Quantum Computing: Transforming the Digital Age

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1 Quantum Computing: Transforming the Digital Age Krysta Svore Quantum Architectures and Computation (QuArC) Microsoft Research Quantum Optimization Workshop 2014

3 Antikythera mechanism (100 BC) Babbage s Difference Engine (proposed 1822) ENIAC (1946) Sequoia (2012) Quantum (2025?) Thanks to Matthias Troyer

4 Is there anything we can t solve on digital computers? 4

5 Some problems are hard to solve NP-Hard QMA-Hard QMA BQP NP P Ultimate goal: Develop quantum algorithms whose complexity lies in BQP\P

6 Quantum Magic: Interference source of particles interference pattern = quantum coherence Classical objects go either one way or the other. Quantum objects (electrons, photons) go both ways. Gives a quantum computation an inherent type of parallelism!

7 Quantum Magic: Qubits and Superposition 0 = = 1 = = single atom g = 0 e = 1 single spin = 0 = 1 ψ = = + = + Information encoded in the state of a two-level quantum system

8 Thanks to Charlie Marcus ψ =

9 Input Output

10 Quantum Magic: Entanglement Nonlocal Correlations!

12 Quantum Magic: Entanglement N non-interacting qubits ψ 0 ψ 1 2*5 distinct amplitudes ψ 2 ψ 4 ψ 3 ψ total = α β 0 1 α β 1 1 α N β N 1 1 Thanks to Rob Schoelkopf State of N non-interacting qubits: ~ N bits of info

13 Quantum Magic: Entanglement General state of N interacting qubits ψ 1 32 distinct amplitudes! ψ 2 Simulating ψ 0 a 200-qubit interacting system requires ~10 60 classical bits! ψ 4 ψ 3 ψ total = c c c 2 N Thanks to Rob Schoelkopf State of N interacting qubits: ~ 2 N bits of info!

14 Quantum Magic: What s the catch? Need coherent control ψ 1 Need strongly Interacting system ψ 0 ψ 2 Decoherence and errors! ψ 4 ψ 3 Avoid interaction with outside environment! Thanks to Rob Schoelkopf

15 Quantum Gates: Digital quantum computation Basic unit: bit = 0 or 1 Computing: logical operation Basic unit: qubit = unit vector α 0 + β 1 Computing: unitary operation NOT NOT α β = β α

16 Quantum Gates: Digital quantum computation Basic unit: bit = 0 or 1 Computing: logical operation Description: truth table A B Y Basic unit: qubit = unit vector α 0 + β 1 Computing: unitary operation Description: unitary matrix XOR gate CNOT gate

17 Quantum power unleashed: super-fast FFT FFT # ops = N log N Example: 1GB of data = 10 Billion ops Quantum FFT # ops = log N Example: 1GB of data = 27 ops (!!!)

18 Any other catches? No-cloning principle I/O limitations output + measure + Quantum information cannot be copied Input: preparing initial state can be costly Output: reading out a state is probabilistic

19 Quantum Algorithms Exist! Shor s Algorithm (1994) Solving Linear Systems of Equations (2010) Quantum simulation (1982) Breaks RSA, elliptic curve signatures, DSA, El-Gamal Exponential speedups Applications shown for electromagnetic wave scattering Exponential speedups Simulate physical systems in a quantum mechanical device Exponential speedups

20 Cryptography

21 15 =

22 15 = 5 3

23 1387 =

24 1387 = 19 73

25 =

26 Example: (n=2048 bits) classically ~7x10 15 years = quantum ~ seconds

27 Breaking RSA and elliptic curve signatures Classical: O exp n 1 3 log n 2 3 Quantum: O n 2 log n

28 Machine learning

data, not just megabytes of limited data No silver bullet approach to learning Good new representations are introduced

29 The Problem in Artificial Intelligence How do we make computers that see, listen, and understand? Goal: Learn complex representations for tough AI problems Challenges and Opportunities: Terabytes of (unlabeled) web data, not just megabytes of limited data No silver bullet approach to learning Good new representations are introduced only every 5-10 years Can we automatically learn representations at low and high levels? Does quantum offer new representations? New training methods?

