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Schrödinger Cats, Maxwell’s Demon and Quantum Error Correction

Schrödinger Cats, Maxwell’s Demon and Quantum Error Correction. Theory SMG Liang Jiang Leonid Glazman M. Mirrahimi ** Shruti Puri Yaxing Zhang Victor Albert** Kjungjoo Noh** Richard Brierley Claudia De Grandi Zaki Leghtas Juha Salmilehto Matti Silveri Uri Vool

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Schrödinger Cats, Maxwell’s Demon and Quantum Error Correction

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  1. Schrödinger Cats, Maxwell’s Demon and Quantum Error Correction • Theory • SMGLiang Jiang • Leonid GlazmanM. Mirrahimi ** • Shruti Puri • Yaxing Zhang • Victor Albert**Kjungjoo Noh** • Richard Brierley • Claudia De Grandi • Zaki Leghtas • Juha Salmilehto • Matti Silveri • Uri Vool • HuaixuiZhengMarios Michael • +….. • Experiment • Michel Devoret • Luigi Frunzio • Rob Schoelkopf • Andrei Petrenko Nissim Ofek • Reinier HeeresPhilip ReinholdYehan LiuZaki LeghtasBrian Vlastakis • +….. • QuantumInstitute.yale.edu

  2. Quantum Computing is a New Paradigm • Quantum computing: a completely new way to store and process information. • Superposition: each quantum bit can be BOTH a zero and a one. • Entanglement: the quantum computer can explore ALL possible outcomes. (Einstein: ‘Spooky action at a distance.’) • Massive parallelism: carry out computations that are impossible on ANY conventional computer. Daily routine engineering and calibration test: Carry out spooky operations that Einstein said were impossible!

  3. 000, 001, 010, 011, 100, 101, 110, 111 The Power of Quantum Information (crude estimate) Even a small quantum computer of 30 qubits will be so powerful its operation is difficult to simulate on a conventional supercomputer. Quantum computers are good for problems that have simple input and simple output but must explore a large space of states at intermediate stages of the calculation.

  4. Applications of Quantum Computing Quantum materials Quantum chemistry Cryptography and Privacy Enhancement Machine learning* *read the fine print

  5. Storing information in quantum states sounds great…, but how on earth do you build a quantum computer?

  6. ATOM vs CIRCUIT Superconducting circuit oscillator Hydrogen atom L C (Not to scale!) ‘Artificial atom’

  7. How to Build a Qubit with an Artificial Atom… Superconducting integrated circuits are a promising technology forscalable quantum computing T = 0.01 K 200 nm Josephson junction:The “transistor of quantum computing” Provides anharmonic energy level structure AlOx tunnel barrier Aluminum/AlOx/Aluminum

  8. Antenna pads are capacitor plates Transmon Qubit Josephson tunneljunction ~1 mm Energy Superconductivity gaps out single-particle excitations Quantized energy level spectrum is simpler than hydrogen Quality factor comparable to that of hydrogen 1s-2p Enormous transition dipole moment

  9. The first electronic quantum processor (2009) Executed Deutsch-Josza and Grover search algorithms Lithographically produced integrated circuit with semiconductors replaced by superconductors. Rob Schoelkopf Michel Devoret DiCarlo et al., Nature 460, 240 (2009)

  10. The huge information content of quantum superpositions comes with a price: Great sensitivity to noise perturbations and dissipation. The quantum phase of superposition states is well-defined only for a finite ‘coherence time’

  11. Exponential Growth in SC Qubit Coherence Cat Code QEC 3D multi-mode cavity “Moore’s Law” for T2 several groups 100-200 us (Delft, IBM, MIT, Yale, …) lowest thresholds for quantum error correction NIST/IBM, Yale, ... MIT-LL NbTrilayer R. Schoelkopf and M. Devoret Oliver & Welander, MRS Bulletin (2013)

  12. Girvin’s Law: There is no such thing as too much coherence. We need quantum error correction!

  13. TheQuantum Error CorrectionProblem I am going to give you an unknown quantum state. If you measure it, it will change randomly due to state collapse (‘back action’). If it develops an error, please fix it. Mirabledictu: It can be done!

