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Quantum Computing Lecture 1: Basic Concepts

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Quantum reality is information-theoretic and computable
Lecture 1: Quantum Computing basics (hardware)
Lecture 2: Advanced concepts (control software between macroscale reality and quantum microstates)
Lecture 3: Speculative application (B/CI neuronanorobot network)

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Quantum Computing Lecture 1: Basic Concepts

  1. 1. Quantum Computing Lecture 1: Basic Introduction Mountain View CA, July 28, 2020 Slides: http://slideshare.net/LaBlogga “The laws of physics present no barrier to reducing the size of computers until bits are the size of atoms” — Richard P. Feynman (1985) Melanie Swan
  2. 2. 28 July 2020 Quantum Computing Theoretical Model of Quantum Reality  Quantum reality is information-theoretic and computable  Lecture 1: Quantum Computing basics (hardware)  Lecture 2: Advanced concepts (control software between macroscale reality and quantum microstates)  Lecture 3: Application (B/CI neuronanorobot network) 1
  3. 3. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 2 Quantum Computing 1. Basic Introduction
  4. 4. 28 July 2020 Quantum Computing Feynman: Universal Quantum Computer 3 Sources: Feynman, R.P. (1985). Quantum Mechanical Computers. Foundations of Physics. 16(6):507-31. Feynman, R.P. (1982). Simulating physics with computers. International Journal of Theor. Physics. 21(6):467-88.  “The laws of physics present no barrier to reducing the size of computers until bits are the size of atoms and quantum behavior holds sway” (1985)  Vision: build a “universal quantum simulator” in the structure of nature (1982)  Simulate field theories with lattice works of spins
  5. 5. 28 July 2020 Quantum Computing 4 (abstract) Computational infrastructure is more powerful when it is in the same shape as the underlying 3D structure of physical reality (concrete) Quantum Computing Tipping Points:  universal quantum computing chips  exotic superconducting materials deployment  quantum optics: global quantum photonic telecommunications networks Thesis
  6. 6. 28 July 2020 Quantum Computing Quantum Scale 5 QCD: Quantum Chromodynamics  “Quantum” = anything at the scale of atomic and subatomic particles  Theme: ability to manipulate physical reality at increasingly smaller scales Subatomic particles Matter particles: fermions (quarks) Force particles: bosons (gluons) Scale Entities Physical Theory 1 1 x101 m Humans Newtonian mechanics 2 1 x10-9 m Atoms, ions, photons Quantum mechanics (nanotechnology) 3 1 x10-15 m Subatomic particles QCD/gauge theories 4 1 x10-35 m Planck length Planck scale Atoms Quantum objects: atoms, ions, photons
  7. 7. 28 July 2020 Quantum Computing Quantum: many exponential speed-ups 1. Bit (0 or 1) 2. Qubit (0 and 1 in superposition) 3. Qudit (more than 2 values in superposition)  Microchip generates two entangled qudits each with 10 states, for 100 dimensions total, for more than six entangled qubits could generate (Imany, 2019 ) 4. Optics (time and frequency multiplexing)  Existing telecommunications infrastructure  Global network not standalone computers in labs 5. Optics (superposition of inputs and gates) 6 Classical Computing Quantum Computing Source: Imany et al. (2019). High-dimensional optical quantum logic in large operational spaces. npj Quantum Information. 5(59):1-10.
  8. 8. 28 July 2020 Quantum Computing 7 What is Quantum Computing? Quantum Computing is using quantum-mechanical properties (SEI: superposition, entanglement, and interference) to perform computation with 2n scaling (e.g. 9-qubit system tests 512 states (29)
  9. 9. 28 July 2020 Quantum Computing Quantum smartphone ship date?  Technology is notoriously difficult to predict  I think there is a world market for maybe five computers - Thomas J. Watson, CEO, IBM, 1943 8 Source: Strohmeyer, R. (2008). The 7 Worst Tech Predictions of All Time. PCWorld. D-Wave Systems 10-feet tall, $15m Current: Ytterbium- 171 isotopes at 1 Kelvin (-458°F) Actual room- temperature superconductor: ??
