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<title-slide titletype="EAI ICISML 2022" title="" modulenumber="" subtitle="Quantum Data Management and Quantum Machine Learning for Data Management: State-of-the-Art and Open Challenges"></title-slide>

---
# .darkblue[Quantum Mechanics]

.reference[Picture: <a href="https://commons.wikimedia.org/wiki/File:Hydrogen_Wave.gif" target="_blank">Source</a>]

.more-more-condensed.no-margin[
<table>
<tbody>
<tr>
<td style="width:80%">
.more-more-condensed[
- .darkblue[Very small particles and light behave differently from objects in normal life] 
- .darkblue[Mechanics of light and matter at the atomic and subatomic scale are described by quantum theory]
  - forming the underlying principles of chemistry and most of physics
- .darkblue[Quantum theory has brought us the information age with] its disruptive .darkblue[technologies of] 
  - .darkblue[transistors], 
  - .darkblue[lasers], 
  - .darkblue[nuclear power], and 
  - .darkblue[superconductivity]...
  - .bold.darkred[...and now also quantum computers!]
]
</td>
<td style="width:20%;vertical-align:top;line-height:0.6;" class="padding-left">
<img src="../../img/qc/intro/Hydrogen_Wave.gif" align="top" class="fullwidth"></img><br/>
.smaller-font[.darkblue[Wavefunctions of the electron] in a hydrogen atom at different energy levels. .darkblue[Brighter areas represent a higher probability] of finding the electron.]
</td>
</tr>
</tbody>
</table>
]

---
# Architectures of .darkblue[Emergent Hardware]
.reference[Extended from <a target="_blank" href="http://www.imprs-dynamics.mpg.de/pdfs/Plessl_talk.pdf">C. Plessl, Accelerating Scientific Computing with Massively Parallel Computer Architectures, IMPRS Winter School, Wroclaw, 2012</a>]

---
# <img src="../../img/keynotes/QuantumComputer.svg" align="top" width="10%"></img> .darkblue[Quantum Computer]

.reference[<a href="https://doi.org/10.1145/3410566.3410593" target="_blank">T. Bittner, S. Groppe. Avoiding blocking by scheduling transactions using quantum annealing. .em[IDEAS '20]</a>]

.more-more-condensed[
<table>
<tbody>
<tr>
<td style="width:65%">
<ul>
<li> use of .darkblue[quantum-mechanical phenomena such as superposition and entanglement] to perform computation</li>
<li> Different types of quantum computer, e.g.
  <ul><li> .darkblue[Universal Quantum Computer]
      <ul><li> uses <span class="darkblue">quantum logic gates</span> arranged in a circuit to do computation</li>
	      <li> <span class="darkblue">measurement</span> (sometimes called observation) assigns the observed variable to a single value</li>
      </ul></li>
  <li> .darkblue[Quantum Annealing]
      <ul><li> <span class="darkblue">metaheuristic for finding the global minimum</span> of a given objective function over a given set of candidate solutions</li>
          <li> i.e., some way to solve a special type of <span class="darkblue">mathematical optimization problem</span></li>
      </ul>
  </li>
</ul>
]
</td>
<td style="width:45%" class="textcenter">
<img src="../../img/qc/bloch/QCFullAdder.svg" align="top" class="fullwidth"></img><br/>
.smaller-font.darkblue[Quantum Circuit (Full Adder)]<br/>
<img src="../../img/ideas20/SimulatedVsQuantumAnnealing.svg" align="top" class="fullwidth"></img><br/>
.smaller-font.darkblue[Simulated versus Quantum Annealing]<br/>
</td>
</tr>
</tbody>
</table>

---
# .darkblue[Classical versus Quantum Computing]

.more-more-condensed.small-font[
<table class="result tablesmallpadding no-margin">
<tr>
<th style="width:15%"></th>
<th style="width:40%">Classical</th>
<th style="width:45%">Quantum</th>
</tr>
<tr>
<th>Information Unit</th>
<td style="vertical-align:top;">.bold[Bi]nary Digi.bold[t] (.darkblue[Bit]):
<ul>
<li>basis of a .darkblue[2-level system]</li>
<li>can be .darkblue[in state $0$ or $1$]</li>
</ul>
</td>
<td style="vertical-align:top;">.bold[Qu]antum .bold[Bit] (.darkblue[Qubit]):
<ul>
<li>basis of a .darkblue[2-level quantum system]</li>
<li>can be .darkblue[in state $|0\rangle$, $|1\rangle$ or in] a .darkblue[linear combination of both states]</li>
</ul>
</td>
</tr>
<tr>
<th>Operation</th>
<td style="vertical-align:top;">.darkblue[Logic Gate:]
<ul>
<li>performs .darkblue[on 1 or more bits to produce] a single .darkblue[bit output]</li>
</ul>
</td>
<td style="vertical-align:top;">.darkblue[Quantum Logic Gate:]
<ul>
<li>performs .darkblue[on 1 or more qubits to change the quantum state of] a .darkblue[single qubit]</li>
</ul>
</td>
</tr>
<tr>
<th>Example Operation</th>
<td style="vertical-align:top;">.darkblue[NOT]/Inverter:<br/>
<table><tbody><tr><td>Digital Circuit:</td><td><img src="../../img/qc/intro/ClassicalNotCircuit.svg" align="top" width="150em"></img></td></tr></tbody></table><br/>
<table style="text-align:center;line-height:0.9;" class="smaller-font" class="tablepadding">
<tbody>
<tr>
<td style="background-color:#d9ffb3">$In$</td>
<td style="background-color:#ffb3d1">$Out$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$0$</td>
<td style="background-color:#ffb3d1">$1$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$1$</td>
<td style="background-color:#ffb3d1">$0$</td>
</tr>
</tbody>
</table>

