 cells are used for normalization, which has 4 histograms.
  • Normalization will make it scale/multiplication invariant
  • Each block will represent 36x1 element vector
• Intensity: brightness of the pixel
• Saturation: HSV color space, the amount of gray in the color
• Calculate the HoG feature vector
  • Each of the 36x1 vectors in each blocks are concatenated into one big vector
  • Size of the vector will be 36xN, where N is the number of blocks in the image
• Hog feature extractor

LBP, Local Binary Pattern​

To describe the image textures

$LBP_{P,R}(x_c, y_c) = \sum_{p=0}^{P-1} s(g_p - g_c) \cdot 2^p$

• An eifficient texture operator which labels each pixels of an image by thresholding their neighbours.
• A powerful feature for texture classification
• LBP operator is to describe the image textures using two measures namely, local spatial patterns and the gray scale constract of its strength.
• $S(x)$ is a thresholding function
• $(x_c, y_c)$ is the center pixel in the 8 pixel neighbourhood
• $g_c$ is gray level of the center pixel
• $g_p$ is gray value of a smpling point in an equally spaced circular neighbourhood of P sampling points and radius R around the point $(x_c, y_c)$

1. Sample pixel neighbourhood
2. Difference result
3. Thresholding result

ANN​

$L(a, y) = -(y \log a + (1-y) \log (1-a))$ $GD(w, b) = x = \frac{1}{m} \sum_{i=1}^{m} L(a^{(i)}, y^{(i)})$

Push & Pull Factors​

• Techonology - Push (Supply-side Pushing Innovation)
• Demand - Pull (Demand-side Pulling Innovation)

Technology Push	Demand Pull
Starts with Scientific Breakthrough	Starts with Customer need
iPad	Zoom (COVID-19)
VR Headset	Selfie Stick
Post-it Notes	Tesla Model 3

Disruptive Innovation​

• Creative Destruction
  • a process by which new innovations and technological advancements ("creative")
  • desmantle long-standing economic structures, practices, and organizations ("destruction")
  • while creating new markets and opportunities
• Disruptive Innovation
  • a process where a smaller company successfully challenges estabilished businesses bgy offering simpler, more affordable, or more accessible products or services.
  • low-cast, low-performance, alternative, improve over time and displace established playwers
• Innovator's Dilemma
  • successful, well-managed companies often fail when disuptive technologies emerge
  • even when they do everything "right" according to traditional management principles.

Sustaining Innovation	Disruptive Innovation
Improves existing products	Creates new markets or value
Higher margins	Initially lower margins
High-end customers	Low-end market segments

• Sustaining Innovation: Tesla improving battery range
• Disruptive Innovation: Netflix replacing Blockbuster

Attention Economy​

• Human attention a scarce resource
• The attention economy is made up of anything trying to capture our limited attention.

Responsible Innovation​

• Innovation can create benefits (growth, efficiency, solutions) but also risks (inequality, pollution, privacy loss).

• Responsible Innovation is about developing new techonologies, products, or services in a way that is ethically acceptatble, socially desirable, and environmentally sustainable, while actively considering their potential impacts on society.

• Anticipation: Exploring possible risks, unintended consequences, and long-term effects.

• Reflexivity: Innovators reflecting on their own values, assumptions, and biases.

• Inclusion: Engaging stakeholders (citizens, users, regulators, communities), not just engineers or investors shaping outcomes.

• Responsiveness: Ability to change direction if concerns arise.

Product questions	Process questions	Purpose questions
How will the risks and benefits be distributed?	How should standards be drawn up and applied?	Why are researchers doing it?
What other impacts can we anticipate?	How should risks and benefits be defined and measured?	Are these motivations transparent and in the public interest?
How might these change in the future?	Who is in control?	Who will benefit?
What don't we know about?	Who is taking part?	What are they going to gain?
What might we never know about?	Who will take responsibility if things go wrong?	What are the alternatives?
-	How do we know we are right?	-

