Adiabatic quantum computing

1. Adiabatic quantum computing Andrew J. Landahl This work was supported in part by the Laboratory Directed Research and Development program at Sandia National Laboratories.

2. Miniaturization Moore’s Law: Nanotechnology is inevitable. Faster = smaller! Ferainet al., Nature (2011); doi:10.1038/nature10676 TODAY: Controllably-engineered single-atom transistors exist Shout-out to Purdue’s Gerhard Klimeck& NanoHUBsoftware. Lansbergen, Nature Nanotechnology (2012); doi:10.1038/nnano.2012.23 Fuechsle et al., Nature Nanotechnology (2012); doi:10.1038/nnano.2012.21 Nanotechnology mayor may not access new quantum phenomena • Entanglement • Superposition • Interference • Indeterminism • Non-locality • Non-clonability Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

3. Quantum algorithms A computer accessing quantum phenomena could do amazing things Exponential speedups for some problems!* Shout-out to Sabre Kais! Quantum chemistry Cryptanalysis Knot identification Over 40 quantum algorithms with speedups over their classical counterparts known http://math.nist.gov/quantum/zoo *Over fastest-known classical algorithms. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

4. Quantum computing It’s hard to predict what the applications for macroscopic quantum phenomena will be Superconductors Lasers To build useful large-scale quantum computers, we need three things: • Advanced quantum hardware(e.g., nanofabrication) • Advanced quantum software(e.g., quantum error correction) • Advanced quantum architectures(e.g., adiabatic architectures) Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

5. Quantum computing hardware AMO hardware (Atomic, Molecular, and Optical) Trapped ion quantum chip Trapped neutral atoms Nuclearmagnetic resonance Photonic quantum chip TODAY: 14-qubit entangled state generated. TODAY: 60,000 parallel2-qubit gates demonstrated. TODAY: 12-qubit circuits benchmarked. TODAY: 10-qubit photonic chip demonstrated. Monzet al. (2011), doi:10.1103/PhysRevLett.106.130506 Anderliniet al. (2007), doi:10.1038/nature06011 Negrevergneet al. (2006), doi:10.1103/PhysRevLett.96.170501 Matthews et al. (2009), doi:10.1038/nphoton.2009.93 CMP hardware (Condensed Matter Physics) Semiconductor quantum-dot chip Superconducting quantum chip Nitrogen vacancies in diamond Topological quantum chip D-Wave Systems, Inc.special-purpose chip TODAY: Zero qubits; FQHE anyons in question. Majorana fermions in topological insulators look promising. TODAY: 128-qubit (superconducting flux) quantum annealing algorithms. Debate about “quantumness.” TODAY: 1-qubitGaAs gates (spin); 1-qubit Sidevice demonstrated (charge). TODAY: 3-qubit entanglement (phase); 3-qubit error correction (charge); 2-qubit CNOT gate (flux). TODAY: 2-qubit gates demonstrated. Neeleyet al. (2010), doi:10.1038/nature09418 Reed et al. (2011), doi:10.1038/nature10786 Plantenberget al. (2007), doi:10.1038/nature05896 Folettiet al. (2009), doi:110.1038/nphys1424 Gorman et al. (2005), doi:10.1103/PhysRevLett.95.090502 van der Saret al. (2012), arXiv:1202.4379 Bondersonet al. (2011), doi:PhysRevLett.106.130505 Bondersonet al. (2010), arXiv:1003.2856 Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

6. Quantum computing software Quantum computing “software” can help manage imperfect hardware: Z Open-loop “software”: (no feedback) Passive: Decoherence-free subspace Encode information so it is invisible to (quasi-collective) noise Simultaneous bit flips will not affect encoded data Y X ZIZI Active: Dynamical decoupling “Pulse” system regularly to allow (quasi-constant) noise to cancel itself. Cancels unknown rotation about Y axis Closed-loop “software”: (uses feedback) Parities of first two & second two qubits identifies any single bit flip Ideal processing: Quantum error correction Encode information, measure error “syndromes,” and correct them. Faulty processing: Fault-tolerant quantum computing Encode computation, add redundancy to QEC. Flip all bits to perform logical bit flip. Repeat parity measurements to boost confidence. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