  10. 10. 28 July 2020 Quantum Computing Quantum Computing impact  Why is it important?  Immanent as substantial new computing paradigm  Immediate: upgrade to new global cryptography standards  Ongoing: substantial step-ups in processing power  When is it coming?  Maybe within 10 years, early commercial systems shipping now  Do all problems become solvable?  No, one-tier improvement in problem solving complexity  How can I try it?  1-minute per month free cloud access D-Wave Systems, IBM  Program and test algorithms 9
  11. 11. 28 July 2020 Quantum Computing Computational Complexity and Quantum Computing 10  Computational complexity: amount (time and space) of computing resources required to solve a problem  QC: one-tier improvement in computational complexity  Canonical Traveling Salesperson Problem: check twice as many cities in half the time using a quantum computer  Solve the next tier of designated problem difficulty with the current tier’s computational resource (in time and space)  NP becomes solvable in P, EXP becomes solvable in NP  Example: factoring large numbers becomes time-reasonable P: polynomial time (e.g. solvable in human-reasonable amount of time); NP: non-polynomial (not solvable in human-reasonable amount of time); EXP: exponential (requires exponential time/space to solve) Computational Complexity
  12. 12. 28 July 2020 Quantum Computing Google: Quantum Advantage (October 23, 2019)  First quantum computer to solve a problem classical computers cannot solve timely  53-qubit Sycamore chip (one damaged qubit)  Task: random circuit sampling (provable randomness)  Sampling versus one answer (i.e. Shor’s factoring, Grover’s search)  Google: Sycamore repeats a random circuit sampling process a million times in 200 seconds (stores circuits in RAM)  Claim: the most powerful classical computer (supercomputer) would take 10,000 years to do the same task  IBM counterclaim: no, the calculation could be performed in 2.5 days (write circuits to hard disk and then sample)  Write circuits to 250 petabytes of hard disk (Summit Oak Ridge National Lab supercomputer) and check with vector matrix multiplication 11 Source: Arute et al. Quantum supremacy using a programmable superconducting processor. Nature. 574:505-11, and https://www.scottaaronson.com/blog/?p=4372
  13. 13. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 12 Quantum Computing 1. Basic Introduction
  14. 14. 28 July 2020 Quantum Computing  A qubit (quantum bit) is the basic unit of quantum information, the quantum version of the classical binary bit 13 What is a Qubit? Bit always exists in a single binary state (0 or 1) Qubit exists in a state of superposition, at every location with some probability, until collapsed into a measurement (0 or 1) Classical Bit Quantum Bit (Qubit) Source: https://www.newsweek.com/quantum-computing-research-computer-flagship-eu-452167
  15. 15. 28 July 2020 Quantum Computing Qudit (quantum information digit)  Qudits: quantum information digits that can exist in more than two states  A qubit exists in a superposition of 0 and 1 before being collapsed to a measurement at the end of the computation  A qutrit exists in the 0, 1, and 2 states until collapsed for measurement (triplet is useful for quantum error correction)  7 and 10 qudits tested  4 optical qudits achieved the processing power of 20 qubits  Motivation: generalize known quantum computing techniques to higher level systems 14 Sources: Qudits: Fernando Parisio; Michael Kues. “It from Bit” Wheeler, J.A. (1990). Information, Physics, Quantum: The Search for Links. In Proc. 3rd Int. Symp. Foundations of Quantum Mechanics, Tokyo, 1989, pp.354-368. Qutrit stabilizer code on a torus It from Bit -> It from Qubit -> It from Qudit The Wheeler Progression
  16. 16. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 15 Quantum Computing 1. Basic Introduction
  17. 17. 28 July 2020 Quantum Computing  Any stable two-level quantum-mechanical system might be used as a qubit  If can obtain 0s and 1s usable in computation 16 How are Qubits made?