Sustainability​

• No poverty
• Zero hunger
• Good health and Well-being
• Quality education
• Gender equality
• Clean water and Sanitation
• Affordable and Clean energy
• Decent work and Econnomic growth
• Industry, Innovation and Infrastructure
• Reduced Inequalities
• Sustainable Cities and Communities
• Responsible consumption and Production
• Climate action
• Life below water
• Life on land
• Peace, Justice, and Strong Institutions
• Partnerships for the goals

Sustainability Dilemma​

Externailities​

Impacts on third parties

• Ecology / Environmental
  • Bio-diversity
  • Habitat loss
  • Pollution
  • Carbon footprint
• Social - human side
  • Human trafficking
  • Working conditions
  • Child labour
  • Social cohesion
  • Addiction and psychological damages

Internal Perspectives​

• Economic - Business sustainability
  • Solvency
  • Regulations
  • Management
  • Succession planning
  • Disaster management
  • Short-term thinking / goals
  • Fiduciary obligations to Shareholders

Type of ML Systems​

• Supervised Learning
• Unsupervised Learning
• Semi-supervised Learning
• Reinforcement Learning
• Batch and Online Learning
  • Whether system can learn on the fly
• Instance-based and Model-based Learning
  • Comparing data points or detect patterns in training data to build a predictive model

Evaluation Metrics​

Interesction over Union (IoU)​

• a metric used for the evaluation of object detection detectors
• how good is the predicted bounding box for an object detected closely matches.

$IoU = \frac{Area\ of\ Overlap}{Area\ of\ Union}$

Digital Image​

• made of picture elements (pixels)
• an array or a matrix of Pixels arranges in columns and rows
• Each Pixel has its own intesity value, or brightness
• Intensity values in digital images are defined by bits.
  • 8 bits image = 256 (2^8) intensity values (0-255)
• Black & White images have a single 8-bits intensity range.

Image Processing Basics​

• Image dimension = $5 \times 5 \times 3$
• Number of Channels = 3 (Red, Green, Blue)
• So, 24-bit color dpeth (8 bits per channel)
  • Each pixel has 3 intensity values (R, G, B) each in the range of 0-255
  • Total number of possible colors = $256^3$ (16,777,216)

Image Processing Types​

• Image Enhancement
• Image Restoration
• Image Segmentation
• Image Recognition & Classification
• Image Compression
• Image Transformation
• Image Filtering
• Morphological Processing
• Color Image processing
• 3D Image Processing

Image Thresholding (Segmentation)​

• Easist method for image segmentation
• Converts gray-scale image into a binary image
  • $f(x,y) < \text{Threshold} \Rightarrow 0$ (black)
  • $f(x,y) \geq \text{Threshold} \Rightarrow 255$ (white)

Image Thresholding methods​

• Histogram shape: Peaks, valleys, and curvature of the histogram are analyzed to determine the optimal threshold value.
• Clustering based: The Otsu method, good for bimodal distribution
• Adaptive thresholding: Instade of a single threshold, have thresholds for different regions in the image.

Image Transformation​

• Rotation
• Translation
• Uniform Scaling
• Non-Uniform Scaling
• Reflection
• Shearing

Edge Detection (Image Filtering)​

• Edge?
  • The points/pixels in an image where brightness/intensities changes sharply.
  • A simple and fundamental tools in image processing and computer vision, useful in feature detection/extraciton
• Canny Edge detection
• Sobel Edge detection
• How to detect edges?

Prewitt Filters​

• Vertical Edge detector: $\begin{bmatrix} 1 & 0 & -1 \\ 1 & 0 & -1 \\ 1 & 0 & -1 \end{bmatrix}$
• Horizontal Edge detetor: $\begin{bmatrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ -1 & -1 & -1 \end{bmatrix}$

Sobel Filters​

• Vertical Edge detector: $\begin{bmatrix} 1 & 0 & -1 \\ 2 & 0 & -2 \\ 1 & 0 & -1 \end{bmatrix}$
• Horizontal Edge detetor: $\begin{bmatrix} 1 & 2 & 1 \\ 0 & 0 & 0 \\ -1 & -2 & -1 \end{bmatrix}$

Morphological Processing​

• Dilation: Shrinks the image pixels from the boundaries of objects in an image, making them thicker.
• Erosion: Adds pixels to the boundaries of objects in an image, making them thinner.

