Quantum Computing Kitty Yeung, Ph.D. in Applied Physics Creative - - PowerPoint PPT Presentation
Introduction to Quantum Computing Kitty Yeung, Ph.D. in Applied Physics Creative Technologist + Sr. PM Microsoft www.artbyphysicistkittyyeung.com @KittyArtPhysics @artbyphysicistkittyyeung June 21, 2020 Hackaday, session 12 Other
Kitty Yeung, Ph.D. in Applied Physics Creative Technologist + Sr. PM Microsoft www.artbyphysicistkittyyeung.com @KittyArtPhysics @artbyphysicistkittyyeung June 21, 2020 Hackaday, session 12 Other communities, session 4
Computing every Sun
hardware, programming), Q&A
http://docs.microsoft.com/quantum
https://github.com/Microsoft/QuantumKatas/
throughout the week
ൿ |𝜒± =
ۧ |01 ± ۧ |10 2
and ൿ |𝜚± =
ۧ |00 ± ۧ |11 2
Bell states Take ۧ |𝜚+ as an example, upon measuring the first qubit, one obtains two possible results:
ۧ |𝜚′ = ۧ |00 with probability ½.
ۧ |𝜚′′ = ۧ |11 with probability ½. If the second qubit is measured, the result is the same as the above. This means that measuring
Math insert – entangled states cannot be factored back to individual qubits-------------- Remember in section 1.1, a two-qubit state can be obtained by doing a tensor product
two individual qubits. For example, |𝜚±ൿ =
|00ۧ±|11ۧ 2
=
1 2 1 2
. If we want to factor it back to two separate qubits as in 𝑏 𝑐 ⊗ 𝑑 𝑒 , then this set of equations need to be simultaneously satisfied 𝑏𝑑 =
1 2 , 𝑏𝑒 = 0, 𝑐𝑑 = 0 and 𝑐𝑒 = 1 2 . Unfortunately, it is impossible. This set of
equations has no solution. It can only be 50% chance of getting |00ۧ = 1 0 ⊗ 1 0 or |11ۧ = 0 1 ⊗ 0 1 .
Check out more commonly made mistakes https://quantumfactsheet.github.io/
𝐷𝑂𝑃𝑈 = 1 1 1 1 𝐷𝑂𝑃𝑈| ۧ 10 = 1 1 1 1 1 = 1 = | ۧ 11 . Similarly, 𝐷| ۧ 00 = | ۧ 00 , 𝐷| ۧ 01 = | ۧ 01 and 𝐷| ۧ 11 = | ۧ 10 .
Math insert - Matrix multiplication ------------------------------------------------------------------- Gates are N by N matrices that multiply to state with 2N vector elements. They follow the rules such that 𝑏 𝑐 𝑑 𝑒 𝑦 𝑧 = 𝑏𝑦 + 𝑐𝑧 𝑑𝑦 + 𝑒𝑧 , 𝑏 𝑐 𝑑 𝑒 𝑓 𝑔 ℎ 𝑗 𝑦 𝑧 𝑨 = 𝑏𝑦 + 𝑐𝑧 + 𝑑𝑨 𝑒𝑦 + 𝑓𝑧 + 𝑔𝑨 𝑦 + ℎ𝑧 + 𝑗𝑨 ′ and so on.
Target B controlled by A CNOT
Try proving this table
manipulate qubit states (vectors) through matrix multiplications unitarity 𝑉⟊𝑉 = 𝐽 So that it is reversible and probabilities add up to 1
Math insert – unitary, adjoint or Hermitian conjugate ----------------------------------------------------- In math, unitarity means 𝑉⟊𝑉 = 𝐽, where 𝐽 is the identity matrix and the “⟊” symbol (reads “dagger”) means adjoint or Hermitian conjugate of matrix 𝑉. It can be further written as 𝑉⟊ = (𝑉∗)𝑈 = (𝑉𝑈)∗, where “T” denotes transpose and “*” complex conjugate: 𝑉1 𝑉2 ⋮ 𝑉𝑂
𝑈
= 𝑉1 𝑉2 … 𝑉𝑂 and if 𝑏 = 𝑏0 + 𝑗𝑏1, then 𝑏∗ = 𝑏0 − 𝑗𝑏1 by definition. Therefore, 𝑏 𝑐 𝑑 𝑒
⟊
= 𝑏∗ 𝑑∗ 𝑐∗ 𝑒∗ .
Superdense Coding Teleportation CHSH Game
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