  18. 18. 28 July 2020 Quantum Computing 1. Superconductors 2. Photonics 3. Trapped ions 17 Source: Economist, Architecture Race for Quantum Computers, 20 June 2015. Top 3 Qubit Generation Methods (2015)
  19. 19. 28 July 2020 Quantum Computing Top 3 Qubit Generation Methods (2020) 18 1. Superconductors  Commercial systems (on-premises and cloud-based)  IBM & Rigetti: controllable gate model superconductors (~19 qubits) for all computational problems  D-Wave Systems: less-controllable quantum annealing machines (2048 qubits) for optimization problems 2. Photonics 3. Trapped ions Shipping Research
  20. 20. 28 July 2020 Quantum Computing D-Wave Systems Quantum Annealing  Solve optimization problems as low energy landscape  Setup: qubits exist across the landscape in superpositions of 0/1 (quantum wave function)  Like a fog blanketing the problem space  Annealing cycle: runs and the fog layer condenses to one point as the global minimum of the landscape  Qubit spins flip back and forth until settling into the lowest- energy state of the system  Readout: lowest-energy state is optimal answer  Spin glass analogy (flexible spins funnel to lowest energy)  Holographic annealing  Use AdS/CFT correspondence to map boundary-bulk energy operators to readout solution in one fewer dimensions 19 Image Source: Qolynes et al (2014) Frustration in biomolecules
  21. 21. 28 July 2020 Quantum Computing Commercial Status by Platform 20 Source: Synthesized from QCWare Organization Qubit Method # Qubits Status 1 IBM (Almaden CA) Superconducting (gate model) 19 (50) Available 2 D-Wave Systems (Vancouver BC) Superconducting (quantum annealing) 2048 Available 3 Rigetti Computing (Berkeley CA) Superconducting (gate model) 19 Available 4 Google (Mountain View CA) Superconducting (gate model) 53 (72) Built, unreleased 5 Intel/Delft (Netherlands) Superconducting 49 Built, unreleased 6 Quantum Circuits (New Haven CT) Superconducting Unknown Research 7 IonQ (College Park MD) Trapped Ions 23 Built, unreleased 8 Alpine Quantum Tech (Innsbruck) Trapped Ions Unknown Research 9 Microsoft (Santa Barbara CA) Majorana Fermions Unknown Research 10 Nokia Bell Labs (Princeton NJ) FQH State Unknown Research 11 Xanadu Photonics (Toronto ON) Photonics Unknown Research 12 PsiQuantum (Palo Alto CA) Photonics Unknown Research  Tipping point: universal quantum computing chips
  22. 22. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 21 Quantum Computing 1. Basic Introduction
  23. 23. 28 July 2020 Quantum Computing Physical Qubit Generation Method #1 Superconducting Circuits 22 Source: http://news.mit.edu/2014/cheaper-superconducting-computer-chips-1017  Idea: extend semiconductor product line  Use existing global fab infrastructure  Produce superconducting chips  Superconductors: materials with zero electrical resistance when cooled below a certain critical temperature  More than half of the periodic table elements  Electrons travel unimpeded (no energy dissipation)  20% of electricity is lost due to resistance  At critical temperature, two electrons (usually repelling) form a weak bond (a Cooper pair) that can tunnel through metal with no resistance Superconducting circuit Superconducting chip
  24. 24. 28 July 2020 Quantum Computing Key enabling technology: Materials advance “Room-temperature” Superconductors 23  Implication: cool with liquid nitrogen not helium  “Desktop” computing without bulky cryogenic equipment  Initial superconducting materials (1986): copper oxides  Bismuth strontium calcium and yttrium barium copper oxide  New wider range of materials (2008)  Metal-based compounds of iron, aluminum, copper, niobium  Experimental high-pressure materials (2015)  Hydrogen sulfide and lanthanum superhydride Superconducting Material Critical Temperature Discovery 1 Ordinary superconducting materials Below 30 K -303 °C 1911 2 High-temperature superconducting materials 138 K -135 °C 1986 3 Room-temperature superconducting materials 203 K -70 °C 2015 4 High room-temperature superconducting materials 260 K -13 °C 2019
