The Development of a Quantum Computer in Silicon Professor Michelle Simmons Director, Centre of Excellence for Quantum Computation and Communication Technology, Sydney, Australia December 4th, 2013 Outline Short history of development of quantum computing |1> Comparison of classical and quantum computing B |0> Experimental requirements for the practical realisation of a quantum computer: the 7 DiVincenzo criteria Leading contenders in the solid state B0 Current status of silicon based quantum computing Bac A Brief History of Quantum Computing 1982: Richard Feynman, at the First Conference on the Physics of Computation held at MIT, proposed a basic model for a quantum computer that would exploit the potential of massive quantum parallelism. 1994: Peter Shor discovers the factorisation algorithm for large numbers theoretically capable of breaking today’s public key cryptosystems. 1995: Peter Shor and Andrew Steane simultaneously proposed the first schemes for quantum error correction. 1996 Lou Grover propose an exhaustive search algorithm that showed for a system of n possibilities you can find the answer in n look-ups quantum mechanically compared with n/2 classically. 1998 Ray LaFlamme experimentally demonstrates error correction in a trichoroethylene molecule using liquid state NMR Classical versus quantum bits Conventional Quantum Computer Computer 0, 1 |0>, |1> bits qubits information is stored in “bits”. information is stored in A bit can be “quantum bits” or qubits, either 0 or 1. which can be a combination of 0 and 1. Quantum state of a two-level system such as spin or charge of 31P nucleus |1> charge spin B |0> Classical versus quantum computation Classical computer - can check many different possibilities in rapid succession Quantum computer - can check many different possibilities in parallel Digital1 informationcomputer - : 1 # qubits classical possibilities power search A, B, C, … Z London Tokyo 0 or 1 2 00, 01, 10, 11 4 2 computers - twice as fast. One searches A-L, other M-Z. 000, 001, 010, 011 8 100, 101, 110, 111 N 2N 3 computers - 3 as fast. Quantum computer’s power doubles Digital information : 0 every time another qubit is added Superposition, 1 spin: A 30-qubit quantum computer would be = 1|0> + 2|1> more powerful than a supercomputer.. Entanglement, 2 spins: As for 300 qubits…. =1|00> + 2|01> + 3|10> + 4|11> Difficult problems: the travelling salesman 1E+33 1E+30 Older than universe 1E+27 1E+24 1600 years 1E+21 1E+18 Problem: A salesman has to travel to many cities and 100 secs 1E+15 wants to work out the shortest possible route 1E+12 Number of routes of Number 1E+09 1E+06 1000 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Number of cities 14 cities: 1011 routes for a classical 1GHz computer (109 operations/sec) it would take 100 seconds 22 cities: 1019 routes it would take 1600 years 28 cities What can quantum computers do? Quantum computers will not necessarily outperform classical computers but need to use algorithms that exploit quantum parallelism. Current record is RSA-768 165181 417953 1024-bit number in 3,000 years easy hard Quantum computer minutes = 69037894493 Applications: physical modelling (climate, engineering); simulations (chemistry, materials), database searching (bioinformatics); factorisation (data security) Algebraic and Number Theoretic Algorithms (11 algorithms); e.g. factorising Oracular Algorithms (29 algorithms); e.g. searching, linear differential equations Approximation and Simulation Algorithms (10 algorithms); e.g. simulation, adiabatic algorithms Experimental Requirements for Quantum Computing Devices Relaxation and coherence times The longitudinal relaxation time, T1 is the time- scale for the exponential decay of a non- equilibrium polarization of spins to give up its Zeeman energy to the lattice. it represents the maximum time available for a quantum computation The transverse relaxation time, T2 The amplitude of the net transverse magnetisation decays as the magnetic moments move out of phase with one another (shown by the small black arrows). Arise from spin-spin interactions. The overall term for the observed loss of phase coherence is T2* relaxation, which combines the effect of T2 relaxation and additional de-phasing caused by local variations (inhomogeneities) in the applied magnetic field, e.g. by the presence of other nuclear spins. Overview: Qubits in the Solid State • Superconducting qubits offer flexibility and strong coupling to external fields BUT have relatively short coherence times (<0.1ms) • Microscopic systems are given by nature and can easily be made identical with long coherence times (>1ms) BUT they operate slowly due to weak coupling to external fields. Z.L. Xiang, Rev. Mod. Phys. 85, 623 (2013). DiVincenzo Criteria for a scalable system Although weakly There must be a readout coupled to the outside method to determine the world, the qubits must state of each qubit at the nevertheless be strongly end of the computation. coupled together to perform logic-gate A quantum register of operations multiple qubits must be prepared in an addressable form and isolated from environmental influences, which cause the delicate quantum states to decohere. 