</td>
<td style="vertical-align:top;">.darkblue[NOT]/Pauli<sub>$x$</sub>-Gate:<br/>
<table class="no-padding no-margin"><tbody><tr><td>Quantum Circuit:</td><td><img src="../../img/qc/bloch/NOT.svg" align="top" width="150em"></img></td></tr>
<tr><td>Alternatively:</td><td><img src="../../img/qc/bloch/XGate.svg" align="top" width="150em"></img></td></tr></tbody></table>
<table style="text-align:center;line-height:0.9;" class="smaller-font" class="tablepadding">
<tbody>
<tr>
<td style="background-color:#d9ffb3">$In$</td>
<td style="background-color:#ffb3d1">$Out$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$|0\rangle$</td>
<td style="background-color:#ffb3d1">$|1\rangle$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$|1\rangle$</td>
<td style="background-color:#ffb3d1">$|0\rangle$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$</td>
<td style="background-color:#ffb3d1">$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$\frac{3\cdot i}{5}|0\rangle+\frac{4}{5}|1\rangle$</td>
<td style="background-color:#ffb3d1">$\frac{4}{5}|0\rangle+\frac{3\cdot i}{5}|1\rangle$</td>
</tr>
</tbody>
</table>

</td>
</tr>
</table>
]

---
# Representation of a .darkblue[Qubit in Bloch-Sphere]

.more-more-condensed[
- Angels .darkblue[$\theta$ and $\phi$] can be associated with .darkblue[spherical coordinates on] the so-called .darkblue[Bloch-sphere]:
<div class="textcenter">
<img src="../../img/qc/bloch/BlochSphere.svg" align="top" width="95%"></img>
</div>
]

---
# .darkblue[Classical Measurement/Observation]

.more-more-condensed[
- The .darkblue[state is not destroyed] by a measurement/observation in classical systems:

<div class="textcenter">
<img src="../../img/qc/bloch/ClassicalMeasurement.svg" align="top" width="85%"></img>
</div>
]

---
# .darkblue[Quantum Measurement/Observation] 1/2

.more-more-condensed[
- The .darkblue[state is not destroyed] by a measurement/observation in quantum mechanical systems .darkblue[for state $|0\rangle$ and $|1\rangle$]:

<div class="textcenter">
<img src="../../img/qc/bloch/MeasurementBasisStates.svg" align="top" width="85%"></img>
</div>
]

---
# .darkblue[Quantum Measurement/Observation] 2/2

.more-more-condensed[
- During observation a .darkblue[superposition state collapses to $|0\rangle$ or $|1\rangle$ according to] corresponding .darkblue[probabilities]:

<div class="textcenter">
<img src="../../img/qc/bloch/MeasurementSuperposition.svg" align="top" width="85%"></img>
</div>
]

---
# .darkblue[Measurement/Observation along other axis] (here y-axis)

.more-more-condensed[
- However, observation typically according to z-axis

<div class="textcenter">
<img src="../../img/qc/bloch/MeasurementYAxis.svg" align="top" width="90%"></img>
</div>
]

---
# .darkblue[Generator for True Random Numbers]

.more-more-condensed[
- .darkblue[Commercially available], see e.g.
  - <a href="https://www.magiqtech.com/solutions/network-security/" target="_blank">https://www.magiqtech.com/solutions/network-security/</a>
  - <a href="https://www.idquantique.com/random-number-generation/" target="_blank">https://www.idquantique.com/random-number-generation/</a>

<div class="textcenter">
<img src="../../img/qc/bloch/RandomGenerator.svg" align="top" width="70%"></img>
</div>
]

---
# .darkblue[Determining the states $(\theta,\phi)$ of identical prepared Qubits]

<div class="more-more-condensed small-font no-margin no-padding">
<table>
<tr>
<td class="small-font">
<ul><li> .darkblue[After one measurement] in one of the axis $(x, y, z)$, the .darkblue[qubit collapses to $|0_a\rangle$ or $|1_a\rangle$] with $a\in\{x, y, z\}$</li>
<li> .darkblue[As more identical prepared qubits are measured] in $a$ axis.darkblue[, as more] the measured distribution of $|0_a\rangle$ and $|1_a\rangle$ is getting closer to $P_{0_a}$ and $P_{1_a}\Rightarrow$ .darkblue[$\theta, \phi$ can be determined]</li>
</ul>
</td>
<td width="70%">
<div class="textcenter">
<img src="../../img/qc/bloch/EnsembleMeasurement.svg" align="top" width="100%"></img>
</div>
</td>
</tr>
</table>
</div>

---
# .darkblue[No-Cloning-Theorem] of 1 Qubit

.more-more-condensed.small-font[
- .darkblue[Only not perfect copying] possible of information in one of the $(x, y, z)$ axis.darkblue[, other information] of superposition .darkblue[gets lost]

<div class="textcenter">
<img src="../../img/qc/bloch/NoCloningTheorem.jpg" align="top" width="100%"></img>
</div>
]

---
# Operations via .darkblue[Quantum Logic Gates]

.more-more-condensed.no-margin.no-padding[
- .darkblue[quantum logic gates for 1 qubit: often rotation around one axis]
  - Relatively general quantum logic gate: rotation around a specified angle $\theta$:
	   
<table>
</tbody>
<tr>
<td style="vertical-align: top;" width="45%">
<div class="textcenter">
<img src="../../img/qc/bloch/BlochSphereNaked.svg" align="top" width="100%"></img>
</div>
</td>
<td style="vertical-align: top;" class="small-font">
Rotation operator for rotation around $x$-axis:<br/>
<img src="../../img/qc/bloch/RotationGateFormula.svg" align="top" width="500em"></img><br/>e.g. .bold[Pauli<sub>$x$</sub>-Gate]:<br/>

<table class="result small-font tablesmallpadding small-font">
<tbody>
<tr>
<th>Rotation Matrix</th>
<td>.small-font[$NOT = \left[\\begin{array}{cc} 0 & 1 \\\\ 1 & 0 \\end{array}\right]$]</td>
</tr>
<tr>
<th>Quantum Circuit</th>
<td><img src="../../img/qc/bloch/NOT.svg" align="top" width="150em"></img><br/>
Alternatively: <img src="../../img/qc/bloch/XGate.svg" align="top" width="150em"></img>
</td>
</tr>
<tr>
<th>Table of in- & outputs:</th>
<td>