Issue​

• Mac storage setting didn't show the actual storage usage, and it was always showing "Other" taking up a lot of space.
• It also didn't check cache files, which took up at least 10GiB of space.

CLI​

• Mole
• mo clean

GUI​

• OmniDiskSweeper
• Click "Macintosh HD" and "Sweep Macintosh HD Drive..."
• You can manually select the files to delete including cache files.

Community​

• US: Hacker News
• KR: Geeknews
• BR: Tabnews
• JP: Qiita
• CN: 掘金

Launching service​

• US: Product Hunt

Ket​

$|\psi\rangle = \begin{pmatrix} \psi_0 \\ \psi_1 \end{pmatrix}$

$|0\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}$

$|1\rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$

$|\psi\rangle = \psi_0 |0\rangle + \psi_1 |1\rangle \\ \quad = \psi_0 \begin{pmatrix} 1 \\ 0 \end{pmatrix} + \psi_1 \begin{pmatrix} 0 \\ 1 \end{pmatrix}$

Matrices​

• Matrices represent linear transformations (quantum gates). A general 2x2 matrix is: $A = \begin{pmatrix} \alpha_{00} & \alpha_{01} \\ \alpha_{10} & \alpha_{11} \end{pmatrix}$
• Identity matrix: $I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$
• Linearity: $A(|\psi\rangle + |\phi\rangle) = A|\psi\rangle + A|\phi\rangle$

Bra and Daggers​

Dagger​

• Conjugate Transpose: swap rows/columns and complex-conjugates every entry.
• Ket becomes Bra: $|\psi\rangle^\dagger = \begin{pmatrix} \psi_0 \\ \psi_1 \end{pmatrix}^\dagger = \begin{pmatrix} \overline{\psi_0} & \overline{\psi_1} \end{pmatrix} = \langle\psi|$
• For a matrix: $A^\dagger = \begin{pmatrix} \overline{\alpha_{00}} & \overline{\alpha_{10}} \\ \overline{\alpha_{01}} & \overline{\alpha_{11}} \end{pmatrix}$
• Key Identities:
  • $(\alpha A)^\dagger = \overline{\alpha} A^\dagger$
  • $(A^\dagger)^\dagger = A$
  • $(AB)^\dagger = B^\dagger A^\dagger$

Hermitian and Unitary Matrices​

• Hermitian: $H^\dagger = H$
  • Self-adjoint matrices, their eigenvalues are always real.
  • Observables in quantum mechanics are Hermitian.
• Unitary: $U^\dagger U = UU^\dagger = I$
  • The inverse of a unitary matrix is its conjugate transpose.
  • Unitary matrices preserve norms

Inner Product​

• The angle between two vectors $|\psi\rangle$ and $|\phi\rangle$ is defined as bra-ket: $\langle\psi|\phi\rangle = (\overline{\psi_0} \overline{\psi_1}) \begin{pmatrix} \phi_0 \\ \phi_1 \end{pmatrix} = \overline{\psi_0}\phi_0 + \overline{\psi_1}\phi_1$
• Important properties:
  • Order Matters: $\langle\psi|\phi\rangle \neq \langle\phi|\psi\rangle$
  • But $\langle\psi|\phi\rangle = \overline{\langle\phi|\psi\rangle}$ (Complex Conjugate)
  • The modulus is symmetric: $|\langle\psi|\phi\rangle| = |\langle\phi|\psi\rangle|$
• The Magnitude of a vector is given by: $\| |\psi\rangle \|^2 = \langle\psi|\psi\rangle = |\psi_0|^2 + |\psi_1|^2$