30 Deep networks learn complex representations Desired outputs l 1 l 2 l j l J object recognition High-level features hv 1 vh 2 vh ji vh IJ 1 object properties Mid-level features hv 1 vh 2 vh ji vh JI 1 textures Difficult to specify exactly Low-level features Input hv 1 vh 2 hv ji hv JI 1 v 1 v 2 v i v I 1 edges pixels Deep networks learn these from data without explicit labels Analogy: layers of visual processing in the brain

31 What are the primary challenges in learning? Desire: learn a complex representation (e.g., full Boltzmann machine) Intractable to learn fully connected graph poorer Can we learn representation a more complex Pretrain layers? Learn simpler graph with faster train time? Desire: efficient computation of true gradient Intractable to learn actual objective poorer representation Approximate the gradient? Desire: training time close to linear in number of training examples Slow training time slower Can speedup model of innovation training on a quantum computer? Build a big hammer? Look for algorithmic shortcuts? representation on a quantum computer? Can we learn the actual objective (true gradient) on a quantum computer?

32 Training RBM - Classical for each epoch for i=1:n CD(V_i, W) dldw += dldw end W = W + ( /N) dldw end //until convergence //each training vector //CD given sample V_i and parameter vector W //maintain running sum //take avg step CD Time: # Epochs x # Training vectors x # Parameters ML Time: # Epochs x # Training vectors x (# Parameters) 2 x 2 v + h

33 Training RBM - Quantum for each epoch for i=1:n CD(V_i, qml(v_i, W) W) dldw += dldw end W = W + ( /N) dldw end //until convergence //each training vector //CD //qml: given Use sample q. computer V_i and tp parameter Approx. to vector sample WP(v,h) //maintain running sum //take avg step qml Time ~ # Epochs x # Training vectors x # Parameters!!! qml Size (# qubits) for one call ~ v + h + K, K 33

34 Quantum simulation

35 What does quantum simulation do? Physical Systems Quantum Chemistry Superconductor Physics Quantum Field Theory Computational Applications Emulating Quantum Computers Linear Algebra Differential Equations

36 Quantum simulation Particles can either be spinning clockwise (down) or counterclockwise (up) = = There are 2 5 possible orientations in the quantum distribution. Cannot store this in memory for 100 particles.

Quantum Simulation for Quantum Chemistry Ultimate problem: Simulate molecular dynamics of larger systems or to higher accuracy Want to solve system exactly Current solution: 33% supercomputer usage

37 Quantum Simulation for Quantum Chemistry Ultimate problem: Simulate molecular dynamics of larger systems or to higher accuracy Want to solve system exactly Current solution: 33% supercomputer usage dedicated to chemistry and materials modeling Requires simulation of exponential-size Hilbert space Limited to spin-orbitals classically Quantum solution: Simulate molecular dynamics using quantum simulation Scales to 100s spin-orbitals using only 100s qubits Runtime recently reduced from O(N 11 ) to O N 4 O(N 6 ) 37

Quantum Chemistry Can quantum chemistry be performed on a small quantum Improving Quantum Algorithms for Quantum Chemistry: M. B. computer: Dave Wecker, The Bela Trotter Bauer, Step Bryan Size K.

Doherty, Matthias Troyer We present several improvements to the standard Trotter-Suzuki based As quantum computing Ferredoxin The technology simulation improves of molecules (Feand is quantum a

$of quantum chemistry on a quantum computers with a small However, but non-trivial recent studies number \cite{wbch13a,hwbt14a} 2 S of N 2 ) used in many metabolic reactions > 100 qubits computer.$

