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Simulating a Quantum Computer: Grover's Search Algorithm with Error Correction
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Att simulera en kvantdator : Grovers sökalgoritm med felhantering (Swedish)
Abstract [en]

Classical simulations of quantum computers give us an insight into various things such as what quantum algorithms can achieve, whether it is possible to verify that they function as postulated, the difficulties that have to be overcome before quantum computers can be realized, as well as how we can handle these difficulties. We build a Python library to simulate a quantum computer that can perform all quantum algorithms by defining an universal gate set, from which all quantum gates – and thereby all circuits – can be constructed. We implement two algorithms that both highlight two important aspects of quantum computing: Grover’s quantum search algorithm, which demonstrates the efficiency of quantum algorithms and their superiority over their classical counterparts by searching an unsorted list quadratically faster; and an error correcting code, the Shor code, which highlights the cost of correcting the possible errors in a quantum computer.We test the rigidity of Grover’s algorithm by introducing errors without correction, and find that the algorithm shows resilience to smaller 1-qubit Pauli errors, but looses its efficiency under larger errors and thus the need for Pauli error correction arise.

Abstract [sv]

Klassiska simuleringar av kvantdatorer ger oss en inblick i vad kvantalgoritmer kan åstadkomma, hur vi kan verifiera att algoritmerna fungerar, vilka problem vi måste lösa innan kvantdator- erna blir en verklighet, samt hur vi kanske kan hantera problemen. Vi bygger ett bibliotek i Python för att simulera en kvantdator som kan utföra alla kvantalgoritmer genom att definiera en grinduniversalmängd, ur vilken alla kvantgrindar – och därmed alla kretsar – kan konstrueras. Vi implementar två algoritmer som båda belyser två viktiga aspekter hos kvantberäkning: Grover’s kvantsökning, som demonstrerar effektiviteten hos kvantalgoritmer över deras klassiska analoger, samt en felhanteringsalgoritm, Shorkoden, som kan jämka Paulifel och är betydelsefull för att förstå vikten hos felkorrigering.Vi prövar motståndskraften hos Grovers algoritm genom att utsätta den för slumpmässiga ro- tationer hos en qubit, och finner att algoritmen är resistent mot mindre Paulifel, men snabbt slutar producera meningsfulla resultat vid större Paulifel.

Place, publisher, year, edition, pages
2018. , p. 33
Series
TRITA-SCI-GRU ; 2018-118
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-231739OAI: oai:DiVA.org:kth-231739DiVA, id: diva2:1229790
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Examiners
Available from: 2018-07-02 Created: 2018-07-02 Last updated: 2018-07-02Bibliographically approved

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