Orthonormal of the Computational Basis​

• The basis states $|0\rangle$ and $|1\rangle$ are orthonormal: $\langle 0|0\rangle = 1, \quad \langle 1|1\rangle = 1, \quad \langle 0|1\rangle = 0, \quad \langle 1|0\rangle = 0$
• This simplifies inner products enormously when working with the computational basis: $\langle\psi|\phi\rangle = (\overline{\psi_0}\langle0| + \overline{\psi_1}\langle1|) (\phi_0|0\rangle + \phi_1|1\rangle)$
• All corss terms vanish due to orthogonality, leaving: $= \overline{\psi_0}\phi_0 \langle0|0\rangle + \overline{\psi_0}\phi_1 \langle0|1\rangle + \overline{\psi_1}\phi_0 \langle1|0\rangle + \overline{\psi_1}\phi_1 \langle1|1\rangle$ $= \overline{\psi_0}\phi_0 + \overline{\psi_1}\phi_1$

Outer Products​

• The outer product of two vectors produces a matrix: $|\psi\rangle\langle\phi| = \begin{pmatrix} \psi_0 \\ \psi_1 \end{pmatrix} \begin{pmatrix} \overline{\phi_0} & \overline{\phi_1} \end{pmatrix} = \begin{pmatrix} \psi_0\overline{\phi_0} & \psi_0\overline{\phi_1} \\ \psi_1\overline{\phi_0} & \psi_1\overline{\phi_1} \end{pmatrix}$
• Basis outer products: $|0\rangle\langle1| = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}, \quad |1\rangle\langle0| = \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}$
• Any matrix can be expanded in terms of outer products of the computational basis: $A = \alpha_{00} |0\rangle\langle0| + \alpha_{01} |0\rangle\langle1| + \alpha_{10} |1\rangle\langle0| + \alpha_{11} |1\rangle\langle1|$

The Qubit​

A qubit is the fundamental unit of quantum information

$|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$

• where $\alpha, \beta \in \mathbb{C}$ are complex numbers such that $|\alpha|^2 + |\beta|^2 = 1$ (normalization condition).
• Any normalized single-qubit state can be parameterized using two angles $\theta$ and $\phi$ (real numbers): $|\psi\rangle = \cos\theta|0\rangle + e^{i\phi}\sin\theta|1\rangle$
• Key difference from a bit: a bit is either 0 or 1, while a qubit can be in a superposition of both states simultaneously until measured.

Measurement​

• When you measure a qubit $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$ in the computational basis, you get:
  • $|0\rangle$ with probability $|\alpha|^2$
  • $|1\rangle$ with probability $|\beta|^2$

Outcome	Probability	Post-measurement State
0	$	\alpha
1	$	\beta

• The result of measuring a qubit is a single classical bit.
• For $|\psi\rangle = \cos\theta|0\rangle + e^{i\phi}\sin\theta|1\rangle$:
  • Probability of measuring $|0\rangle$: $\cos^2\theta$
  • Probability of measuring $|1\rangle$: $\sin^2\theta$
  • The phase $\phi$ does not affect measurement outcomes.

One-Qubit Gates​

Pauli Matrices​

Unitary matrics

$\mathbb{I} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \quad X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, \quad Y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}, \quad Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$

• $X$ is the quantum NOT gate:
  • $X|0\rangle = |1\rangle$
  • $X|1\rangle = |0\rangle$
• $Z$ filps the phase of $|1\rangle$:
  • $Z|0\rangle = |0\rangle$
  • $Z|1\rangle = -|1\rangle$
• All three $(X, Y, Z)$ are both Hermitian and unitary.

Hadamard Gate​

$H = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$

• $H$ creates superpositions:
  • $H|0\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$
  • $H|1\rangle = \frac{|0\rangle - |1\rangle}{\sqrt{2}}$
• $H$ also "un-does" superpositions:
  • $H\left(\frac{|0\rangle + |1\rangle}{\sqrt{2}}\right) = |0\rangle$
  • $H\left(\frac{|0\rangle - |1\rangle}{\sqrt{2}}\right) = |1\rangle$

Rotation Gate​

$R(\theta) = \begin{pmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{pmatrix}$

• $R(\theta)$ rotates the state vector by an angle $\theta$ in the $|0\rangle$-$|1\rangle$ plane.