38 Quantum Chemistry Can quantum chemistry be performed on a small quantum Improving Quantum Algorithms for Quantum Chemistry: M. B. computer: Dave Wecker, The Bela Trotter Bauer, Step Bryan Size K. Required Clark, Matthew for Accurate B. Quantum Hastings, Simulation D. Wecker, of B. Quantum Bauer, M. Chemistry Troyer Hastings, Matthias Troyer David Poulin, M. B. Hastings, Dave Wecker, Nathan Wiebe, Andrew C. Doherty, Matthias Troyer We present several improvements to the standard Trotter-Suzuki based As quantum computing Ferredoxin The technology simulation improves of molecules (Feand is quantum a widely anticipated algorithms application used of quantum in the simulation computers. of quantum chemistry on a quantum computers with a small However, but non-trivial recent studies number \cite{wbch13a,hwbt14a} 2 S of N 2 ) used in many metabolic reactions > 100 qubits computer. have cast a First, shadow we modify on this how hope Jordan-Wigner by transformations are appear feasible in the revealing near including future that the the question complexity energy of possible in gate count transport of such implemented simulations in photosynthesis increases reduce with their the cost number from linear of or logarithmic in the applications of small quantum spin orbitals computers N as N8, gains which importance. becomes prohibitive One even number for molecules of orbitals of to modest a constant. size N 100. Our modification This does not require frequently mentioned study application was partly is Feynman's based on original a scaling proposal analysis of of the Trotter additional step ancilla required qubits. for an Then, ensemble we demonstrate of how many operations simulating quantum systems, random and artificial in particular molecules. the Here, electronic we revisit structure this analysis can be and parallelized, find instead leading that the to a scaling further is linear decrease in the parallel of molecules and materials. Intractable closer to this N6 in paper, worst on we case a analyze classical for real the model computer molecules depth we have of the studied, circuit, indicating the cost that of the a small random constant factor increase in computational requirements ensemble for fails one to of accurately the standard capture algorithms the statistical to properties number of of qubits real-world required. molecules. Thirdly, Actual we modify the term order in the perform quantum chemistry scaling may on a be quantum significantly computer. better We than focus this on due to Trotter-Suzuki averaging effects. decomposition, We then present significantly reducing the error at given the quantum resources First alternative required paper: simulation to find the scheme ground ~300 and state million show of a that years it can Trotter-Suzuki sometimes to solve outperform timestep. existing A final improvement schemes, but modifies the Hamiltonian molecule twice as large that as this what possibility current classical depends computers crucially on can the solve details to of reduce the simulated errors introduced molecule. We by the obtain non-zero Trotter-Suzuki timestep. All exactly. We find that Second while further such improvements a paper: problem requires ~30 using a about version years a of ten-fold the to coalescing solve of these (10 scheme techniques 7 reduction) of \cite{wbch13a}; are validated this using scheme numerical simulation and increase in the number is based of qubits on over using current different technology, Trotter steps the for different detailed terms. gate The method counts are we given use to for bound realistic the molecules. required increase in the complexity number of gates simulating that can a given be coherently molecule is efficient, in contrast to approach of Third paper: ~300 seconds to solve (another 10 3 reduction) executed is many orders \cite{wbch13a,hwbt14a} of magnitude larger. This which suggests relied that on exponentially for costly classical exact simulation. quantum computation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed. H = pq h pq a p a q pqrs h pqrs a p a q a r a s

39 Quantum Chemistry H = pq h pq a p a q pqrs h pqrs a p a q a r a s

Application: Nitrogen Fixation Ultimate problem: Find catalyst to convert nitrogen to ammonia at room temperature Reduce energy for conversion of air to fertilizer Current solution: Uses Haber

40 Application: Nitrogen Fixation Ultimate problem: Find catalyst to convert nitrogen to ammonia at room temperature Reduce energy for conversion of air to fertilizer Current solution: Uses Haber process developed in 1909 Requires high pressures and temperatures Cost: 3-5% of the worlds natural gas production (1-2% of the world s annual energy) Quantum solution: ~ qubits: Design the catalyst to enable inexpensive fertilizer production 40

Capture at point sources Results in 21-90% increase in energy cost Quantum

41 Application: Carbon Capture Ultimate problem: Find catalyst to extract carbon dioxide from atmosphere Reduce 80-90% of emitted carbon dioxide Current solution: Capture at point sources Results in 21-90% increase in energy cost Quantum solution: ~ qubits: Design a catalyst to enable carbon dioxide extraction from air 41

scaling Clustering, regression, classification Better model training Can we harness interference to

42 Quantum Algorithm Opportunities Quantum simulation Machine learning Cryptography Extend q. chem. method to solid state materials E.g., high temp. superconductivity ~ 2000 qubits; linear or quad. scaling Clustering, regression, classification Better model training Can we harness interference to produce better inference models? RSA, DSA, elliptic curve signatures, El-Gamal What questions should we pose to a quantum computer?

43 Requirements for Quantum Computation Quantum algorithms: Design real-world quantum algorithms for small-, medium- and largescale quantum computers Quantum hardware architecture: Architect a scalable, fault-tolerant, and fully programmable quantum computer Quantum software architecture: Program and compile complex algorithms into optimized, targetdependent (quantum and classical) instructions

44 Quantum Computing through the Ages Age of Scalability Age of Algorithms Age of Quantum Error Correction Age of Quantum Feedback Age of Measurement Age of Entanglement Age of Coherence We are ~ here M. Devoret and R. Schoelkopf, Science (2013)

45 Quantum Hardware Technologies Ion traps NV centers Superconductors Quantum dots Linear optics Topological

46 46

47 Sent Classical Error Correction 0 1-p p p p Probability p of having a bit flipped Repetition code: redundantly encode, majority voting Received Reduces classical error rate to 3p 2 2p 3 Can we do this for quantum computing? Some reasons to think no: No cloning theorem Errors are continuous (or are they?) Measurements change the state Thanks to Rob Schoelkopf

Different Error Correction Architectures Standard QEC Surface Code Modular Approach Switchable Router 1,000 7 or 910,000 physical actual 10 2 10qubits 4 /logical for few qubits/ every module logical!