7. Quantum computing architectures Quantum computing architectures dictate how information is organized and processed. Quantum 101: Schrodinger’s Equation: Continuous variables: Discrete variables: (Unitary) solution: Unitary-based architectures: Turing-machine: Program: Sequence of (tape, head, table) state changes. Tape is infinite. Answer: Tape state after unitary sequence. Circuit: Program: Uniform family of sequences of gates (constant-sized transformations). Answer: Full state after unitary gate sequence. Hamiltonian-based architectures: Quantum walk: Program: Uniform family of time-independent Hamiltonians (graph adjacency matrices). Answer: Full state after evolution by the Hamiltonian. Adiabatic: Program: Uniform family of “adiabatic” interpolating paths between time-independent Hamiltonians. Answer: Full state after evolution by the Hamiltonian; approximates ground state of final Hamiltonian. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

8. Scale How big is “big enough” for a quantum computer to be useful? • World record simulated (error-free) universal quantum computer: 42 qubits. Example of a quantum circuit simulated by Jugene Jugene: 9th fastest supercomputer • Qubits needed to hold more amplitudes than atoms in the observable universe: 266 qubits.* *Holevo’s Theorem: Only 266 bits’ worth can be read out. • Qubits needed to simulate an ideal circuit on 300 ideal qubits with a realistically faulty quantum computer: Over a billion qubits!† †Gates in ideal circuit: 109, qubit error rate: 10−6, 2-qubit gate error rate: 10−4, 1-qubit gate error rate: 10−3. The circuit architecture is a siren song! While the gates & qubits may be simple, enormous numbers of them may be needed in realistic devices to be useful. Monzet al. (2011), doi:10.1103/PhysRevLett.106.130506 De Raedtet al. (2007), doi:10.1016/j.cpc.2006.08.007 Holevo (1973), http://mi.mathnet.ru/eng/ppi903 Steane (2007), http://www.rintonpress.com/xqic7/qic-7-3/171-183.pdf Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

9. Adiabatic quantum physics • Adiabatic: Impassible [Greek: ἀ- ("not"), διὰ- ("through"), and βαῖνειν ("to pass”)]. Qualitative: Thermodynamic adiabatic process: No heat transfer into or out of system. Quantum adiabatic process: No population transfer into or out of a specified energy eigenspace. Somewhat more quantitative: Schrödinger equation: Adiabatic theorem: If the initial state is , then in the limit as , the final state is . Holonomic evolution: If the initial state is degenerate, and the degeneracy is preserved through the entire evolution, then the final state is really , where depends on the path taken in Hamiltonian space. Adiabatic approximation: If , then the evolution is adiabatic with high probability. Akin to quasistatic classical mechanics. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

10. Adiabatic quantum computation AQC in four easy steps… Encode the solution to a problem in the ground state of a final Hamiltonian Hf. Turn on an initial Hamiltonian Hi and initialize the system in an eigenstate (usually the ground state). Deform the Hamiltonian from Hi to Hf along some interpolation path that is “adiabatic.” Measure the final state to get the solution. N.B. AQC is digital quantum computation, albeit continuously in time. Ising Hamiltonians naturally solve “QUBO” (Quadratic Unconstrained Binary Optimization) QUBO: QUBO is NP-hard; a hotly debated question is whether the gap shrinks exponentially or polynomially with n for worst-case QUBO problems. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