The Bloch Sphere​

Every single-qubit state $|\psi\rangle = \cos\theta|0\rangle + e^{i\phi}\sin\theta|1\rangle$ maps to a point on the surface of a unit sphere

• $\theta$ is polar angle from north pole
• $\phi$ is azimuthal angle around equator
• $|0\rangle$ is at the north pole
• $|1\rangle$ is at the south pole
• $\frac{|0\rangle + |1\rangle}{\sqrt{2}}$ is on the equator at $\phi=0$

Exercises​

1. For any two-dimensional state vector $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$, it holds that $|\alpha|^2 + |\beta|^2 = 1$.
2. Measuring a qubit in the $\{|0\rangle, |1\rangle\}$ basis yields a probabilistic outcome when both $\alpha$ and $\beta$ are non-zero.
3. A global phase factor $e^{i\gamma}$ applied to a qubit state does not change the probabilities of measurement outcomes in the computational basis.
4. The Bloch sphere represents all pure single-qubit states as points on the surface of the sphere.
5. A real $2 \times 2$ matrix is a valid quantum gate only if it is unitary, not merely invertible.
6. The Pauli-X gate flips $|0\rangle$ to $|1\rangle$ and $|1\rangle$ to $|0\rangle$.
7. When a qubit is measured in a given basis, the state collapses to the basis state corresponding to the measurement outcome.
8. Unitary matrices preserve the norm of any vector they act on.
9. If $|\psi\rangle = \cos(\theta)|0\rangle + e^{i\phi}\sin(\theta)|1\rangle$, then the probability of measuring $|0\rangle$ is $\cos^2(\theta)$.
10. The state $\frac{1}{2}|0\rangle + \frac{\sqrt{3}}{2}|1\rangle$ is properly normalized.
11. If $|\psi\rangle = \frac{1}{\sqrt{3}}|0\rangle + \sqrt{\frac{2}{3}} e^{i\pi/4}|1\rangle$, then the probability of measuring $|0\rangle$ is $\frac{1}{3}$.
12. The states $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ and $\frac{1}{\sqrt{2}}(|0\rangle - |1\rangle)$ are orthogonal.
13. The Pauli-X matrix $X = \begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$ satisfies $X^2 = I$, where $I$ is the $2 \times 2$ identity matrix.
14. Applying the Pauli-Z gate $Z = \begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$ to $\frac{1}{\sqrt{2}}(|0\rangle + i|1\rangle)$ produces $\frac{1}{\sqrt{2}}(|0\rangle - i|1\rangle)$.

Market Structure​

	Perfect Competition	Monopolistic Competition	Oligopoly	Monopoly
Number of firms	Almost Infinite	Many	Few	One
Barriers to Entry	No barriers	No barriers / Low barriers	Some barriers	High barriers
Influence over Price	Price Taker	Limited	Some	Price Maker
Nature of Product	Homogeneous	Differentiated	Similar, Differentiated	No close substitutes
Examples	Common agricultural products	Fast-food restaurants	Auto Industry	Utilities

Porter's 5 Competitive Forces​

1. Threat of New Entrants: Profitable industries that yield high returns will attract new firms. New entrants eventually will decrease profitability for other firms in the industry.
2. Threat of Substitutes: A substitute product uses a different technology to try to solve the same economic need.
3. Bargaining Power of Customers: The market outputs. The ability of customers to put the firm under pressure, which also affects the customer's sensitivity to price changes.
4. Bargaining Power of Suppliers: The market inputs. Suppliers of raw materials, components, labor, and services (such as expertise) to the firm can be a source of power over the firm when there are few substitutes.
5. Competitive rivalry: For most industries the intensity of competitive rivalry is the major determinant of the competitiveness of the industry.