48 Different Error Correction Architectures Standard QEC Surface Code Modular Approach Switchable Router 1,000 7 or 910,000 physical actual qubits 4 /logical for few qubits/ every module logical!! qubits per logical (+ concatenation!) threshold ~ 1% good local gates (10-4?) remote gates fair (90%?) Thanks to Rob Schoelkopf Overhead required in known schemes: threshold ~ 10-4 many ops., syndromes per QEC cycle large system to see effects? then construct QEC as software layer?

49 Image courtesy of Charlie Marcus

50 Image courtesy of Leo Kouwenhoven

51 Image courtesy of Leo Kouwenhoven 51

52 Topology provides natural immunity to noise! Microsoft Confidential - Do Not Distribute

54 Epitaxial growth of InAs (or InSb) nanowires

55 Hardware provides error correction: Only ~10-100s for every logical???

A Software Architecture for Quantum Computing The LIQUi platform [Wecker, Svore, 2014] High-level Quantum Algorithm Quantum Gates Quantum Function Implementation Quantum Circuit Decomposition Quantum

56 A Software Architecture for Quantum Computing The LIQUi platform [Wecker, Svore, 2014] High-level Quantum Algorithm Quantum Gates Quantum Function Implementation Quantum Circuit Decomposition Quantum Circuit Optimization Quantum Error Correction Simulation Runtime Environments Target-dependent Optimization Layout, Scheduling, Control Target-dependent Representation Classical Control/Quantum Machine Instructions

57 Circuit for Shor s algorithm using 2n+3 qubits Stéphane Beauregard Largest we ve done: 14 bits (factoring 8193) 14 Million Gates 30 days

58 As defined in: Circuit for Shor s algorithm using 2n+3 qubits Stéphane Beauregard let op (qs:qubits) = CCAdd a cbs AddA' N bs QFT' bs CNOT [bmx;anc] QFT bs CAddA N (anc :: bs) CCAdd' a cbs // Add a to Φ b // Sub N from Φ a + b // Inverse QFT of Φ a + b N // Save top bit in Ancilla // QFT of a+b-n // Add back N if negative // Subtract a from Φ a + b mod N QFT' bs // Inverse QFT X [bmx] // Flip top bit CNOT [bmx;anc] // Reset Ancilla to 0 X [bmx] // Flip top bit back QFT bs // QFT back CCAdd a cbs // Finally get Φ a + b mod N

60 LIQUi let let for to do let for to do let for to let let QftOp = adjoint QftOp

61 Conclusions Quantum computers exploit interference and superposition to solve problems. How big/fast does a quantum computer have to be to have an advantage? [Boixo, Ronnow et al 13] [Wecker, Bauer et al 14] What are the right questions to ask a quantum computer? [Wiebe, Braun, Lloyd 12] [Wiebe, Grenade et al 13] Exponential speedups for certain simulation, cryptography, linear algebra problems. How do you compile, test, and debug quantum algorithms? [Wiebe, Kliuchnikov 13] [Bocharov, Gurevich, Svore 13] [Wecker, Svore Geller 14] What other problems does a quantum computer solve better or faster?

62 QuArC Doug Carmean Vadym Klichnikov Alex Bocharov Yuri Gurevich Alan Geller Dave Wecker Krysta Svore Ken Reneris Martin Roetteler Burton Smith Nathan Wiebe

63 Station Q Maissam Barkeshli Bela Bauer Parsa Bonderson Meng Cheng Michael Freedman Matthew Hastings Roman Lutchyn Mike Mulligan Chetan Nayak Kevin Walker Zhenghan Wang Jon Yard

64 University Partners David Reilly U. Sydney Charlie Marcus NBI Leo Kouwenhoven Delft Amir Yacoby Harvard Dale Van Harlingen UIUC Mike Manfra Purdue Chris Palmstrom UCSB Bert Halperin Harvard Sankar Das Sarma U Maryland Matthias Troyer ETH Zurich

Quantum Computing: Transforming the Digital Age

CRA Snowbird 2014 Quantum Computing: Transforming the Digital Age Krysta Svore Quantum Architectures and Computation (QuArC) Microsoft Research Antikythera mechanism (100 BC) Babbage s Difference Engine