<table style="text-align:center;line-height:0.9;" class="smaller-font" class="tablepadding">
<tbody>
<tr>
<td style="background-color:#d9ffb3">$In$</td>
<td style="background-color:#ffb3d1">$Out$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$|0\rangle$</td>
<td style="background-color:#ffb3d1">$|1\rangle$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$|1\rangle$</td>
<td style="background-color:#ffb3d1">$|0\rangle$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$</td>
<td style="background-color:#ffb3d1">$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$\frac{3\cdot i}{5}|0\rangle+\frac{4}{5}|1\rangle$</td>
<td style="background-color:#ffb3d1">$\frac{4}{5}|0\rangle+\frac{3\cdot i}{5}|1\rangle$</td>
</tr>
</tbody>
</table>

</td>
</tr>
</tbody>
</table>

</td>
</tr>
</tbody>
</table>
]

---
# .darkblue[Controlled NOT (CNOT)]-Gate

.more-more-condensed[
- ".em[.darkblue[If] the .darkblue[control bit] is set, .darkblue[then] it .darkblue[flips] the .darkblue[target bit].]"

<table class="result small-font tablesmallpadding small-font">
<tbody>
<tr>
<th>Quantum Circuit</th>
<th>Table of in- & outputs</th>
<th>Rotation Matrix $R$</th>
</tr>
<tr>
<td><img src="../../img/qc/bloch/CNOT.svg" align="top" width="220em"></img></td>
<td>

<table style="text-align:center;line-height:0.9;" class="smaller-font" class="tablepadding">
<tbody>
<tr>
<td colspan="2" style="background-color:#d9ffb3"><b>Inputs</b></td>
<td style="background-color:#ffb3d1"><b>Output</b>
</td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>Control $C$</b></td>
<td style="background-color:#d9ffb3;width:3em;"><b>Target $T_{before}$</b></td>
<td style="background-color:#ffb3d1;width:3em;"><b>Target $T_{after}$</b></td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;">$|0\rangle$</td>
<td style="background-color:#d9ffb3;width:3em;">$|0\rangle$</td>
<td style="background-color:#ffb3d1;width:3em;">$|0\rangle$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;">$|0\rangle$</td>
<td style="background-color:#d9ffb3;width:3em;">$|1\rangle$</td>
<td style="background-color:#ffb3d1;width:3em;">$|1\rangle$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;">$|1\rangle$</td>
<td style="background-color:#d9ffb3;width:3em;">$|0\rangle$</td>
<td style="background-color:#ffb3d1;width:3em;">$|1\rangle$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;">$|1\rangle$</td>
<td style="background-color:#d9ffb3;width:3em;">$|1\rangle$</td>
<td style="background-color:#ffb3d1;width:3em;">$|0\rangle$</td>
</tr>
<tr>
<td colspan="3" style="background-color:#ffb3d1;width:3em;">$R\cdot\frac{1}{\sqrt{2}}(|01\rangle+|11\rangle) = \frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$</td>
</tr>
</tbody>
</table>

</td>
<td>
$\left[\\begin{array}{cccc} 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 \\\\  \\end{array}\right]$<br/>
</td>
</tr>
</tbody>
</table>

- .darkblue[reversible] gate: 2 applications of CNOT retrieves the original input
- .darkblue[Classical analog] of the CNOT gate .darkblue[is] a .darkblue[reversible XOR] gate (i.e., they have analogous in- & and outputs for $\\{|0\rangle, |1\rangle\\}$ inputs)
- $|a,b\rangle \mapsto |a,a\oplus b\rangle$, where $\oplus$ is XOR
]

---
# .darkblue[Bell States via Entanglement]

.reference[<a href="https://doi.org/10.1126/science.aan3211" target="_blank">Yin et al., "Satellite-based entanglement distribution over 1200 kilometers". Quantum Optics. 356: 1140–1144, 2017</a>]

.more-more-condensed[
<table class="result small-font tablesmallpadding">
<tbody>
<tr>
<th>Entanglement</th>
<th>Quantum Circuit</th>
<th>Table of in- & outputs</th>
</tr>
<tr>
<th>Correlated</th>
<td><img src="../../img/qc/bloch/CorrelatedBellState.svg" align="top" width="160em"></img></td>
<td>

<table style="text-align:center;line-height:0.9;" class="smaller-font">
<tbody>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>$A$</b></td>
<td style="background-color:#ffb3d1;width:3em;"><b>$B$</b></td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>$|0\rangle$</b></td>
<td style="background-color:#ffb3d1;width:3em;"><b>$|0\rangle$</b></td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>$|1\rangle$</b></td>
<td style="background-color:#ffb3d1;width:3em;"><b>$|1\rangle$</b></td>
</tr>
<tr>
<td colspan="3" style="background-color:#ffb3d1;width:3em;" style="text-align="right"><b>$\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$</b></td>
</tr>
</tbody>
</table>

</td>
</tr>
<tr>
<th>Anti-Correlated</th>
<td><img src="../../img/qc/bloch/AntiCorrelatedBellState.svg" align="top" width="160em"></img></td>
<td>

<table style="text-align:center;line-height:0.9;" class="smaller-font">
<tbody>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>$A$</b></td>
<td style="background-color:#ffb3d1;width:3em;"><b>$B$</b></td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>$|0\rangle$</b></td>
<td style="background-color:#ffb3d1;width:3em;"><b>$|1\rangle$</b></td>
</tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>$|1\rangle$</b></td>
<td style="background-color:#ffb3d1;width:3em;"><b>$|0\rangle$</b></td>
</tr>
<tr>
<td colspan="3" style="background-color:#ffb3d1;width:3em;" style="text-align="right"><b>$\frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)$</b></td>
</tr>
</tbody>
</table>

</td>
</tr>
</tbody>
</table>
- .darkblue[Entangled qubits] .darkblue[at different locations] .darkblue[are] still .darkblue[entangled] (phenomena appears to happen .darkblue[instantaneously ignoring speed of light]: open question in physics)
  - As of 2017 experimentally verified for distances of up to 1200 kilometers
- .darkblue[Succeeding operations on entangled qubits] do not change the state of the other entangled qubits if the operation is not a measurement
]