Threat of New Entrants​

Barriers to entry ⬆️, Profits ⬆️

• How difficult it is for new business to enter an industry and compete with already established ones.
• Many competitors lead to lower average profits
• Threat of New Entrants:
  • Barriers to entry
  • Economies of scale
  • Brand loyalty
  • Capital requirements
  • Cumultative experience
  • Government policies
  • Access to distribution channels
  • Switching costs

Threat of Substitute Products​

• A substitute product or service is an alternative that serves the same purpose for the customers, from a different industry.
• For example,
  • Taxi vs. Uber
  • Train vs. Plane
  • Tea vs. Coffee vs. Soft Drinks
• Threat of Substitutes Products:
  • Number of substitute products available
  • Buyer propensity ot substitute
  • Relative price performance of substitute
  • Perceived level of product differentiation
  • Switching costs

Bargaining Power of Customers and Suppliers​

• Bargaining power of customers:
  • Number of customers
  • Size of each customer order
  • Differences between competitors
  • Price sensitivity
  • Buyer's ability to substitute
  • Buyer's information availability
  • Switching costs
• Bargaining power of suppliers:
  • Number of suppliers
  • Size of suppliers
  • Uniqueness of each supplier's product
  • Focal company's ability to substitute

Rivalry among Existing Competitors​

• The extent of competition within an industry
• Price wars
• Rivalry among existing competitors:
  • Number of competitors
  • Diversity of competitors
  • Industry concentration
  • Industry growth
  • Quality differences
  • Brand loyalty
  • Barriers to exit
  • Switching costs
• For example,
  • Woolworths vs. Coles
  • Apple vs. Samsung

KANO Model​

• Expected (Basic or Must-be) Attribute: whose presence doesn't directly increase satisfaction, but their absence causes extreme dissatisfaction.
  • car: a functioning brake is a must be quality
  • hotel: providing a clean room is a basic necessity
• One-Dimensional (Performance) Attribute: can both satisfy and dissatisfy customers depending on their execution.
  • car: acceleration
  • hotel: waiting service at a hotel
• Attractive (Delight) Attribute: differentiate products and services, creating a "wow factor" and delighting customers when present, but causing no dissatisfaction when absent.
  • car: advanced parking sensor
  • hotel: providing free food
• Indifferent Attribute
  • car: the color of the car
  • hotel: highly polite speacking and very prompt responses not be necessary to satisfy customers
• Reverse Attribute
  • web: auto-playing videos/audio
  • venue: unnecessary security checks at the entrance of a venue

Possible movement of Attributes' place​

• As customer expectations change with the level or performance from competing products, attributes can move from delighter to performance need and then to basic need.

Profit Model​

• Ad-Supported: Provide content or services for free to one party while selling listneners, viewers, or "eyeballs" another party.
• Auction: Allow a merket-and its users-to set the price for goods and services.
• Bundled Pricing: Sell in a single transaction two or more items that could be sold as standalong offerings.
• Cost Leadership: Keep variable costs low and sell high volumes at low prices.
• Disaggregated Pricing: Allow customers to buy exactly-and only-what they want.
• Financing: Capture revenue not from the direct sale of a product but from structured payment plans and after-sale interest.
• Flexible Pricing: Vary prices for an offering based on demand.
• Float: Receive payment prior to building the offering; earn interest on that money prior to delivering the goods.
• Forced Scarcity: Limit the supply of offerings available, by quantity, time frame, or access, to drive up demand and/or prices.
• Freemium: Offer basic services for free while charging a premium for advanced or special features.
• Installed Base: Offer a "core" product for slime margins (or even a loss) to drive demand and loyalty; then realize profit on additional products and services.
• Licensing: Grant permission to a group or individual to use your offering in a defined way for a specified payment.
• Membership: Charge a time-based payment to allow access to locations, offerings, or services that non-members don't have.
• Metered Use: Allow customeres to pay only for what they use.
• Microtransactions: Sell many items for as little as a dollar-or even only one cent- to drive impulse purchases.
• Premium: Price at a higher margin than competitors, usually for a superior product, offering, experience, service, or brand.
• Risk Sharing: Waive standrad fees or costs if certain metrics aren't achieved, but receive outsize gains when they are.
• Scaled Transactions: Maximize margins by pursuing high-volume, large-scale transactions when unit costs are relatively fixed.
• Subscriptiuon: Create predictable cash flows by charging customers upfront (a one time or recurring fee) to have access to the product or service orver time.
• Switchboard: Connect multiple sellers with multiple buyers. The more buyers and sellers who join, the more valuable the switchboard becomes.
• User-Defined: Invite customers to set the prcie they wish to pay.

