Quantum Optics and Quantum Informatics 7.5hp (FKA173) Introductory Lecture

Transcription

1 Quantum Optics and Quantum Informatics 7.5hp (FKA173) Introductory Lecture Fasrummet (A820) 09:00 Oct Lectures: Jonas Bylander and Thilo Bauch Excercises: Edoardo Trabaldo and Marco Scigliuzzo Lab work: Jonas Bylander and Marco Scigliuzzo

2 Goals of the course After the course you should be able to: explain the properties of the Jaynes-Cummings model derive the Hamiltonian of an electronic circuit use the Bloch equations to describe the dissipative dynamics of a two-level system explain the basic features of a quantum measurement process Explain and experimentally perform manipulations and measurements of the state of a superconducting qubit analyze the properties of simple quantum algorithms communicate the basic features of quantum computing and Shor's algorithm and teleportation and quantum cryptography to a friend. ( and to know whether a MSc thesis in this field is interesting.)

3 Why Quantum Computing? Illustration: Binary search 0 0 Start 1) Choose path (001) 2) Test 1 L J

4 Classical search Repeat ~2 n times: 1) Choose new path (101) 2) Test Start J Optimized flight schedule, New active drug-molecule, any combinatorial problem,...

5 Quantum Search(?) Quantum superposition: 1) Choose all paths ( 0>+ 1>) ( 0>+ 1>) ( 0>+ 1>) Start 0> 1> 0> 1> 0> 1> 0> 1> 0> 1> 0> 1> 0> 1> J But what about reading out the answer???

6 The superposition collapses when measured. Like Schrödinger s cat. We get one random output. Peter Shor at IBM shows...

7 Peter Shor at IBM (1994) Crypto guys (NSA) gets concerned -> research money

8 Quantum computing so far A coherent superposition c 0 0>+c 1 1> Exponential speed-up in Factorization (Shor -94) Searching N -> N 0.5 (Grover -96) Quantum simulations Many qubits and decoherence: explore the Quantum/Classical frontier

9 Quantum computing big open questions Can we really build a quantum computer? The environment induces dephasing (loss of phase coherence) and dissipation (energy loss), which makes the qubits behave classically, like ordinary bits. What real problems, in addition to factoring, can be solved by quantum computing? Or equivalently: In exactly what way is a quantum computer more powerful than a classical computer?

10 Quantum Informatics Quantum Computing and Qubits What is a qubit (quantum bit)? We need matter qubits. They can use photons to interact. Photons are flying qubits. Good for quantum communication! They don t interact with each other. -> Bad for quantum computing!

11 The origin of uncertainty/superposition Quantum Physics the wave nature of matter ~ de Broglie (France) Nobel -29 Heisenberg (Germany) Nobel -32 Schrödinger (Austria) Nobel -33 The double slit experiment with electrons a controlled superposition of matter in Tübingen by Claus Jönsson Now, also with heavier particles (Zeilinger et al)

12 Matter Qubits e - on He, spins in QD, anyons, Fullerenes,... Atoms and Ions in traps Superconducting electrical circuits

13 Matter Qubits e - on He, spins in QD, anyons, Fullerenes,... Atoms and Ions in traps Superconducting electrical circuits Nobel prize 2012 to Serge Haroche and David J. Wineland for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems

14 Atomic qubits Qubit=Two different electronic states of an atom or ion in a trap Manipulated and read out by lasers and ccd Eight qubits (qubyte) realized! (2005) Fourteen coupled qubits realized! (2011) Difficult to scale up Pictures from the group of Prof. Rainer Blatt, Innsbruck

15 Atom-field interaction Quantum Optics and the Jaynes- Cummings model Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter. A two level atom (qubit) interacting with a classical field (laser) correspond to the Rabi problem A two level atom (qubit) interacting with a quantum field, e.g. in a cavity, is described by the Jaynes-Cummings hamiltonian Picture from the group of Prof. Jeff Kimble, Caltech Quantum Optics

16 Superconducting qubits Coherent states of superconducting electronics Talkative qubits Easy to couple Difficult to isolate Straightforward to scale up(?) Many researchers at Chalmers work on superconducting qubits (Per Delsing, Jonas Bylander, Floriana Lombardi, Thilo Bauch, Göran Johansson, Sankar Sathyamoorthy, Marco Scigliuzzo, more PhD students both on theory and experiment, MSc thesis students )

17 Superconducting qubits Charge qubit Flux qubit Phase Qubit

18 The transmon A charge qubit in a coplanar waveguide cavity. Very large island, rather insensitive to charge noise. Very promising! Yale University (Schoelkopf, Devoret, Girvin), ETH Zürich (Wallraff), Delft (Leo di Carlo) and Chalmers Qubits in 3D cavities: Coherence times up to 100 microseconds!! (Yale group and IBM group)

19 Qubit Read-out a Quantum Measurement Quantum Information -> Classical Information

20 Quantum Informatics Quantum Communication Teleportation Secure key distribution

21 Teleportation

22 Teleportation (Because of No cloning theorem you cannot copy.) Theory: Bennett and co-workers (IBM, 1993)

23 Teleportation Photon state: Anton Zeilinger and co-workers (Innsbruck, 1997) and (Vienna, 2003) Atomic state: Rainer Blatt and co-workers (Innsbruck, 2004)

24 Quantum Informatics Quantum Communication Teleportation Secure key distribution

25 Secure Key Distribution Theory: Bennett and Brassard (1984) Eve is detected here! (Bennet 2006)

26 Secure Key Distribution Companies selling products: id Quantique in Geneva Running a data archiving network secured using quantum cryptography BBN Technologies in the USA Running The DARPA Quantum Network World's First Quantum Cryptographic Network

27 Goals of the course After the course you should be able to: explain the properties of the Jaynes-Cummings model derive the Hamiltonian of an electronic circuit use the Bloch equations to describe the dissipative dynamics of a two-level system explain the basic features of a quantum measurement process Explain and experimentally perform manipulations and measurements of the state of a superconducting qubit analyze the properties of simple quantum algorithms communicate the basic features of quantum computing and Shor's algorithm and teleportation and quantum cryptography to a friend. ( and to know whether a MSc thesis in this field is interesting.)