Quantum Computing – Progress and Prospects

1. Quantum Computing –Progress and Prospects Tony Hey and Douglas Ross University of Southampton

2. Plan of Lectures • Lecture #1: Introduction to Quantum Information Theory – Fundamentals (Tony Hey) • Lectures #2,3 & 4: Quantum Algorithms in Detail – Bell States, Quantum Teleportation, Grover’s Quantum Search and Shor’s Quantum Factorization (Douglas Ross) • Lecture #5: Quantum Cryptography and Quantum Computing – State of the Art (Tony Hey)

3. Quantum Cryptography and Quantum Computing - State of the Art Tony Hey Director of e-Science EPSRC, Swindon Tony.Hey@epsrc.ac.uk

4. The Quantum Age “The nineteenth century was known as the machine age, the twentieth century will go down in history as the information age. I believe the twenty-first century will be the quantum age.” Paul Davies 1996

5. Outline of Lecture • What is a Quantum Algorithm? • Quantum Cryptography • Quantum Computing Technologies • Quantum Error Correction • Experiments at Southampton • Conclusions

6. What is a Quantum Algorithm? • Superposition is not specific to quantum mechanics • Can write 2 qubit Hadamard gate as 4x4 matrix acting on 4-d column vectors representing (0,0), (1,0), (0,1) and (1,1) states • Implement 2 qubit Hadamard gate in conventional electronics with four input wires and four output wires • Logically reversible, no entanglement

7. An Electronic Analogue of Grover’s Quantum Search • Superposition not specifically quantum - entanglement and measurement are quantum specific • Without genuine multi-particle quantum entanglement see that we need number of wires to rise exponentially with the number of qubits for our electronic analogue simulation • Suspect that this is true more generally

8. Quantum Cryptography (1) • Application of Quantum Information rather than Quantum Computing • Not really Cryptography – Quantum Key Distribution would be better name • Describe one possible realization using photon polarizations as qubits • Nicholas Gisin and his group in Geneva are one of the leading players in this field

9. Quantum Cryptography (2) One-Time Pads • Most secure cryptosystem – encode each bit of message using different secret random number Encode: M = N + K modulo 2 Decode: M + K modulo 2 = N • Problem: both sender (Alice) and receiver (Bob) need to have copy of same set of keys that eavesdropper (Eve) does not have

10. Quantum Cryptography (3) • Giles Brassard and Charles Bennett proposed using qubits to exchange secret keys in 1984 • BB84 Scheme uses polarization states of photon as qubit • Alice can send photons Either - in Horizontal-Vertical Basis with polarizers set at 0 and 90 degrees Or - in Diagonal Basis with polarizers set at 45 and 135 degrees

11. Quantum Cryptography (4) • Bob can also choose to receive photons either in H-V basis or in Diagonal basis – he does not know Alice’s settings in advance • If Alice sends a ‘1’ using H-V setting but Bob measures photon in Diagonal setting, Bob will measure a ‘1’ 50% of the time and a ‘0’ for the remaining 50% How does this help?

12. Quantum Cryptography (5) • After sending stream of bits in randomly chosen settings, Alice then telephones Bob and they agree which are the ‘good’ bits What use is this? • Suppose Eve is intercepting the bits from Alice and re-sending them on to Bob • Since Eve has to guess which setting Alice used (H-V or Diagonal) there is now a probability of ¼ for Alice and Bob to disagree on the bit sent even when they use the same settings

13. Quantum Cryptography (6) State of the Art • First demonstration system built by Charles Bennett at IBM in 1989 • Many groups now demonstrated real systems transmitting keys down commercial optical fibres over many kilometres e.g. Richard Hughes at LANL, Nicholas Gisin under Lake Geneva, Paul Townsend at BT • Hughes group also demonstrated free space transmission possible

14. Quantum Computing Technologies (1) Four essential requirements for quantum computational hardware: • Must be able to prepare multiple qubits in addressable form • Must be mechanism for performing quantum logic operations • Must be readout mechanism for each qubit at end of computation • System must be adequately isolated from environment for long enough to perform calculation

15. Quantum Computing Technologies (2) Ion Trap Computing Wineland: CNOT gate with 2 Be ions cooled to vibrational ground state Hughes: Addressed trapped Ca ions - sideband cooling ‘soon’ Cavity QED Kimble: Conditional quantum dynamics with single atom & photon Haroche: Successive atoms through cavity NMR ‘Ensemble’ Quantum Computing Chuang: 3 qubit quantum gates using HCCI3 (chloroform) Zurek: GHZ 3 qubit state Jones: NMR realizations of Deutsch’s and Grover’s algorithms

16. Quantum Computing Technologies (3) What about quantum error correction? • Not only bit flips but also quantum phase changes • Caused by interactions with the environment - commonly referred to as ‘decoherence’  Surprisingly Shor and Steane showed that entanglement of extra bits allows error correction 1 qubit  7 qubits  Sophisticated fault-tolerant schemes possible in principle

17. Quantum Computing Technologies (4) • To implement Shor’s algorithm tofactorize l-bit number requires: # of qubits L = 5l + 4 # of gates nG = 25l3+ O(l2) • For 130 digit number (432 bits) need: L = 2000 qubits and nG = 109 gates • With a concatenated quantum error correction scheme Preskill estimates would require: L = 106 qubit system!

18. Southampton Quantum Technology Centre • Multi-disciplinary collaboration between physicists, computer scientists and electronic engineers • Southampton hosts dedicated Silicon Fabrication Facility funded by EPSRC • Silicon oxidation, implantation, diffusion doping, reactive etching • SiGe and selected metals, direct-write electron beam lithography

19. Southampton Quantum Technology Centre Facilities

20. Quantum Computing Technologies • Several groups pursuing ion traps and NMR technologies • Goal of Southampton effort is to build small-scale qubit devices in the solid state that can be easily integrated with conventional technologies • Self-assembled Quantum dots • Josephson Junction Qubits

21. Self-Assembled Ge/SiGe Quantum Dots • grown by MOCVD on Si substrates • 100nm diameter x 50nm high • Single dot spectroscopy • quantum functional Si devices Darren Bagnall and Jeremy Baumberg

22. e e e e Quantum Dot Computers • Lent and Porod of Notre Dame proposed a wireless two-state device called a “cell” • Each cell consists of State 1 - ‘One’ State 2 - ‘zero’ five quantum dots and two electrons • The two electrons repel each other, causing them to move to opposite corners of the device • This yields two states of equal energy in the cell

23. NEC Press Release

24. Josephson Junction Qubits • Superconductors - paired electrons in macroscopic quantum state • Josephson effect - pair tunneling through insulator Josephson Junction (JJ) • Combine JJs to form Single Electron Transistor (SET) or Superconducting Quantum Interference Devices (SQUID) • SETs or SQUIDs form basis for design of charge-coherent or phase-coherent fabrication qubits • Novel techniques with angled deposition S I S

25. Josephson Junction Charge Qubit Peter De Groot and Adrian Potts

26. Conclusions? Feynman “not sure if there was a real problem with quantum mechanics” - “Squeeze the difficulty of quantum mechanics into a smaller and smaller place” Perhaps the foundation of a new multi-billion dollar industry!