11. Adiabatic architecture Theoretically, the adiabatic architecture… • Should be able to run any quantum algorithm, if the repertoire of interactions is sufficiently rich. • Should be robust to • Damping (T1) noise (which occurs in the instantaneous energy eigenbasis). • Dephasing(T2) noise (which shifts energy levels). • Thermal (kT) noise (because of the gap). • Control errors that are adiabatic (because any adiabatic path works). • Should not be robust to • Measurement errors. • Leakage errors. • May be commensurate with some “software” error-suppression techniques. • Has yet to be proven fault-tolerant. • Lacks a clear “blueprint” for universal computing in realistic hardware. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

12. Adiabatic architecture Simulated by Simulated by Simulated by If the adiabatic architecture is so robust, maybe the following is true: 300-qubit ideal circuit 1,000,000,000-qubit fault-tolerant circuit 1,000-qubit ideal AQC 1,200-qubit fault-tolerant AQC Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

13. Adiabatic architecture The important R&D questions to answer are: • Are the theoretical promises of robustness borne out in real hardware? (E.g., in representative AMO and CMP technologies?) • Develop a blueprint for a universal adiabatic architecture for real hardware. • Assess the need for fault-tolerant design for real hardware. • If needed, devise a way to make the adiabatic architecture fault tolerant. An internally-funded Sandia “Grand Challenge” project FY11-FY13 330 µm Objectives of AQUARIUS • Demonstrate special-purpose two-qubit AQC optimization algorithms in • Neutral atoms trapped by a nanofabricated optical array • Semiconductor electrons trapped by nanofabricated structures • Assess the potential for universal fault-tolerant AQC architectures through design & simulation. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

14. AQUARIUS labs & facilities Optical atom trapping & control lab Cryogenic materials & electronics measurement lab Atomic-precision lithography (STM) lab Center for Integrated Nanotechnologies (CINT) Microsystems and Engineering Sciences Applications (MESA) Computer Science Research Institute (CSRI) Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

15. Neutral-atom AQC: Overview Cs level structure World-first demonstration! Phase shift pattern SEM Numerical Microwaves/ two-photon Raman Rydberg interactions Light shifts Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

16. Sandia’s first quantum calculation “LUBO:” Linear Unconstrained Binary Optimization Conclusion: 0 < 1, with high probability Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

17. Semiconductor AQC Theory: Double-well electron qubits Charge qubit Spin qubit Short T2 but easier to work with & stable ground state Long T2 but harder to work with & metastable ground state (Electrical readout for both types, though.) AQUARIUS hardware approach: Near-term (dots) & long-term (donors) Petta, Science, 2005 Ec D- Pair of donors Double quantum dot (DQD) Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

18. DQD Charge qubits: Theory Theory: Set of plausible interactions e • Z interaction • X interaction Metallic connector w/ variable density poly • ZZ interaction oxide - - - - Si Van Weperen, PRL, 2011 Tunable FET coupler design (SNL) • ε = detuning, can modulate by gate voltages ±meV (−12 K to 12K) • β = tunnel barrier height, can tune neV to meV (120 mK to 12 K) • λ = Coulomb interaction, can tune 25-85 µeV (0.25 K to 1 K) sensor sensor coupler Tuning Coulomb interaction by barrier voltage or FET coupler will be difficult! Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

19. DQD QUBO & beyond: Theory Using previously described interactions, can solve QUBO: For small-sized problems, can optimize adiabatic path to increase fidelity • Simulation: Energy gap is 5 to 500 µeV, runtimeis ~1 ns. Universal AQC requires additional interactions: • Open questions: • How plausible is this? • Is Y needed? XX interaction XZ interaction Hollenberget al. (2004), doi:10.1103/PhysRevB.69.113301 Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

20. DQD AQC: Experimental results Charge-sensed a single-well, single-electron quantum dot Current goes through QD when levels lines up 0V -5.5V Last “visible” transition Edge of transport through dot observed! 2V 2V 0V 0V 0V • Two most likely reasons: • Tunnel barrier is gradually turning off (often the case) • Last electron Enhancement gate [V] This case is not gradual and no additional transitions are observed over reasonably large Vtop scan and Vsd  Strong evidence for single-electron occupation! Top plunger [V] Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