---
# .darkblue[Digital versus Quantum Circuits]

.reference[<sup>1</sup>The dotted square marks a superfluous gate if uncomputation to restore the B output is not required. <a href="https://doi.org/10.1007%2Fbf01886518" target="_blank">[Feynman, 1986]</a>]

.more-more-condensed[
<table class="result">
<tr>
<th style="width:5%"></th>
<th style="width:45%">Digital Circuit</th>
<th style="width:55%">Quantum Circuit</th>
</tr>
<tr>
<th>.small-font[Building Blocks]</th>
<td class="textcenter">.small-font[Logic Gates]</td>
<td class="textcenter">.small-font[Quantum Logic Gates]</td>
</tr>
<tr>
<th>.small-font[Full Adder Example]</th>
<td class="textcenter"><img src="../../img/qc/bloch/Full_Adder_using_NAND_gates.svg" align="top" width="98%"></img><br/>.small-font[consists of NAND gates]</td>
<td class="textcenter"><img src="../../img/qc/bloch/QCFullAdder.svg" align="top" width="50%"></img><br/>.small-font[consists of Toffoli and CNOT gates<sup>1</sup>]</td>
</tr>
<tr>
<th>.small-font[In- and Output Full Adder]</th>
<td>

<table style="text-align:center;line-height:0.9;" class="smaller-font">
<tbody><tr>
<td colspan="3" style="background-color:#d9ffb3"><b>Inputs</b></td>
<td colspan="2" style="background-color:#ffb3d1"><b>Outputs</b>
</td></tr>
<tr>
<td style="background-color:#d9ffb3;width:3em;"><b>A</b></td>
<td style="background-color:#d9ffb3;width:3em;"><b>B</b></td>
<td style="background-color:#d9ffb3;width:3em;"><b>C</b><sub>in</sub></td>
<td style="background-color:#ffb3d1;width:3em;"><b>C</b><sub>out</sub></td>
<td style="background-color:#ffb3d1;width:3em;"><b>S</b>
</td></tr>
<tr>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#ffb3d1">0</td>
<td style="background-color:#ffb3d1">0
</td></tr>
<tr>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#ffb3d1">0</td>
<td style="background-color:#ffb3d1">1
</td></tr>
<tr>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#ffb3d1">0</td>
<td style="background-color:#ffb3d1">1
</td></tr>
<tr>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#ffb3d1">1</td>
<td style="background-color:#ffb3d1">0
</td></tr>
<tr>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#ffb3d1">0</td>
<td style="background-color:#ffb3d1">1
</td></tr>
<tr>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#ffb3d1">1</td>
<td style="background-color:#ffb3d1">0
</td></tr>
<tr>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">0</td>
<td style="background-color:#ffb3d1">1</td>
<td style="background-color:#ffb3d1">0
</td></tr>
<tr>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#d9ffb3">1</td>
<td style="background-color:#ffb3d1">1</td>
<td style="background-color:#ffb3d1">1
</td></tr>
</tbody></table>

</td>
<td style="line-height:0.9;">

.small-font[.bold[$|0\rangle$ and $|1\rangle$ as input:] Output is $|0\rangle$ and $|1\rangle$ analogous to digital circuit.<br/>.bold[Superpositions as input:] Superpositions as output with corresponding probabilities for basic quantum states, e.g.:<br/>]

<table style="text-align:center;line-height:0.9;" class="smaller-font">
<tbody>
<tr>
<td style="background-color:#d9ffb3;"><b>A</b></td>
<td style="background-color:#d9ffb3;"><b>B</b></td>
<td style="background-color:#d9ffb3;width:3em;"><b>C</b><sub>in</sub></td>
<td style="background-color:#ffb3d1;width:3em;"><b>C</b><sub>out</sub></td>
<td style="background-color:#ffb3d1;"><b>S</b>
</td></tr>
<tr>
<td style="background-color:#d9ffb3">$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$</td>
<td style="background-color:#d9ffb3">$|0\rangle$</td>
<td style="background-color:#d9ffb3">$|0\rangle$</img></td>
<td colspan="2" style="background-color:#ffb3d1">.bold[ABC<sub>out</sub>S]: $\frac{1}{\sqrt{2}}(|0000\rangle+|1001\rangle)$</td>
</tr>
<tr>
<td style="background-color:#d9ffb3">$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$</td>
<td style="background-color:#d9ffb3"><img src="../../img/qc/bloch/AntiCorrelatedBellState.svg" align="top" width="80em"></img></td>
<td style="background-color:#d9ffb3">$|0\rangle$</img></td>
<td style="background-color:#ffb3d1">$|0\rangle$</td>
<td style="background-color:#ffb3d1">$|1\rangle$</td>
</tr>
</tbody></table>

</td>
</tr>
</table>
]

---
# .darkblue[Timeline of Quantum Computers]
.reference[<a href="https://en.wikipedia.org/wiki/List_of_quantum_processors" target="_blank">Main Data Source</a> Roadmaps: <a href="https://research.ibm.com/blog/ibm-quantum-roadmap" target="_blank">IBM</a> <a href="https://quantumai.google/research" target="_blank">Google</a> <a href="https://doi.org/10.1007/s42354-021-0342-8" target="_blank">Quantum Brilliance</a> <a href="https://www.dwavesys.com/media/xvjpraig/clarity-roadmap_digital_v2.pdf" target="_blank">D-Wave</a> <a href="https://education.jlab.org/qa/mathatom_05.html" target="_blank">#Atoms on Earth</a> <a href="https://www.popularmechanics.com/space/a27259/how-many-particles-are-in-the-entire-universe/" target="_blank">#Particles in Universe</a>]

---
# .darkblue[Noisy Intermediate-Scale Quantum (NISQ)]
.reference[<a target="_blank" href="https://doi.org/10.22331/q-2018-08-06-79">[P'18]</a>]

.more-more-condensed.no-margin.darkblue[
<div class="textcenter">
<img src="../../img/qc/intro/NISQ.svg" align="top" width="70%"></img>
</div>