  14. Quantum Error Correction for an unknown state requires storing the quantum information non-locally in (non-classical) correlations over multiple physical qubits. ‘Logical’ qubit N ‘Physical’ qubits Non-locality: No single physical qubit can “know” the state of the logical qubit.

  15. Quantum Error Correction Cold bath ‘Logical’ qubit Entropy N ‘Physical’ qubits MaxwellDemon N qubits have errors N times faster. Maxwell demon must overcome this factor of N – and not introduce errors of its own! (or at least not uncorrectable errors)

  16. All previous attempts to overcome the factor of N and reach the ‘break even’ point of QEC have failed. With major technological advances a 49-transmon ‘surface code’ might conceivably break even at . [O’Brien et al. arXiv:1703.04136] • However to date, good repeatable (QND) (weight 4) error syndrome measurements have not been demonstrated[Takita et al., Phys. Rev. Lett.117, 210505 (2016)] • ‘Scale up and then error correct’ seems almost hopeless. We need a simpler and better idea... ‘Error correct and then scale up!’

  17. Leghtas, Mirrahimi, et al., PRL 111, 120501(2013). Replace ‘Logical’qubit with this: High-Q (memory) “Hardware-Efficienct Bosonic Encoding” Ancilla qubit Readout N ‘Physical’ qubits • Cavity has longer lifetime (~ms) • Large Hilbert space • Single dominant error channel photon loss: • Single readout channel earlier ideas: Gottesman, Kitaev & Preskill, PRA 64, 012310 (2001) Chuang, Leung, Yamamoto, PRA 56, 1114 (1997)

  18. Photonic Code States Can we find novel (multi-photon) code words that can store quantum information even if some photons are lost? High-Q (memory) Ancilla qubit Readout Ancilla transmon coupled to resonator gives us universal control to make ‘any’ code word states we want.

  19. Quick review of microwave resonators and photonic states

  20. Coherent state is closest thing to a classicalsinusoidal RF signal

  21. Photon number distribution in a coherent state (measured via quantized light shift of qubit transition frequency) Microwaves are particles! N.B. power broadened 100X … 2c New low-noise way to do axion dark matter detection? (arXiv:1607.02529)

  22. We will use Schrödinger cat states of cavity photons (normalization is only approximate)

  23. Parity of Cat States Photon number 10 8 2 0 6 4 Coherent state: Mean photon number: 4 Readout signal Even parity cat state: Only photon numbers: 0, 2, 4, … Odd parity cat state: Only photon numbers: 1, 3, 5, … Spectroscopy frequency (GHz) Schoelkopf Lab

  24. Key enabling technology: ability to make nearly ideal measurement of photon number parity(without measuring photon number!) We learn whether n is even or odd without learning the value of n. Use dispersive coupling: • Measurement is 99.8% QND. (Can be repeated hundreds of times.) • If we can measure parity, we can perform completestate tomography (measure Wigner function)

  25. Wigner Function of a Cat State Vlastakis, Kirchmair, et al., Science (2013) Interference fringes prove cat is coherent (even for sizes > 100 photons) 4 -4 0 4 0 (Yes...this is data.) -4 “P ” even parity vacuum noise Rapid parity oscillations With small displacements “X ”

  26. Using Schrödinger cat states to store and correctquantum information

  27. QUANTUM ERROR CORRECTION Keeping your Cat Alive Courtesy of Mitra Farmand

  28. Encode information in twoorthogonal even-parity code “words” code word Wigner functions: + = Photon loss flips the parity which is the error syndromewe can measure (and repeat hundreds of times). Store a qubit as a superpositionof two cats of same parity

  29. Coherent states are eigenstates of photon destruction operator. Effect of photon loss on code words: After loss of 4 photons cycle repeats: We can recover the state if we know: (via monitoring parity jumps)

  30. We can recover the state if we know: (via monitoring parity jumps) Amplitude damping is deterministic (independent of the number of parity jumps!) Maxwell Demon takes this into account ‘in software.’