21. DQD AQC: Experimental results Charge sensing of a double-well quantum dot • Strategy: • Fill dot region with electrons. • Form a single well. • <Dial down to single electron> • Deform potential to double well. • Balance charge sensor with the dot. It’s easier to start with a many-electron dot first; for AQC single-electron discrimination of a many-electron DQD is sufficient. • Coulomb blockade has richer “honeycomb” structure for DQDs. • We are not at single-electron occupation yet. (Charge sensor balancing TBD.)  However, we have enough to test adiabaticity of evolutions! Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

22. Testing adiabaticity: theory Adiabaticity testing If relaxation and adiabatic evolution both drive one to the ground state, how do we disentangle the causes? | L > Asymmetric toggling: Square-wave pulsing: | R > • As Δt grows, if evolution is nonadiabatic, time-averaged signal will transition from R-R-R-R (too fast to exhibit relaxation) to R-L-R-L-R-L (relaxation).  Finds relaxation timescale! • Rerun experiment at a timescale faster than relaxation, and increase gap by increasing beta. An observed transition from R-R-R-R to R-L-R-L is signature of adiabaticity! relaxation rates Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

23. Testing adiabaticity: experiment We are just now doing preliminary experiments probing the relaxation timescale Testing three square-wave pulse frequencies. Two peaks indicate both R and L populate. One peak indicates only R populates. 215Hz 430Hz 860Hz We’re developing some detailed noise models to allow us to extract T1 from this data. Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

24. Atomic-precision devices M. Y. Simmons et al., U. New South Wales, CQCCT, Australia Start w clean Si(001) 2. Adsorb H resist Self-limiting 1 monolayer 3. Pattern w STM Atomic-precision 4. Adsorb PH3 ~ 100-nm-tall mesa structures Etched alignment marks 8. Add contacts Al depo+liftoff 6. Desorb H anneal 7. Bury P in Si 5. Incorporate P -Anneal➔ Si-P swap -H resist constrains P Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

25. Atomic-precision devices Testing PH3system Start w clean Si(001) 2. Adsorb H resist Self-limiting 1 monolayer 3. Pattern w STM Atomic-precision 4. Adsorb PH3 ~ 100-nm-tall mesa structures Al depo+liftoff Etched alignment marks 5. Incorporate P -Anneal➔ Si-P swap -H resist constrains P 6. Desorb H anneal 8. Add contacts 7. Bury P in Si Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

26. Synopsis • The adiabatic quantum architecture appears on paper to have great implementation robustness, potentially radically reducing the resources needed to implement quantum algorithms • At Sandia, we are investigating this with two proof-of-principle demonstrations in complementary hardware (neutral atoms and semiconductors) • We have run a program our first adiabatic quantum processor (neutrals) and we are learning the adiabaticity timescales of our Si quantum dots to help us get our second (charge qubit) adiabatic quantum processor up and running. • We are exploring potential universal AQC constructions for realistic hardware, and the scale at which fault-tolerance might be necessary • Stay tuned… Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12

27. AQC 2012: Mar. 7-8, Albuquerque, NM Theme: Challenges to implementation Website: https://share.sandia.gov/aqc2012/ Invited speakers: Dr. Mohammad Amin, D-Wave Systems, Inc. Dr. Malcolm Carroll, Sandia National Laboratories Prof. Ivan Deutsch, University of New Mexico Dr. Emily Edwards, University of Maryland Prof. Mark Eriksson, University of Wisconsin Dr. Frank Gaitan, Laboratory for Physical Sciences Dr. Toby Jacobson, Sandia National Laboratories Prof. Daniel Lidar, University of Southern California Dr. Paul Parazzoli, Sandia National Laboratories Dr. Andrew Sachrajda, National Research Council, Canada Prof. Mark Saffman, University of Wisconsin Dr. Rolando Somma, Los Alamos National Laboratories Andrew J. Landahl Purdue Condensed Matter Seminar 3/2/12