- quantum computers with 50-100 qubits: noise in quantum gates limits the size of quantum circuits that can be executed reliably
- Such NISQ devices may be able to perform tasks which surpass the capabilities of today’s classical digital computers with application areas like quantum chemistry, optimization & machine learning
- 100-qubit quantum computers are (only) intermediate technologies
]

---
# .darkblue[Potential of Quantum Algorithms]

.more-more-condensed[
- <a href="https://quantumalgorithmzoo.org/" target="_blank">Quantum Algorithm Zoo</a> .darkgray[as example of collection of .em[important] quantum algorithms]
<table class="result tablesmallpadding small-margin-bottom">
<tbody>
<tr>
<th>Covered Years</th>
<td>1974-today</td>
</tr>
<tr>
<th>#Investigated References</th>
<td>430 .darkgray.smaller-font[(visited on October 2021)]</td>
</tr>
<tr>
<th>#Algorithms</th>
<td>.bold.darkred[64]</td>
</tr>
<tr>
<th>Speedups</th>
<td>
.darkred.bold[Superpolynomial: 31],<br/>
.darkred[Polynomial: 27],<br/>
.darkblue[Constant factor]: 1, .darkblue[Varies]: 3, .darkblue[Various]: 1,<br/>
.darkblue[Unknown]: 1
</td></tr>
</tbody>
</table>
.legend.small-font[.bold[Terminology:]<br/>
$\alpha$: positive constant<br/>
$C(n)$: runtime of the best known classical algorithm<br/>
$Q(n)$: runtime of the quantum algorithm<br/>
Superpolynomial Speedup: $C = 2^{\Omega(Q^\alpha)}$<br/>
Polynomial Speedup: otherwise
]
]

---
# Very Important Quantum Algorithms 1/2: .darkblue[Shor]'s Algorithm<sup>1</sup>

.reference[<sup>1</sup> <a href="https://doi.org/10.1109/SFCS.1994.365700" target="_blank">[Shor, 1994]</a> <sup>2</sup> <a href="https://doi.org/10.1103%2FPhysRevA.54.1034" target="_blank">[Beckman et al., 1996]</a>]

.more-more-condensed.no-margin[
<table>
<tbody>
<tr style="vertical-align:top">
<td style="width:32%" style="vertical-align:top;"><img src="../../img/qc/intro/FactorizationIsHard.svg" align="top" style="vertical-align:top;" class="fullwidth"></img></td>
<td style="width:68%">
<ul>
<li>.darkblue[factoring integers in polynomial time]
  <ul><li>.darkblue[Depth of quantum circuit<sup>2</sup>] to factor integer $N$: $O((log\ N)^2 (log\ log\ N) (log\ log\ log\ N))$</li>
  <li>superpolynomial speedup, i.e., .darkblue[almost exponentially faster than] the most efficient known .darkblue[classical factoring algorithm] (general number field sieve): $O(e^{1.9(log\ N)^{\frac{1}{3}}(log\ log\ N)^{\frac{2}{3}}})$</li>
  </ul>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
- Important for cryptography .darkblue[$\rightarrow$ Post-Quantum Cryptography]
- Most quantum algorithms with .darkblue[superpolynomial speedup] like Shor's algorithm .darkblue[are based on quantum Fourier transforms] .darkgray[(quantum analogue of inverse discrete Fourier transform)]
]

---
# Very Important Quantum Algorithms 2/2: .darkblue[Grover]'s Search Algorithm

.reference[<a href="https://doi.org/10.1145/237814.237866" target="_blank">Lov K. Grover. A fast quantum mechanical algorithm for database search. .em[STOC'96], 1996</a>]

.more-more-condensed[
- .darkblue[Black box] function (oracle) $f:${$0,...,2^b -1$} $\mapsto$ {$true, false$}
- .darkblue[Grover's search] algorithm finds one $x \in${$0,...,2^b -1$},<br/>such that $f(x)=true$
  - if there is only .darkblue[one solution]: $\frac{\pi}{4}\cdot\sqrt{2^b}$ basic steps each of which calls $f$<br/>Let $f'(b)$ be runtime complexity of $f$ for testing $x$ to be true:<br/>.darkblue[$\Rightarrow O(\sqrt{2^b}\cdot f'(b))$]
  - if there are .darkblue[$k$] possible .darkblue[solutions]: .darkblue[$O(\sqrt{\frac{2^b}{k}}\cdot f'(b))$]
- .darkblue[Basis of many other quantum algorithms and applications]
]

---
# .darkblue[Quantum Data Management]

---
# .darkblue[Quantum Data Management - .bold[DM4QC]]

.more-more-condensed[
- What can .darkblue[data management] do .darkblue[for quantum computing]?
   - vision of a <span class="darkblue">database management system</span>
         - offering easy <span class="darkblue">access to quantum computing applications</span> 
		 - by <span class="darkblue">integrating</span> high-level <span class="darkblue">functionalities for quantum computing applications</span>
		      - <span class="darkblue">extension of query</span> language to call quantum computing subroutines
			  - <span class="darkblue">easy storing and accessing the input and output</span> of quantum computing applications in DBMS
			  - <span class="darkblue">automatically choosing of the needed and available quantum resources as well as apply hybrid algorithms</span><ul><li>tailoring in a way that <span class="darkblue">missing resources</span> and support of qubits and circuit depths in quantum computers <span class="darkblue">are overcome by taking over more computations by classical algorithms or simulations of quantum computing</span> on classical hardware</li></ul>
]

---
# .darkblue[Quantum Data Management - .bold[DM4QML]]