  25. 25. 28 July 2020 Quantum Computing Superconducting Circuits 24  Josephson junction: nonlinear superconducting inductors create qubit energy levels  The nonlinearity of the Josephson inductance breaks the degeneracy of the energy level spacings, allowing system to be restricted to only the 2-qubit states  Josephson junctions needed to produce qubits, otherwise superconducting loop is just a circuit  Linear inductors in a traditional circuit are replaced with the Josephson junction, a nonlinear element that produces energy levels with different spacings from each other that can be used as a qubit  Superconducting loop is a SQUID (superconducting quantum interference device) magnetometer (a device for measuring magnetic fields) Josephson: Nobel Prize in Physics (1973) for work predicting the tunneling behavior of superconducting Cooper pairs
  26. 26. 28 July 2020 Quantum Computing Superconducting Circuits: Rigetti 25  Single Josephson junction qubit on a sapphire substrate  Electrical circuit with oscillating current forms the qubits and is and controlled by electromagnetic fields  Substrate embedded in a copper waveguide cavity  Waveguide coupled to qubit transitions to perform computation  Chip: Alternating fixed and tunable transmon qubits  19Q (one qubit not tunable) Source: Otterbach, J.S., et al. (2017). Unsupervised machine learning on a hybrid quantum computer. arXiv: 1712.05771v1
  27. 27. 28 July 2020 Quantum Computing Superconducting Circuits: Google 26  Qubits are electrical oscillators constructed from aluminum (niobium is also used)  Superconducting at 1 K (−272°C)  The oscillator qubits store small amounts of electrical energy  Oscillator in the 0 state has zero energy  Oscillator in the 1 state has a single quantum of energy  Oscillator resonance frequency  6 gigahertz (300 millikelvin)  Sets the energy differential between the 0 and 1 states  Low enough frequency to build with off-the-shelf components  High enough frequency so ambient thermal energy does not scramble the oscillation and introduce errors Superconducting microwave circuit
  28. 28. 28 July 2020 Quantum Computing Physical Qubit Generation Method #2 Quantum Photonics 27 Image Source: PSI Quantum Photon movement  Quantum-mechanical objects  Atom, ion, photon  Optical circuits do not require error correction  Global communications networks built on photonic transfer  Quantum photonics (general)  Single photons represent qubits  Realized in computing chips or in free space  Compute with entangled states of multiple photons (photonic clusters)  Single photons are sent through the chip or free space for the computation and then measured with photon detectors at the other end Quantum photonic processor Quantum photonic wafer Quantum photonic array
  29. 29. 28 July 2020 Quantum Computing Continuous Qubit Optical Interfaces 28 Source: Vuckovic, J. (2020). Stanford Optimized Quantum Photonics; Sapra, N.V., Yang, K.Y., Vercruysse, D., et al. (2020). On-chip integrated laser-driven particle accelerator. Science. 367(6473):79-83  All-optical platform from the beginning  Homogeneous qubits with optical interfaces  Method: exploit color center defects (Fabre effect)  Color centers in diamond (silicon and tin vacancy)  Color centers in silicon carbide (manufacture silicon vacancy in 4H poly tech type (thin film))  Exploit energy level differentials due to missing atoms in the lattice structure  The wavelength between two color centers depends on which atom in the lattice is missing and can be used for computation
  30. 30. 28 July 2020 Quantum Computing Quantum Photonics 29  Diamond center defects method  Introduce impurities to diamond crystal lattice  Implant ion to create nitrogen vacancy  Nitrogen vacancy produces the Farbe center (color center), a defect in a crystal lattice occupied by an unpaired electron  The unpaired electron creates an effective spin which can be manipulated as a qubit  Quantum state can be initialized, manipulated, and measured at room temperature  Uses the same physics and math as for Josephson junctions in microwave chips  But, coherence time limited to spin time Related work: Accelerator-on-a-chip (Stanford Nanoscale and Quantum Photonics Lab) Source: Vuckovic, J. (2020). Stanford Optimized Quantum Photonics; Sapra, N.V., Yang, K.Y., Vercruysse, D., et al. (2020). On-chip integrated laser-driven particle accelerator. Science. 367(6473):79-83