1. A scalable physical system of well- 1 D. DiVincenzo, Fortschritte der Physik- characterized qubits Progress of Physics 48, 771 (2000) Well defined two level quantum system Physical system Name Information support |0> |1> Polarisation encoding Polarisation of light Horizontal Vertical Photon Number of photons Fock state Vacuum Single photon of light Time-bin encoding Time of arrival Early Late Coherent state of Squeezed light Quadrature Amplitude squeezed Phase squeezed state light state Electronic spin Spin Up Down Electrons Electron number Charge No electron One electron Nucleus NMR Spin Up Down Optical lattices Atomic spin Spin Up Down Superconducting charge Charge Uncharged island Charged island qubit (Q=0) (Q=2e) Superconducting Current Clockwise current Counterclockwise Josephson junction Flux qubit current Superconducting phase Energy Ground state First excited state qubit Singly charge Electron localisation Charge Electron on left dot Electron on right dot quantum dot pair Quantum dot Electron spin Spin Projection of spin Projection of spin orientation on “-z” orientation on “+z” direction direction Beyond CMOS: Emerging Materials and Devices DiVincenzo Criteria for a scalable system 2. The ability to initialize the state of the qubits to a simple state 1. A scalable physical system of well- 1 D. DiVincenzo, Fortschritte der Physik- characterized qubits Progress of Physics 48, 771 (2000) Initialisation of electron spin P Donor P P SET drain SET SET-island P |1> SET drain B |0> DiVincenzo Criteria for a scalable system 3. Coherence times >> gate-operation times 2. The ability to initialize the state of the qubits to a simple state 1. A scalable physical system of well- 1 D. DiVincenzo, Fortschritte der Physik- characterized qubits Progress of Physics 48, 771 (2000) Promising proposals for qubits T.D. Ladd, Nature 464, 45 (2010) DiVincenzo Criteria for a scalable system 4. A universal set of quantum gates 3. Coherence times >> gate-operation times 2. The ability to initialize the state of the qubits to a simple state 1. A scalable physical system of well- 1 D. DiVincenzo, Fortschritte der Physik- characterized qubits Progress of Physics 48, 771 (2000) Universal quantum gates Universal: one single computer for different computational tasks In quantum computation all operations must be reversible. An example of a non-reversible gate is an AND gate where two inputs only give one output therefore information is lost. The quantum states of a qubit are a vector in 2D complex vector space. = |0> + |1> A superposition is a linear combination of the 0 and 1 state amplitude with coefficients and . The constraints are that: | |2 + | |2 = 1 Single quantum NOT gate Quantum NOT gate: |0> |1> and |1> |0> But we also have a superposition so |0> + |1> |1> + |0> Logic gate X 2 qubit controlled NOT gate (CNOT) 4 computational basis states: |00> |01> |10> + |11> 2 + 2 + 2 + 2 =1 If the control is 1, flip the target qubit; otherwise do nothing. |00> |00> |01> |01> |10> |11> |11> |10> A universal set of gate operations 100 QNOT 13 CNOT 10 90 =30 MHz/V A-Gate J=0: J-Gate Barrier A-Gate A-Gate 80 - - Si 31 12 70 P 10 60 50 11 J>0: 10 B=2 T: V=0: V>0: 40 J-Gate 2 B/h=56 GHz A-Gate A-Gate A-Gate A-Gate B 30 Barrier Barrier ++ 10 20 Si Si 10 Exchange Frequency (Hz) Frequency Exchange 10 e- Nuclear Resonance Frequency (MHz) Frequency Resonance Nuclear 0 9 10 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 A-Gate Voltage (V) Donor Separation (Å) A-gates control the interaction J-gates control the exchange between a nuclear spin qubit interaction between electron spins. and the electron spin. Bac effectively using an electron spin mediated nuclear spin – nuclear spin interaction. DiVincenzo Criteria for a scalable system 5. A qubit-specific measurement 4. A universal set capability of quantum gates 3. Coherence times >> gate-operation times 2. The ability to initialize the state of the qubits to a simple state 1. A scalable physical system of well- 1 D. DiVincenzo, Fortschritte der Physik- characterized qubits Progress of Physics 48, 771 (2000) Single shot spin read out J. Elzerman et al., Nature 430, 431–435 (2004). DiVincenzo Criteria for a scalable system 6. The ability to interconvert 5. A qubit-specific stationary and measurement flying qubits 4. A universal set capability of quantum gates 3. Coherence times >> gate-operation times 2. The ability to initialize the state of the qubits to a simple state 1. A scalable physical system of well- 1 D. DiVincenzo, Fortschritte der Physik- characterized qubits Progress of Physics 48, 771 (2000) The ability to interconvert stationary and flying qubits Optically addressing dopant atoms in silicon C.