Network​

• Alliances: Share risks and revenues to jointly improve individual competitive advantage.
• Collaboration: Partner with others for mutual benefit.
• Complementary partnering: Leverage assets by sharing them with companies that serve similar markets but offer different products and services.
• Consolidation: Acquire multiple companies in the same market or complementary markets.
• Coopetition: Join forces with someone who would normally be your competitior to achieve a common goal.
• Franchising: License business principles, processes, and brand to paying partners.
• Merger/Acquisition: Combine two or more entities to gain accesss to capabilities and assets.
• Open Innovation: Obtain access to processes or patents from other companies to leverage, extend, and build on expertise, and/or do the same with internal IP and processes.
• Secondary Markets: Connect waste streams, by-products, or other alternative offerings with those who want them.
• Supply Chain Integration: Coordinate and integrate information and/or processes across a company or different parts of the value chain.

Structure​

• Asset Standardization: Reduce operating costs and increase connectivity and modularity by standardizing your assets.
• Competency Center: Cluster resources, practices, and expertise into centers that support functions across the organization to increase efficiency and effectiveness.
• Corporate University: Provide job-specific or company-specific training for managers.
• Decentralized Management: Devolve decision-making governance closer to the people or business interfaces.
• Incentive Systems: Offer rewards (financial or non-financial) to provide motivatino for a particular course of action.
• IT Integration: Integrate technology resources and applications.
• Knowledge Management: Share releavant information internally to reduce redundancy and improve job performance.
• Organizational Design: Make from follow function and align infrastructure with core qualities and business processes.
• Outsourcing: Assign to a vendor responsibility for developing or maintaining a ssystem.

Process​

• Crowdsourcing: Outsource repetitive or challenging work to a large group of semi-organized individuals.
• Flexible Manufacturing: Use a production system that can rapidly react to changes and still operate efficiently.
• Flexible Manufacturing: Use a production system that can rapidly react to changes and still operate efficiently.
• Intellectual Property: Use a proprietary process to commercialize ideas in ways that others cannot copy.
• Lean Production: Reduce waste and cost in your manufacturing process and other operations.
• Localization: Adapt an offering, process, or experience to target a specific culture or region.
• Logistics Systems: Manage the flow of goods, information, and other resources between the point of origin and the point of use.
• On-Demand Production: Produce items after an order has been received to avoid carrying costs of inventory.
• Predictive Analytics: Model past performance data and predict future outcomes to design and price offerings accordingly.
• Process Automation: Apply tools and infrastructure to manage routine activities in order to free up employees for other tasks.
• Process Efficiency: Create or produce more while using less in terms of materials, energy consumption, or time.
• Process Standardization: Use common products, procedures, and policies to reduce complexity, costs, and errors.
• Strategic Design: Employ a purposeful approach that manifests itself consistently across offerings, brands, and experiences.
• User-Generated: Put your users to work in creating and curating the content that powers your offerings.

Product Performance​

• Added Functionality: Add new capabilities to an existing offering.
• Conservation: Design your product so that end users can reduce their use of energy or materials.
• Customization: Enable altering to suit individual requirements or specifications.
• Ease of Use: Make your product simple, intuitive, and comfortable to use.
• Engaging Functionality: Provide an unexpected or newsworthy feature that elevates the customer interaction from the ordinary.
• Environmental Sensitivity: Create offerings that do no harm—or relatively less harm—to the environment.
• Feature Aggregation: Combine a number of existing features from disparate sources into a single offering.
• Focus: Design a product or service for a particular audience.
• Performance Simplification: Omit superfluous details, features, and interactions to reduce complexity.
• Safety: Increase the customer’s level of confidence and security.
• Styling: Impart a noteworthy style, fashion, or image to create a product that customers covet.
• Superior Product: Develop an offering of exceptional design, quality, and/or experience.