  31. 2016: First true Error Correction Engine that works Analog Inputs A prototype quantum computer being prepared for cooling close to absolute zero. MAXWELL’S DEMON Analog Outputs • Commercial FPGA with custom software developed at Yale • Single system performs all measurement, control, & feedback (latency ) • ~15% of the latency is the time it takes signals to move at the speed of light from the quantum computer to the controller and back!

  32. Implementing a Full QEC System: Debugger View (This is all real, raw data.) Ofek, et al., Nature 536, 441–445 (2016).

  33. Process Fidelity: Uncorrected Transmon

  34. System’s Best Component

  35. Process Fidelity: Cats without QEC + =

  36. Process Fidelity: Cats with QEC QEC – NO POST-SELECTION.

  37. Only High-Confidence Trajectories Still keep of data Exclude results with heralded errors

  38. We are on the way! “Age of Qu. Error Correction.” “Age of Quantum Feedback” “Age of Measurement” “Age of Entanglement” “Age of Coherence” Achieved goal of reaching “break-even” point for error correction. Now need to surpass by 10x or more. M. Devoret and RS, Science (2013)

  39. Experiment: ‘Extending the lifetime of a quantum bit with error correction in superconducting circuits,’ Ofek, et al.,Nature 536, 441–445 (2016). Theory: ‘cat codes’ Leghtas, Mirrahimi, et al., PRL 111, 120501(2013). ‘kitten codes’ M. Michael et al., Phys. Rev. X 6, 031006 (2016). ‘New class of error correction codes for a bosonic mode’

  40. Extra Slides

  41. Qubit measures joint parity! Cat in Two Boxes (two-legged cat only) Theoretical proposal by Paris group: Eur. Phys. J. D 32, 233–239 (2005)

  42. Qubit measures joint parity! Cat in Two Boxes - Universal controllability - 3-level qubit can measure Experiment by Yale group: Science352, 1087 (2016)

  43. Theory Entanglement of two logical cat states 9 sigma violation of Bell inequality Experiment Two-cavities:4-dimensional phase space and Wigner functions.

  44. Entanglement of Two Logical Cat-Qubits CHSH: (Milman et al.: evaluate Wigner at 4 points in 4D phase space)

  45. Encoding qubits in cavity photon states Minimal encoding cannot correct errors but has minimal loss rate: Minimal ‘binomial code’ corrects 1 loss: General binomial code corrects L losses, G gains and D dephasing events: M. Michael et al., Phys. Rev. X 6, 031006 (2016) ‘New class of error correction codes for a bosonic mode’

  46. Future work: Cat pumping, non-linear driving and damping 4-photon damping 4-photon drive Stabilize a manifold of 4 coherent states to keep cats alive! Use parity monitoring to correct for single photon loss.

  47. Photon number parity Remarkably easy to measure using our quantum engineering toolbox and Measurement is 99.8% QND

  48. Measuring Photon Number Parity - use quantized light shift of qubit frequency • Gleyzes, S. et al.Nature446, 297 (2007) Sun, Petrenko et al., Nature511, 444 (2014)

  49. Previous Results: Tracking Photon Number Parity Jumps +1 Parity -1 Syndrome msmt time: As photons leave one by one, the sign of the parity changes between +1and-1 Map: ~ 200 ns Detect: ~ 500 ns Fidelity: > 98%, QND ~99.8% Can perform 100’s of QND syndrome measurements per jump time odd even odd even odd even Sun, Petrenko et al., Nature511, 444 (2014).

  50. Using photon number parity to do cavity state tomography

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