  31. 31. 28 July 2020 Quantum Computing Physical Qubit Generation Method #3 Trapped Ions 30 Source: Images: IonQ, College Park MD  Silicon chips store Ytterbium ions in electromagnetic traps  Manipulate in computation with lasers and electromagnetic fields  Ions (atoms stripped of electrons)  Easier to compute with positively or negatively charged ions  Ytterbium ions do not need supercooling, have a long coherence time, and require less error correction
  32. 32. 28 July 2020 Quantum Computing Trapped Ions 31 Source: IonQ, College Park MD 1. Silicon chip with 100 electrodes confines and controls ions in an ultrahigh-vacuum  Electrodes underneath the ions apply electrical potentials to hold the charged particles together in a linear array 2. Lasers initialize the qubits, entangle them through coupling, and produce quantum logic gates to execute the computation 3. At the end of the computation, another laser causes ions to fluoresce if they are in a certain qubit state  Fluorescence collected to measure each qubit and compute the result of the computation Ions trapped in array Trapped-ion quantum processor
  33. 33. 28 July 2020 Quantum Computing Physical Qubit Generation Method #4 Topological Qubits: Majorana Fermions 32  Topological qubits  Qubits made from particles on topological superconductors and electrically controlled in computation based on movement trajectories  Majorana fermions (particle + anti-particle pairs)  Novel quantum phases arising in condensed matter with Cooper pairing states (i.e. quantum computable states) on superconductor edges  Majorana fermions move in trajectories resembling a multi-stranded braid  Use braid wave functions as quantum logic gates
  34. 34. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 33 Quantum Computing 1. Basic Introduction
  35. 35. 28 July 2020 Quantum Computing DiVincenzo Criteria for Universal Computing 34  Quantum computing standards for gate array computing  1: demonstrate a reliable system for making qubits  2-5: perform accurate computation  Qubit formation (criterion #1) 1. A scalable system of well-characterized qubits  Qubit control for computation (criteria #2-5) 2. Qubits that can be initialized with fidelity (to the zero state) 3. Qubits with long-enough coherence time for calculation 4. A universal set of quantum gates 5. Capability to measure any specific qubit in the ending result Source: DiVincenzo, D.P. (2000). The physical implementation of quantum computation. Fortschrit. Phys. 48(9–11):771–83.
  36. 36. 28 July 2020 Quantum Computing Hardware for Qubit Generation and Control 35 Source: Synthesized from QCWare Qubit Type Qubit formation (DiVincenzo criterion #1) Qubit control for computation (DiVincenzo criteria #2-5) 1 Superconducting circuits Electrical circuit with oscillating current Electromagnetic fields and microwave pulses 2 Photonic circuits Single photons (or squeezed states) in silicon waveguides Marshalled cluster state of multi- dimensional entangled qubits 3 Diamond center defects Defect has an effective spin; the two- levels of the spin define a qubit Microwave fields and lasers 4 Trapped ions Ion (atom stripped of one electron) Ions stored in electromagnetic traps and manipulated with lasers 5 Majorana fermions Topological superconductors Electrically-controlled along non- abelian “braiding” path 6 Neutral atoms Electronic states of atoms trapped by laser-formed optical lattice Controlled by lasers 7 Quantum dots Electron spins in a semiconductor nanostructure Microwave pulses  Race to build first universal gate quantum computer  Easy to generate qubits, difficult to compute with fidelity
