The IBM Quantum Computing Platform

Martin Koppenh¨ofer https://www.quantumtheory-bruder.physik.unibas.ch/ Online resources

https://www.quantumtheory-bruder.physik.unibas.ch/ people/martin-koppenhoefer/ quantum-computing-and-robotic-science-workshop.html

installation guide material for this session slides

2 Outline

1 Recap Overview of quantum-computing platforms Bell states

2 Programming the quantum computer with python The qiskit framework Programming session 1

3 Superdense coding Programming session 2

4 Quantum algorithms Deutsch algorithm Programming session 3

3 Recap

spins in large molecules + NMR ions in electromagnetic traps neutral atoms in optical lattices optical quantum computing 31P donor atoms in silicon electron spins in semiconductor quantum dots superconducting electrical circuits ﬂux qubit * charge qubit phase qubit * transmon qubit topological qubits

* online access

4 Recap Bell states

1 2 3 x H 1 |β00i = √ (|00i + |11i) |βxy > 2 CNOT 1 y |β01i = √ (|01i + |10i) 2 1 |β10i = √ (|00i − |11i) 1 input state: |xyi = |00i 2 2 apply Hadamard gate 1 |β i = √ (|01i − |10i) 1 1 11 Hˆ = √1 : 2 2 1 −1 √1 (|00i + |10i) General expression: 2 |β i = √1 (|0yi + (−1)x |1¯yi) 3 apply CNOT gate: xy 2 √1 (|00i + |11i) = |β i 2 00

5 Recap Bell states

6 Recap Bell states on a real quantum processor

7 Programming the quantum computer with python The qiskit framework

8 Programming the quantum computer with python The qiskit framework

Terra Ignis deﬁne quantum algorithms characterize quantum by quantum circuits / pulses hardware adapt quantum circuits to reconstruct quantum states the hardware (transpilation) (tomography) connect to the quantum compensate noise and errors hardware (mitigation) visualize results Aqua Aer predeﬁned algorithms for simulate quantum typical applications algorithms

9 Programming the quantum computer with python Programming session 1

Content deﬁning quantum circuits in python (Terra) state-vector simulator (Aer) QASM simulator (Aer) device imperfections

10 Programming the quantum computer with python Programming session 1

Agenda you will be split into small teams (in breakout rooms) in each breakout room, introduce you quickly to your teammates one participant turns on screen sharing discuss and code together the exercise after a while, the host will close the breakout rooms and let you return to the main session

11 Superdense coding Idea

two parties: Alice (A) and Bob (B) Alice wants to transmit 2 classical bits of information to Bob classically, she needs to send two bits to Bob quantum-mechanically, she can send one qubit to Bob!

12 Superdense coding Idea

Bell states 1 1 |β00i = √ (|00i + |11i) |β01i = √ (|01i + |10i) 2 2 1 1 |β10i = √ (|00i − |11i) |β11i = √ (|01i − |10i) 2 2

Consider that Alice and Bob share a Bell state |β00i Alice can convert this Bell state into any other Bell state herself (with no help from Bob)

σˆx ⊗ 1 |β00i = |β01i

σˆz ⊗ 1 |β00i = |β10i

iσˆy ⊗ 1 |β00i = |β11i

iσˆy =σ ˆz σˆx

13 Superdense coding Protocol

A single qubit can transmit two classical bits of information

ALICE t : |ai |bi |0i |0i a a 0 |0i+|1i b b t : |ai |bi √ |0i 1 2 σz |00i+|11i t : |ai |bi √ 2 2

0 HH a i.e. |ai |bi |β00i 0 b t3: |ai |bi |β0bi BOB t4: |ai |bi |βabi t t t t t t t 0 1 2 3 4 5 6 t6: |ai |bi |ai |bi The information about a and b is encoded in the entangled state of the two-qubit system shared by Alice and Bob

14 Superdense coding Programming session 2

Content transpiling quantum circuits (Terra) error mitigation (Ignis)

15 Quantum algorithms Deutsch algorithm

Is f (x): {0, 1} → {0, 1} balanced or constant? balanced if f (0) = f (1) ⇔ f (0) ⊕ f (1) = 1 constant if f (0) = f (1) ⇔ f (0) ⊕ f (1) = 0

Uˆf : |x, yi → |x, y ⊕ f (x)i quantum circuit implementing y + f (x) mod 2 in the second qubit example: input |xi = √1 (|0i + |1i), |yi = |0i leads to 2 1 √ (|0, f (0)i + |1, f (1)i) 2 ⇒ one “application” of f results in both f (0) and f (1)! but: measurement gives either |0, f (0)i or |1, f (1)i so, quantum parallelism does not help ...?

16 Quantum algorithms Deutsch algorithm

...it does if we transform the information in a clever way: |0> H x x H Uf |1> H y y+f(x) generate use quantum use superposition parallelism interference ﬁnal state is ∝ |f (0) ⊕ f (1)i ⊗ (|0i − |1i) ⇒ measuring the ﬁrst qubit gives a global property of f , namely f (0) ⊕ f (1), using only one evaluation of f (x) this is impossible on a classical computer!

18 Quantum algorithms Programming session 3

Content predeﬁned quantum algorithms (Aqua)

19 Educational material

https://qiskit.org/learn Qiskit textbook Youtube series Coding with Qiskit Online course Introduction to QC

20 Thank you for your attention.