.more-more-condensed[
- What can .darkblue[data management] do .darkblue[for quantum computing and especially .bold[quantum machine learning (QML)]]?
   - <span class="darkblue">trend for DBMS to offer machine learning</span> functionalities
   - <span class="darkblue">machine learning<span> tasks <span class="darkblue">pose additional requirements</span> for
         <ul><li><span class="darkblue">scalable training</span>, where often large-scale data sets are processed in comparison to the (often simple and efficient to perform) application/prediction phase</li>
         <li><span class="darkblue">storing models and their parameters</span> after training for their use in the application/prediction phase</li>
         <li><span class="darkblue">language constructs for expressing complex machine learning tasks in a simple way</span> while combining these language constructs with query languages</li>
         <li><span class="darkblue">automatic choosing and optimizing models and machine learning</span> tasks</li></ul>
   - Open challenges: <span class="darkblue">integration of QML into DBMS</span> and adapting the requirements and solutions to QML and available quantum computers with an additional focus on hybrid algorithms
         - <span class="darkblue">Hybrid algorithms combine a quantum algorithm with a classical algorithm</span> to flexibly adapt the available system configuration of classical and quantum hardware
]

---
# .darkblue[Quantum Data Management - .bold[QC4DM]]

.more-more-condensed[
- What can .darkblue[quantum computing] do .darkblue[for data management]?
   - .darkblue[Speeding up some of the tasks of data management] with high runtime complexity
         - Examples: <span class="darkblue bold">Optimizing queries and transaction schedules</span> 
]

---
# Using .darkblue[Hardware Accelerator] for optimizing Queries / Transaction Schedules
.reference[<a href="https://doi.org/10.1145/3410566.3410593" target="_blank">[BG20a]</a> <a href="http://nbn-resolving.de/urn:nbn:de:101:1-2020112218332015343957" target="_blank">[BG20b]</a>  <a href="https://doi.org/10.1145/3472163.3472164" target="_blank">[GG21]</a>]

---
# .darkblue[Approaches for Query/Transaction Schedule Optimization]

---
# .darkblue[Algorithms] .small-font30[(used e.g. in Query Optimization)] .darkblue[and their Quantum Counterparts]

.more-more-condensed.small-font[
<table class="result tablesmallpadding margin-bottom">
<tbody>
<tr>
<th>Query Optimization Approach</th>
<th>Basic Algorithm</th>
<th>Quantum Computing Counterpart</th>
</tr>
<tr>
<td><a href="https://doi.org/10.1145/582095.582099" target="_blank">[S+79]</a></td>
<td>Dynamic Programming <a href="https://doi.org/10.1038/nbt0704-909" target="_blank">[E04]</a></td>
<td><a href="https://arxiv.org/pdf/1906.02229.pdf" target="_blank">[R19]</a> <a href="https://epubs.siam.org/doi/pdf/10.1137/1.9781611975482.107" target="_blank">[A+19]</a></td>
</tr>
<tr>
<td><a href="https://doi.org/10.1145/38713.38722" target="_blank">[IW87]</a>, QA: <a href="https://doi.org/10.14778/2947618.2947621" target="_blank">[TK16]</a></td>
<td>Simulated Annealing <a href="https://doi.org/10.1126%2Fscience.220.4598.671" target="_blank">[KGV83]</a></td>
<td><a href="https://doi.org/10.1038/nature10012" target="_blank">[J+11]</a></td>
</tr>
<tr>
<td><a href="https://doi.org/10.1145/3211954.3211957" target="_blank">[MP18]</a> <a href="https://doi.org/10.1109/ICDE48307.2020.00116" target="_blank">[Y+20]</a> <a href="https://doi.org/10.1145/3329859.3329875" target="_blank">[W+19]</a> <a href="http://arxiv.org/abs/1905.06425" target="_blank">[O+19]</a></td>
<td>Reinforcement Learning <a href="https://doi.org/10.1007/BF00453370" target="_blank">[BSB81]</a></td>
<td><a href="https://doi.org/10.1038/s41586-021-03242-7" target="_blank">[S+21]</a> <a href="https://doi.org/10.1007/11539117_97" target="_blank">[DCC05]</a></td>
</tr>
<tr>
<td><a href="http://www.vldb.org/conf/1994/P085.PDF" target="_blank">[GPK94]</a></td>
<td>Random Walk <a href="https://books.google.com/books?hl=de&lr=&id=WnSoBtMiU2oC&oi=fnd&pg=PA1&dq=M.N.+Barber,+B.W.+Ninham,+Random+and+Restricted+Walks:+Theory+and+Applications,++Gordon+and+Breach,+New+York,+1970&ots=AxF58L4AL1&sig=PArEXcaS26QhyTZiYKPc5ekxEsA" target="_blank">[BN70]</a></td>
<td><a href="https://doi.org/10.1103/PhysRevA.48.1687" target="_blank">[ADZ93]</a> <a href="https://doi.org/10.1145/380752.380757" target="_blank">[A+01]</a></td>
</tr>
<tr>
<td><a href="https://minds.wisconsin.edu/bitstream/handle/1793/59438/TR1004.pdf?sequence=1" target="_blank">[BFI91]</a></td>
<td>Genetic Algorithm <a href="http://dx.doi.org/10.1038/scientificamerican0792-66" target="_blank">[H92]</a></td>
<td><a href="https://doi.org/10.1155/2013/730749" target="_blank">[W+13]</a></td>
</tr>
<tr>
<td><a href="https://doi.org/10.1007/978-981-13-2285-3_45" target="_blank">[TC19]</a></td>
<td>Ant Colony Optimization <a href="https://www-public.imtbs-tsp.eu/~gibson/Teaching/Teaching-ReadingMaterial/ColorniDorigoManiezzo91.pdf" target="_blank">[CDM91]</a> <a href="https://doi.org/10.1109/MCI.2006.329691" target="_blank">[DBS06]</a></td>
<td><a href="https://doi.org/10.1007/978-3-540-74769-7_31" target="_blank">[WNF07]</a> <a href="https://arxiv.org/abs/2010.07413" target="_blank">[G+20]</a></td>
</tr>
<tr>
<td><a href="https://doi.org/10.1145/3035918.3064039" target="_blank">[TK17]</a></td>
<td>Mixed Integer Linear <a href="https://doi.org/10.1007/BF01584074" target="_blank">[BGG+71]</a> Programming <a href="https://doi.org/10.1287/opre.50.1.42.17798" target="_blank">[D02]</a></td>
<td><a href="https://doi.org/10.1103/physrevlett.103.150502" target="_blank">[HHL09]</a> <a href="https://doi.org/10.4230/LIPICS.STACS.2012.636" target="_blank">[A12]</a> <a href="https://doi.org/10.1137/16m1087072" target="_blank">[CKS17]</a> <a href="https://doi.org/10.1103/physrevlett.122.060504" target="_blank">[SSO19]</a> <a href="https://doi.org/10.1145/3498331" target="_blank">[AL22]</a> <a href="https://doi.org/10.1145/3498331" target="_blank">[AL22]</a></td></tr>
</tbody>
</table>
.legend.darkgray.no-margin[This list is not complete...]