  37. 37. 28 July 2020 Quantum Computing Quantum Programming  Standard gates  Hadamard gate: acts on one qubit to put it in a superposition  CNOT gate: acts on two qubits to flip one  Toffoli gate: acts on three or more qubits to implement the six Boolean operators (AND, conditional AND, OR, conditional OR, exclusive OR, and NOT)  Computing paradigms  Classical computing relies on electrical conductivity  Boolean algebra (true/false, and/or) to manipulate bits  Quantum computing relies on quantum mechanics  Linear algebra to manipulate matrices of complex numbers (i.e. the amplitudes of possible states) 36
  38. 38. 28 July 2020 Quantum Computing Standardized Tools 37  Bernstein-Vazirani algorithm (1997)  “Hello, World!” of quantum: extract specific bits from a string  Variational quantum eigensolver (VQE) (Peruzzo, 2014)  Find the eigenvalues of a matrix; An eigensolver is a program designed to calculate solutions to 3D problems  Quantum approximate optimization algorithm (QAOA) (Farhi, 2014)  Combinatorial optimization problems (Traveling Salesman Problem, find a “good” solution (acceptable answer) in polynomial time (a reasonable amount of time); max-cut partition function, solve as energy landscape minimization
  39. 39. 28 July 2020 Quantum Computing Goal: Standard Gate Array Computing 38  2n scaling: 9-qubit system (29) represents 512 states Source: D-Wave Systems, A Machine of a Different Kind, Quantum Computing, 2019
  40. 40. 28 July 2020 Quantum Computing Quantum Computing Roadmap 39  Long-term: Universal quantum computing  Universal computation devices using fault-tolerant quantum information processors  Error correction required (system noise overwhelms coherent wave activity of qubit particles)  Available now: NISQ devices (noisy intermediate- scale quantum)  Error correction not required  Applications in optimization, simulation, machine learning, and cryptography Source: Preskill, J. (2018). Quantum Computing in the NISQ era and beyond. Quantum. 2(79):1-20.
  41. 41. 28 July 2020 Quantum Computing 40 Sources: Preskill, J. (2018). Quantum computing in the NISQ era and beyond. Quantum 2(79):1–20. https://amitray.com/roadmap-for-1000-qubits-fault-tolerant-quantum-computers/ Quantum Computing Roadmap  Long-term applications  Shor’s factoring algorithm (could break current cryptography standard (RSA))  Grover’s search algorithm (faster search through large data sets)
  42. 42. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 41 Quantum Computing 1. Basic Introduction
  43. 43. 28 July 2020 Quantum Computing Quantum Computing Applications  Cryptography and security  Certifiable randomness (entropy) and quantum statistics  Quantum machine learning  Optimization, nitrogen sequestration  Simulation  Exotic materials, molecular dynamics, drug discovery  Emulation and pathology resolution  Quantum computing for the brain 42
  44. 44. 28 July 2020 Quantum Computing Quantum Cryptography  Quantum computing implicated in eventually being able to break existing cryptographic standards (2048-bit RSA)  2019 US National Academies of Sciences report  “unlikely within 10 years” however methods improving  Solution: US NIST developing next-generation standards  Lattice cryptography (complex 3D arrangements of atoms)  Instead of the difficulty of factoring large numbers (RSA 2048) or any other number theory-based methods (e.g. discrete log)  Overall mathematical shift to group theory (lattices) from number theory (factoring) 43 Source: Grumbling, E. & Horowitz, M. (2019). Quantum Computing: Progress and Prospects. Washington, DC: US National Academies of Sciences, p 157.
  45. 45. 28 July 2020 Quantum Computing 44 NIST Next-generation Cryptography  NIST: 26 of 69 algorithms advance to post-quantum crypto semifinal (Jan 2019)  Public-key encryption (17)  Digital signature schemes (9)  Approaches: lattice-based, code-based, multivariate  Lattice-based: target the Learning with Errors (LWE) problem with module or ring formulation (MLWE or RLWE)  Code-based: error-correcting codes (Low Density Parity Check (LDPC) codes)  Multivariate: field equations (hidden fields and small fields) and algebraic equations Source: NISTIR 8240: Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process, January 2019, https://doi.org/10.6028/NIST.IR.8240.
