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Quantum Computers – Is the Future Here? Tal Mor – CS.Technion QIPA Dec. 2015 128 ?? [ 2011 ; sold to LM ] D-Wave Two :512 ?? [ 2012 ; sold to NASA + Google ] D-Wave Three: 2,048 ?? [ 2016 ?? ] Content • Quantum information and computation – what for? • Quantum Bits and Algorithms • Implementations – Current Status • “Semi-Quantum” Computing • Conclusions Quantum Information – what for? • First, quantum computers can crack some of the strongest cryptographic systems (e.g. RSA) • Second, they might be useful for various other things as well (simulating quantum systems etc.) • Quantum cryptography provides new solutions to some cryptographic problems • Quantum cryptography may become useful ALSO if (new) classical algorithms will crack RSA • Quantum Teleportation and quantum ECC can enlarge distance for secure quantum communication • Satellite quantum communication CREDIT: Science/AAAS Quantum Computers – what for? • Quantum computers can crack RSA because they can factorize large numbers of n digits in polynomial time! O(n2 log n) • A “classical computer will have to work “subexponenital time” O(exp[(n log n)1/3]) CREDIT: Science/AAAS Quantum Computers – what for? (2) • Quantum computers might be useful for various other things as well….. Mainly - simulating quantum systems: – Fully understanding the complicated electronic structures of molecules and molecular systems – Predicting reaction properties and dynamics – Designing well controlled state preparation – Analyzing protein folding – Understanding photosynthetic systems – HHL. Etc. Etc. Etc. • The HOPE is to have advantage already with 30-100 qubits CREDIT: Science/AAAS Quantum Computers – what for? (3) • Quantum algorithms applied onto small “quantum computers” might be useful for various QUANTUM TASKS….. Mainly - manipulating quantum systems: – Algorithmic cooling of spins, for improving MRI/MRS/NMR/ESR is one of my team’s goals. – We collaborate on this topic with the one of the largest quantum computing centers – in Waterloo.Canada. – As said before: quantum ECC can enlarge distance for secure quantum communication CREDIT: Science/AAAS D-Wave collaborations (Wikipedia) In 2011 ,Lockheed Martin signed a contract with D-Wave Systems to realize the benefits based upon a quantum annealing processor applied to some of Lockheed's most challenging computation problems. The contract includes the purchase of a “128 qubit Quantum Computing System”. In 2013, a “512 qubit system” was sold to Google and NASA. D-WAVE: Superconducting flux qubit MW Johnson et al. Nature 473, 194-198 (May 2011) However, their “qubits” are highly limited. Similar Technology with less limited qubits reached 3-5 qubits, no more! So what is the TRUTH?? The Qubit In addition to the regular values {0,1} of a bit, and a probability distribution over these values, the Quantum bit can also be in a superposition www.cqed.org/IMG/jpg/compdoublemobilemz.jpg The Qubit (2) A superposition state α|0› + β|1› Intereference (as in waves) scienceblogs.com http ://upload.wikimedia.org/wikipedia/commons/2/2c/Two_sources_interference.gif The Qubit (2) A superposition state α|0› + β|1› Intereference (as in waves) scienceblogs.com http ://upload.wikimedia.org/wikipedia/commons/2/2c/Two_sources_interference.gif The Qubit (2) A superposition state α|0› + β|1› … with |α|2 + |β|2 = 1 scienceblogs.com http ://upload.wikimedia.org/wikipedia/commons/2/2c/Two_sources_interference.gif The Qubit (3) • |+› = (1/√2) |0› + (1/√2) |1› Is a state of a particle in BOTH arms! • But this is ALSO a state of a particle … in both arms |-› = (1/√2) |0› - (1/√2) |1› The amplitude 1/√2 means a probability of 1/2 to find the particle if we look for it, in one arm or another [In general: α|0› + β|1› P(0)=|α|2 and P(1)= |β|2 ] The Qubit (4) • The two arms meet - there is an interference • This is so due to Linearity of quantum mechanics • |0› → |+› = (1/√2) |0› + (1/√2) |1› |1› → |-› = (1/√2) |0› - (1/√2) |1› • We get › › › |+ = (1/√2) |0 + (1/√2) |1 → › › › - (1/√2) |1›] (1/√2) [(1/√2) |0 + (1/√2) |1 ] + (1/√2) [(1/√2) |0 › = |0 “Constructive/Destructive Interference” Two Qubits - Entanglement α|00› + β|11› brusselsjournal.com Initialization (via Hadamard transformation) • Single qubit: |0› |+› = [|0›+|1›] / (1/√2) • Two qubits: |00› |++› = (1/2) [|00›+|01›+|10›+|11›] • For n qubits: |++ … +› = 1/(2n/2) ∑ i=0 |i› A superposition over all 2n possible values 16 Initialization (via Hadamard transformation) • Single qubit: |0› |+› = [|0›+|1›] / (1/√2) • Note: the Hadamard transformation is also responsible for the interference!!! |+› |0› |-› |1› 17 n Qubits – parallel computing • Prepare a superposition over 2n states • Run your algorithm in parallel • Interference enhances the probability of the desired solution futuredocsblog.com • Peter Shor factorized large numbers (in principle) using Shor’s algorithm! • Several other problems in NP were also solved • Current quantum architecture reaches 13-14 qubits (NMR, ion trap); far from being practical… Will quantum computers factorize large numbers? • If ‘yes’ – this is a revolution in Computer Science • If ‘no’ – this is a revolution in Physics • So let’s assume it will… but maybe not so soon! • Can we predict when? 19 futuredocsblog.com Implementations 1. Ion trap (qubit is the ground-state vs excited-state of an electron attached to an ion; “many” ions in one trap) 2. NMR (qubit is the spin of a nuclei on a molecule; “many” spins on a molecule) 3. Josephson-Junction qubits (magnetic flux) 4. Optical qubits (photons) • Etc… Example – ion trap Reached 14 (8) qubits • Nobel Prize and Wolf Prize • sciencedaily.com NIST Example - NMR Reached 13 qubits • Scalability problem • Resolved via Algorithmic Cooling* • tudelft.nl robert.nowotniak.com Examples 3+4 Josephson Junctions (8-9 qubits, DWAVE 8**?) • Q. Optics (6-7 qubits) • Sufficient for some ECC • The Australian Centre of Excellence for Quantum Computation and Communication Technology Current status of fullyquantum computing • Despite the Nobel prize – we have no clue when ion traps will reach 25 qubits • Despite of 20M $ DWAVE computers already sold – we have no clue if JJ qubits are of any good; We do know (Shin, Smith Smolin, Vazirani; 2014) that there is probably no reason to believe that the DWAVE model is quantum**. Current status of fullyquantum computing • Optmism – due to Moore’s Law for VLSI • Optimism – Semi QC Limited QC Models: Semi-quantum computing • D-Wave’s AQC[???]; Other Q. Sim.? • One Clean Qubit * (closely related to NMR) • Linear Optics (closely related to Q. Optics) Three Extremely Important Questions: • What algorithms can the limited models run? [OCQ – Trace estimation; LO – boson sampling] • What kind of Quantumness/Entanglement is there? • Do they scale much easier/better than full QC? (no) Conclusions • Zero conclusions about the future of full QC • Some optimism about semi-quantum computing • Many more questions than answers, both theoretically and experimentally Thanks Appendix – DJ Algorithm • Initialization (1 slide) • Parallel computing (1 slide) • Deutsch’s Algorithm (6 slides): 1. Deutsch Problem (1 slide) 2. Classical solution (1 line) 3. Quantum solution (the remaining 5 slides) 28 Initialization ( via Hadamrd Transformation) • Single qubit: |0› |+› = [|0›+|1›] / (1/√2) • Two qubits: |00› |++› = (1/2) [|00›+|01›+|10›+|11›] • For n qubits: |++ … +› = 1/(2n/2) ∑ i=0 |i› A superposition over all 2n possible values 29 Parallel Computing The quantum computer computes in parallel • If we know to classically apply U onto |00…0000›, onto |00…0001› etc, efficiently, we also immediately know how to apply it to that superposition |++…++++› • We get parallel computing over 2n values! • Interference yields the desired outcome!! 30 The first quantum algorithm (Deutsch, 1989) • We are given a black box calculating f(x), where x is a single bit, 0 or 1, and f(x) is also a single bit • We do not care what is f(0) and f(1), we only want to know if f(0)=f(1) [ is f constant? ] • Each call to the black box costs 1 Billion dollars, if we guess correctly the answer, we win 1.5 Billion dollars, if we fail we lose 2 Billions dollars! Can we become rich? 31 The first quantum algorithm (Deutsch, 1989) (2) • Classically we lose of course…. • With a quantum BOX – we may become rich! • We do not care for f(0) and f(1), we only need [f(0)==f(1)] ; We calculate this DIRECTLY!! • We shall use an additional (ancilla) qubit for keeping the result f(x): |x›|0› → |x›|f(x)› • We also plan that: |x›|1› → |x›|f(x)`› Did we become rich? 32 The first quantum algorithm (Deutsch, 1989) (3) • • • • • • We plan the transformation: |x›|0› → |x›|f(x)› We plan also: |x›|1› → |x›|f(x)`› We prepare our ancilla: |-› = [|0›-|1›] / (1/√2) We apply |x›|-› → |x›[|f(x)› - |f(x)`›] / (1/√2) For x=0 we get: |0›[|f(0)› - |f(0)`›] / (1/√2) For x=1 we get: |1›[|f(1)› - |f(1)`›] / (1/√2) Did we become rich? 33 The first quantum algorithm (Deutsch, 1989) (4) • For x=0 we get: |0›[|f(0)› - |f(0)`›] / (1/√2) • For x=1 we get: |1›[|f(1)› - |f(1)`›] / (1/√2) • But…. We prepare a superposition for x as well: [|0›+|1›] / (1/√2)… • And we get { |0›[|f(0)› - |f(0)`›] + |1›[|f(1)› - |f(1)`›] } / 2 Did we become rich? 34 The first quantum algorithm (Deutsch, 1989) (5) { |0›[|f(0)› - |f(0)`›] + |1›[|f(1)› - |f(1)`›] } / 2 • Case 1: f(0)=f(1)=b [ f is constant ]: { |0›[|b› - |b`›] + |1›[|b› - |b`›] } / 2 { [|0› + |1›] |b› - [|0› + |1›] |b’› } / 2 • Case 2: f(0)=c ; f(1)=c’: { |0›[|c› - |c`›] + |1›[|c’› - |c›] } / 2 { [|0› - |1›] |c› - [|0› - |1›] |c’› } / 2 35 Did we become rich? The first quantum algorithm (Deutsch, 1989) (6) Let’s apply Hadamard transformation onto the left qubit, and then measure it: • Case 1: f(0)=f(1)=b [ f is constant ]: { [|0› + |1›] |b› - [|0› + |1›] |b’› } / 2 [|0›|b› - |0› |b’›] / √2 = |0›[|b› - |b’›] / √2 • Case 2: f(0)=c ; f(1)=c’: { [|0› - |1›] |c› - [|0› - |1›] |c’› } / 2 [|1›|c› - |1› |c’›] / √2 = |1›[|c› - |c’›] / √2 We became rich! 36