.no-margin[
- Please check my lecture about quantum computing:<br/><a href="https://www.ifis.uni-luebeck.de/~groppe/lectures/qc" target="_blank">https://www.ifis.uni-luebeck.de/~groppe/lectures/qc</a>]
]

---
# .darkblue[Quantum Machine Learning - Data encoding and Quantum Model]

.reference[<a href="https://doi.org/10.1038/s41586-019-0980-2" target="_blank">Havlíček et al. Supervised learning with quantum-enhanced feature spaces. Nature 567, 209–212, 2019</a>]

.more-more-condensed[
<div class="textcenter">
<img src="../../img/qc/ml/QuantumModel.svg" align="top" class="fullwidth"></img>
</div>
<table class="fullwidth darkblue">
<tbody>
<tr>
<td>Relations to Join</td>
<td style="text-align:right">Join Order</td>
</tr>
</tbody>
</table>
]

---
# How can we .darkblue[build] a .darkblue[quantum model]?

.reference[Adapted from <a href="https://github.com/qiskit-community/qiskit-presentations/tree/master/2021-11-29_12-02_eqtc" target="_blank">A. Dekusar, J. Gacon, Qiskit Machine Learning: Quantum algorithms for supervised learning, EQTC, 2022</a> <a href="https://doi.org/10.1088/2058-9565/ab4eb5" target="_blank">[B+'19]</a> <a href="https://doi.org/10.1038/s41467-021-22539-9" target="_blank">[H+'21]</a>]

.more-more-condensed[
<table class="tablesmallpadding">
<tbody>
<tr>
<td style="width:30%">.darkblue.bold[Solution Space]</td>
<td style="width:70%">.darkblue[.bold[Hardware-efficient] Ansatz]</td>
</tr>
<tr>
<td><img src="../../img/qc/ml/ChoosingAnsatz.svg" align="top" class="fullwidth"></img></td>
<td><img src="../../img/qc/ml/HardwareEfficientAnsatz.svg" align="top" class="fullwidth"></td>
</tr>
<tr>
<td colspan="2">.darkblue[.bold[Problem-specific] ansatz]</td>
</tr>
<tr>
<td colspan="2" class="small-font24">.darkblue[Use knowledge about problem to choose ansatz!]</td>
</tr>
<tr>
<td colspan="2" class="small-font24">Example: Does the .darkblue[wave function of the quantum states only] have .darkblue[real amplitudes]?</td>
</tr>
<tr>
<td colspan="2" class="small-font24">.darkblue[Many different quantum circuits] for machine learning models, see [B+'19]</td>
</tr>
</tbody>
</table>
]

---
# .darkblue[Variants]

.reference[<a href="https://doi.org/10.1002/qute.201900070" target="_blank">[SJA'19]</a>]

.more-more-condensed[
<table class="tablesmallpadding result">
<tbody>
<tr>
<th style="width:20%">Entanglement Layer</th>
<th style="width:20%">Linear</th>
<th style="width:24%">Circular</th>
<th style="width:36%">Fully Connected</th>
</tr>
<tr>
<th>Circuit</th>
<td><img src="../../img/qc/ml/LinearEntanglementLayer.svg" align="top" class="fullwidth"></img></td>
<td><img src="../../img/qc/ml/CircularEntanglementLayer.svg" align="top" class="fullwidth"></td>
<td><img src="../../img/qc/ml/FullyConnectedEntanglementLayer.svg" align="top" class="fullwidth"></td>
</tr>
<tr>
<th>#Gates for $n$ qubits</th>
<td><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height: 0.43056em;"></span><span class="strut bottom" style="height: 0.43056em; vertical-align: 0em;"></span><span class="base"><span class="mord mathit">n</span></span></span></span> − 1</td>
<td>$n$</td>
<td>$\binom{n}{2}$</td>
</tr>
</tbody>
</table>

- .darkblue[Different combinations of x ,y and z] rotation gates in the rotation layer
- In variants .darkblue[rotation layer and entanglement layer are combined into] one by using .darkblue[controlled rotation gates]
]

---
# .darkblue[QML 4 Join Order Optimization]

.reference[<a href="https://doi.org/10.1038/s41467-022-32550-3" target="_blank">[C+22] Caro et al. Generalization in quantum machine learning from few training data. Nat Commun 13(4919), 2022.
</a>]

.more-more-condensed.small-font[
<div class="center">
<img src="../../img/keynotes/qc/QML4JoinOrder.svg" align="top" class="fullwidth"></img>
</div>

- .darkblue[Variational quantum circuits (VQCs) beat classical neural networks] for join order optimization
- Contributions in other domains report .darkblue[learning on fewer data points]/faster learning [C+22], which is not observed here
]

---
# .darkblue[Open Challenges] for QC for Databases

<div class="more-more-condensed">
<ul class="no-margin"><li>Replacing basic algorithms with their .darkblue[QC counterparts in query optimizations for speeding up databases]</li>
<li>.darkblue[What should be the properties of a quantum computer] (e.g. #qubits, latencies of gates) to achieve certain speedups.darkblue[?]</li>
<li>.darkblue[How to combine classical and quantum computing algorithms to achieve good speedups with few qubits?]<br/>.darkgray[(...for running database optimizations on current available quantum computers...)]</li>
<li>.darkblue[What other (database) domains] besides query and transaction schedule optimizations benefit from quantum computers.darkblue[?]<br/>.darkgray[(In short: those based on mathematical optimization problems, but also other...?)]</li>
</ul>