  46. 46. 28 July 2020 Quantum Computing Nature’s Quantum Security Features 45 Source: Swan et al. (2020). Quantum Computing. London: World Scientific.  Reality is information-theoretic  Computational complexity class of quantum information (BQP/QSZK) has access to  Security features naturally built into quantum mechanical domains Principle Security Feature 1 No-cloning theorem Cannot copy quantum information 2 No-measurement principle Cannot measure quantum information without damaging it (eavesdropping is immediately detectable) 3 Quantum statistics Provable randomness: distributions could only have been quantum- generated (implications for quantum cryptography) 4 Quantum error correction Error correction via ancilla (larger state of entangled qubits) 5 BQP/QSZK computational complexity Quantum information domains compute quickly enough to perform their own computational verification (zero-knowledge proofs)
  47. 47. 28 July 2020 Quantum Computing Killer App: Quantum Machine Learning 46  Machine Learning and Quantum Computing  Statistical methods with probabilistic output Sigmoidal Function 3D Hilbert Space 0 1 0 1 Machine Learning Quantum Computing Source: Image: machine learning object recognition: Anandkumar (2014). Tensor models for machine learning.
  48. 48. 28 July 2020 Quantum Computing Quantum Optical Neural Networks 47  Classical neural network architecture  Hidden layers are rectified linear units (ReLUs) and the output neuron uses a sigmoid activation function to map the output into the range (0, 1)  Quantum optical neural network architecture  Inputs are single photon Fock states. The single-site nonlinearities are given a Kerr-type interaction applying a phase quadratic in the number of photons. Readout is given by photon-number-resolving detectors, which measure the photon number at each output mode Source. Steinbrecher, G.R. et al., (2019). Quantum Optical Neural Networks. npj Quantum Information. 5(60):1-9. Quantum Optical Neural NetworkClassical Neural Network
  49. 49. 28 July 2020 Quantum Computing Quantum Optimization Use Cases (D-Wave) 48 Sources: Hetzner, C. (2019). VW, Canadian tech company D-Wave team on quantum computing. Automotive News Canada; Fassler, J. (2018). Hey Amazon, Kroger’s new delivery partner operates almost entirely on robots. New Food Economy.  UK online grocer Ocado’s automated warehouses:  1100 robots, 250,00 items, 3m instructions  Optimization algorithm coordinates hundreds of robots passing within 5 millimeters of each other at speeds of 4 meters per second, fulfilling 65,000 orders per week  Volkswagen: 418-taxi network in Beijing  Optimize travel time, implement resulting traffic management system in Lisbon and beyond  AdTech for web browser promotion placement
  50. 50. 28 July 2020 Quantum Computing Simulating Chemistry  Molecular dynamics  Can simulate millions of atoms at present  Need quantum computing to capture quantum- mechanical interactions between electrons 49 Sources: Univ. of Illinois at Chicago/Argonne National Lab/Univ. of Southern California; Kandala et al. (2017). Nature. 549, 242 7-qubit superconducting circuit (false color) to simulate a beryllium hydride molecule (IBM)
  51. 51. 28 July 2020 Quantum Computing Chips: CPU -> GPU -> TPU -> QPU  GPU (graphics processing unit)  3D graphics cards for fast matrix multiplication  TPU (tensor processing unit) (Edge TPU 2018)  Flow through matrix multiplications without having to store interim values in memory  QPU (quantum processing unit) (Sycamore 2020)  Solve problems quadratically or polynomially faster exploiting SEI Properties (superposition, entanglement, interference) 50 TPU processing cluster and Sycamore quantum superconducting chip Tipping point: universal quantum computing chips
  52. 52. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 51 Quantum Computing 1. Basic Introduction
  53. 53. 28 July 2020 Quantum Computing Quantum Optical Networks 52  Quantum photonics could be at the center of future global communications networks just as optical networking is today  Many ways to make qubits for computing on standalone machines  For a larger architecture of networked machines, electrical signals must be converted to optical signals  Photonics: core global telecoms network technology  Future: “Cisco for optical routers”  Quantum photonics: next-gen telecoms Image Source: Walther, P. (2018). Photonic Quantum Computing. Vienna Center for Quantum Science and Technology. Integrated quantum optical switch