Product System​

• Complements: Sell additional related or peripheral products or services to a customer.
• Extensions/Plug-ins: Allow additions from internal or third-party resources that add functionality.
• Integrated Offering: Combine otherwise discrete components into a complete experience.
• Modular Systems: Provide a set of individual components that can be used independently, but gain utility when combined.
• Product Bundling: Put together several products for sale as one combined offering.
• Product/Service Platforms: Develop systems that connect with other partner products and services to create a holistic offering.

Service​

• Added Value: Include an additional service or function as part of the base price.
• Concierge: Provide premium service by taking on tasks for which customers don’t have time.
• Guarantee: Remove customer risk of lost money or time from product failure or purchase error.
• Lease or Loan: Let customers pay over time to lower their upfront costs.
• Loyalty Programs: Provide benefits and/or discounts to frequent and high-value customers.
• Personalized Service: Use the customer’s own information to provide perfectly calibrated service.
• Self-Service: Provide users with control over activities that would otherwise require an intermediary to complete.
• Superior Service: Provide service(s) of higher quality, efficacy, or which offer(s) a better experience than any competitor.
• Supplementary Service: Offer ancillary services that fit with your offering.
• Total Experience Management: Provide thoughtful, holistic management of the consumer experience across an offering’s lifecycle.
• Try Before You Buy: Let customers test and experience an offering before investing in it.
• User Communities/Support Systems: Provide a communal resource for product and service support, use, and extension.

Channel​

• Context-Specific: Offer timely access to offerings that are appropriate for a specific location, occasion, or situation.
• Cross-Selling: Offer appealing additional products, services, or information that will enhance an experience in situations where customers are likely to want to buy them.
• Diversification: Add and expand into new or different channels.
• Experience Center: Create space that encourages your customers to interact with your offerings—but purchase them through a different (and often lower cost) channel.
• Flagship Store: Create a retail outlet to showcase quintessential brand and product attributes.
• Go Direct: Skip traditional retail channels and connect directly with customers.
• Indirect Distribution: Use others as resellers who take responsibility for delivering an offering to the final user.
• Multi-Level Marketing: Sell bulk or packaged goods to an affiliated but independent sales force that turns around and sells it for you.
• Non-Traditional Channels: Employ novel and relevant avenues to reach and service customers.
• On-Demand: Deliver goods in real-time whenever or wherever they are desired.
• Pop-Up Presence: Create a noteworthy but temporary environment to showcase and/or sell offerings.

Brand​

• Brand Extension: Offer a new product or service under the umbrella of an existing brand.
• Brand Leverage: Allow others to use your brand name to lend them your credibility and extend your company’s reach.
• Certification: Develop a brand or mark that signifies and ensures certain desirable characteristics in third-party offerings.
• Co-Branding: Combine brands to mutually reinforce key attributes or enhance the credibility of an offering.
• Component Branding: Brand a discrete piece of the offering to make the whole appear more valuable.
• Private Label: Provide goods made by others packaged under your company’s brand.
• Transparency: Let customers see into your operations and participate with your brand and offerings.
• Values Alignment: Make your brand stand for a big idea or a set of values and express them consistently in all aspects of your company.

Customer Engagement​

• Autonomy and Authority: Grant users the power to shape their own experience.
• Community and Belonging: Facilitate visceral connections to make people feel they are part of a group or movement.
• Curation: Create a distinct point of view to build a strong identity for yourself and give your followers exactly what they want.
• Experience Automation: Remove the burden of repetitive tasks from users to simplify their lives and make new experiences seem magical.
• Experience Enabling: Extend the realm of what’s possible to offer a previously improbable experience.
• Experience Simplification: Reduce complexity and focus on delivering specific experiences exceptionally well.
• Mastery: Help customers to obtain great skill or deep knowledge of some activity or subject.
• Personalization: Alter a standard offering to allow the projection of the customer’s identity.
• Status and Recognition: Offer cues that confer meaning, allowing users—and those who interact with them—to develop and nurture aspects of their identity.
• Whimsy and Personality: Humanize your offering with small flourishes of on-brand, on-message ways of seeming alive.

Reference​

• Keeley, L., Walters, H., Pikkel, R., & Quinn, B. (2013). Ten Types of Innovation: The Discipline of Building Breakthroughs. John Wiley & Sons, Incorporated.