---
<h1 style="line-height:32px">.darkblue[QC4DB: .small-font36[Accelerating Relational Database Management Systems via Quantum Computing]]</h1>

.more-more-condensed[
<table class="result tablesmallpadding small-font">
<tbody>
<tr>
<th>Name:</th>
<td colspan="2">.darkblue[QC4DB]: Accelerating Relational Database Management Systems via Quantum Computing</td>
</tr>
<tr>
<th>Proj. Web:</th>
<td colspan="2"><a href="https://www.quantentechnologien.de/forschung/foerderung/anwendungsnetzwerk-fuer-das-quantencomputing/qc4db.html" target="_blank">Project Website@Quantentechnologien</a></td>
</tr>
<tr>
<th>Funded by:</th>
<td colspan="2">BMBF, Fördermaßnahme .darkblue[Anwendungsnetzwerk] für das Quantencomputing</td>
</tr>
<tr>
<th>Duration:</th>
<td colspan="2">3 years</td>
</tr>
<tr>
<th>Volume:</th>
<td colspan="2">1.8M Euros</td>
</tr>
<tr>
<th>Topics:</th>
<td colspan="2">.darkblue[Optimizing] an open source relational .darkblue[database] management system <ul class="no-margin"><li>.darkblue[Queries]</li><li>.darkblue[Transaction Schedules]</li></ul></td>
</tr>
<tr>
<th>Partners:</th>
<td style="width:48%"><img src="../../img/keynotes/qc/UzL.jpg" align="bottom" width="300px"></img> (Coord.)</td>
<td><img src="../../img/keynotes/qc/QB.jpg" align="top" width="200px"></img></td>
</tr>
<tr>
<th>Expertises:</th>
<td>Hardware-Acceleration of Databases</td>
<td>Room Temperature Diamond Quantum Accelerators/qbOS</td>
</tr>
<tr>
<th>Website:</th>
<td><a href="https://www.ifis.uni-luebeck.de/~groppe/" target="_blank">https://www.ifis.uni-luebeck.de/~groppe/</a></td>
<td><a href="https://quantumbrilliance.com/" target="_blank">https://quantumbrilliance.com/</a></td>
</tr>
</tbody>
</table>
]

---
# .darkblue[Hybrid Multi-Model Multi-Platform (HM3P) Database]

.reference[S. Groppe, J. Groppe, Hybrid Multi-Model Multi-Platform (HM3P) Databases, DATA 2020.]

.more-condensed[
<img src="../../img/keynotes/HM3PDatabase.svg" align="top" width="100%"></img>
<span class="darkgreenbackground filledCircle">+</span> full and uniform .darkgreen[data integration] at database level<br/>
<span class="darkgreenbackground filledCircle">+</span> .darkgreen[performance]: fully optimized across different data models<br/>
<span class="darkgreenbackground filledCircle">+</span> transparent .darkgreen[fault-tolerance]<br/>
<span class="darkgreenbackground filledCircle">+</span> SQL .darkgreen[standards]: .small-font22[relational ('87), XML ('03), temporal ('11), JSON ('16), Multi-dimensional Arrays ('19), schemaless ('19), streams ('20?), property graphs ('21?)]<br/>
<span class="darkgreenbackground filledCircle">+</span> <span class="bold">.darkgreen[features of different] types of .darkgreen[databases running on different platforms] can be used
</span>]

---
# Using .darkblue[Hardware Accelerator] for optimizing Transaction Schedules
.reference[<a href="https://doi.org/10.1145/3410566.3410593" target="_blank">T. Bittner, S. Groppe, Avoiding Blocking by Scheduling Transactions using Quantum Annealing, IDEAS 2020</a>]

---
# .small-font32.bold[.darkblue[2 Phase Locking (2PL)] versus .darkblue[Strict Conservative 2PL]]
.reference[<a href="https://doi.org/10.1145/3410566.3410593" target="_blank">T. Bittner, S. Groppe, Avoiding Blocking by Scheduling Transactions using Quantum Annealing, IDEAS 2020</a>]

.more-condensed[
- .darkblue[required locks] to be determined by
  - .darkblue[static analysis] of transaction, .darkgray[or if static analysis is not possible:]
  - an .darkblue[additional phase at runtime] before transaction processing
      - <span class="darkgray">A. Thomson et al., "Calvin: Fast distributed transactions for partitioned database systems", SIGMOD 2012.</span>
]

---

# .em[Optimizing] .darkblue[Transaction Schedules]

.reference[$^*$ M.R. Garey, D.S. Johnson and R. Sethi, The Complexity of Flowshop and Jobshop Scheduling, 1(2):117-129, 1976]

.more-more-condensed[
- Variant of job shop schedule problem (JSSP):
  - Multi-Core CPU
      - Process whole <span class="darkblue">job (here transaction) on core X</span>
  - .darkblue[Schedule: $\forall$ cores: Sequence of jobs] to be processed
  - What is the .darkblue[optimal schedule] for minimal overall processing time? 
- .darkgray[Additionally to JSSP:]<br/>.darkblue[Blocking transactions not] to be processed .darkblue[in parallel]
- Example:
<table class="fullwidth">
<tr>
<td style="width:30%"><img src="../../img/keynotes/BlockingTransactions.svg" align="top" width="100%"></img><div class="small-font18 textcenter">Black: Blocking transactions</div></td>
<td style="width:5%"></td>
<td style="width:30%"><img src="../../img/keynotes/DistributionOfTransactions.svg" align="top" width="100%"></img><div class="small-font18 textcenter">Transaction schedule</div></td>
<td style="width:35%">.more-more-condensed[
- JSSP is among the .darkblue[hardest combinatorial optimizing problems]$^*$
- $\Rightarrow$ .darkblue[Hardware accelerating] the optimization of transaction schedules
]</td>
</tr>
</table>
]

---
# <img src="../../img/keynotes/QuantumComputer.svg" align="top" width="10%"></img> .darkblue[Quantum] versus .darkblue[Simulated Annealing]