  54. 54. 28 July 2020 Quantum Computing Scalable Global Quantum Networks 53  Quantum internet  Security, privacy, scalability  Quantum key distribution, quantum routers, quantum repeaters, quantum simulators, quantum components, quantum memory 1. Homogeneous scalable qubits (standalone machines) 2. Efficient optical interfaces (networked machines)  Quantum transducers convert microwave to optical  Optical interfaces (optical superconducting)  Microwave interfaces (Josephson junction superconducting) Source: Vuckovic, J. (2020). Stanford Optimized Quantum Photonics; Sapra, N.V., Yang, K.Y., Vercruysse, D., et al. (2020). On-chip integrated laser-driven particle accelerator. Science. 367(6473):79-83
  55. 55. 28 July 2020 Quantum Computing Scalable Global Quantum Networks 54  Two methods currently in development  Microwave superconducting platform interfaced to optical networks with electrical-optical interconnects  Optical platform with continuous qubit optical interfaces  Photonic Integrated Circuits (PICs) Source: Vuckovic, J. (2020). Stanford Optimized Quantum Photonics; Sapra, N.V., Yang, K.Y., Vercruysse, D., et al. (2020). On-chip integrated laser-driven particle accelerator. Science. 367(6473):79-83 Quantum Photonic Processors All-optical Platform Superconducting Processors Optical-Electrical Interconnects Driver: quantum computing Drivers: 5G, data center, 100GbE All OpticalOptical-Electrical Chips Global Comms Networks
  56. 56. 28 July 2020 Quantum Computing Quantum Photonic Spacetime Multiplexing 55  Standard quantum computing speed-up  Space accelerated by testing states of 3D space  Superposition of inputs  Optical quantum computing speed-up  Time accelerated by testing permutations of gate order  Superposition of gate order and inputs Sources: Procopio et al. 2015. Experimental Superposition of Orders of Quantum Gates. Nature Communications. 6(7913):1-6; Walther, P. (2018). Photonic Quantum Computing. Vienna Center for Quantum Science and Technology. Quantum Photonic Gate Superposition Parallel to time-space manipulation in global fiberoptic communications TDM/WDM: time- division wave-division multiplexing
  57. 57. 28 July 2020 Quantum Computing  Agenda  What is a Qubit?  How are Qubits made?  Qubit methods technical deep dive  Quantum Programming  Applications  The Future: Quantum Photonics  Conclusion 56 Quantum Computing 1. Basic Introduction
  58. 58. 28 July 2020 Quantum Computing Risks and Limitations  Implementation stalls  Qubits are more sensitive to environmental noise than bits  Error correction stalls  Unable to move past contemporary 50-70 qubit machines to million-qubit machines  Materials discovery stalls  Cannot find actual room-temperature superconductors  Limitations of underlying physical theories  Quantum mechanics  Need beyond-probability methods that emphasize spectra, entanglement, entropy (irreversibility), and field flux  Technology cycle is too early 57
  59. 59. 28 July 2020 Quantum Computing 58 Conclusion  High-dimensionality is a central theme in science and technology development  Not just 3D but higher-dimensionality  Nature’s built-in quantum security features  No cloning, no measurement, zero-knowledge proofs, quantum statistics & error correction  Killer app: quantum machine learning  Statistical methods with probabilistic output  Apps in general:  Cryptography, superconducting materials simulation, quantum computing for the brain  The future: quantum optical networks
  60. 60. 28 July 2020 Quantum Computing 59 (abstract) Computational infrastructure is more powerful when it is in the same shape as the underlying 3D structure of physical reality (concrete) Quantum Computing Tipping Points:  universal quantum computing chips  exotic superconducting materials deployment  quantum optics: global quantum photonic telecommunications networks Thesis
  61. 61. Quantum Computing Lecture 1: Basic Introduction Mountain View CA, July 28, 2020 Slides: http://slideshare.net/LaBlogga Thank you! Questions? Melanie Swan

Quantum reality is information-theoretic and computable Lecture 1: Quantum Computing basics (hardware) Lecture 2: Advanced concepts (control software between macroscale reality and quantum microstates) Lecture 3: Speculative application (B/CI neuronanorobot network)

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