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In Search of a Magic Quantum Error-Be-Gone Bottle: Decoherence, Errors, and Quantum Architecture in 2040

Delve into the future of quantum computing as we explore the critical aspect of error correction and fault tolerance in shaping the design of quantum computers. Discover the complexities and challenges involved in implementing fault-tolerant techniques, understanding quantum architecture specifications, and the interplay between physical implementations, gate operations, decoherence, shuttling speeds, and more. Uncover the emerging methodologies like local codes, concatenation, and Kitaev’s Toric Codes that promise fault-tolerant quantum computation. Explore the distinct phases of matter that correspond to classical and quantum computing, and envision what a quantum computer might look like in practice. Join us on a journey to unravel the mysteries of fault-tolerant quantum computation and envision the future quantum hardware landscape.

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In Search of a Magic Quantum Error-Be-Gone Bottle: Decoherence, Errors, and Quantum Architecture in 2040

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  1. In Search of a Magic Bottle of Error-Be-Gone Decoherence errosol Dave Bacon Caltech Department of Physics Institute for Quantum Information

  2. The Future Visualize 2040: what will a quantum computer look like? Linear Optics + a bit Experimentalists all just thought Ion Traps Electron Spins Josephson Junctions Optical Lattices Quantum Architecture?

  3. Fault Tolerant Quantum Architecture? At the lowest level we must perform quantum error correction and use fault-tolerant techniques. Today’s talks on quantum error correction will drastically influence what a quantum computer looks like… What is the “best” way to do this?

  4. “Best?” Objection: BEST depends on strengths and weaknesses of particular physical implementations theory brain trust physical implementation gate speeds gate accuracies gate costs forms of decoherence decoherence times shuttling speeds shuttling accuracies cooling rates calibration errors degree of parallelism geometric constraints fabrication constraints quantum architecture specification plans suitable for founding qIntel

  5. Two Paths local codes concatenation even today TWO styles are emerging

  6. Concatenation probability of failure level qubits 0 1 qubit p cp2 1 n qubits c(cp2)2 2 n2 qubits 2k k (cp) /c nk qubits exponential decrease in # qubits if p<1/c=pthresh

  7. Threshold Theorem A quantum circuit with k gates can be simulated with error probability e using O(k poly(log(k/e))) gates on hardware whose components fail with probability p less than some threshold pthresh under caveats A, B, C, D,… faulty components almost certainly not faulty

  8. Concatenation and Locality Concatenation is hierarchical how to merge with local bare qubits? despite: moving or swapping qubits creates error rate proportional to distance moved THERE IS STILL A THRESHOLD THEOREM Daniel Gottesman, 1999

  9. Are there non-hierarchical ways to do fault-tolerant quantum computation?

  10. Kitaev’s Toric Codes qubits on links 2 encoded qubits 1 encoded qubit syndrome measurements involve only four qubit local measurements! vertex operators BUT: diagnosing error is not a local process. plaque operators

  11. Local Codes Can we find a fully local code? syndrome + diagnosis and correction + fault-tolerant In 4 dimensions there is a fully local code (sit down silly string theorists)

  12. Physics and Toric Codes qubits on links 2 encoded qubits ground state is the toric code! energy required to excite out of code: at low temperatures we can freeze out errors. error correction still needed vertex operators plaque operators

  13. Rant mode ON The Physics Guarantee What is the phase of matter corresponding to the computer? There are distinct PHYSICAL and DYNAMICAL reasons why robust classical computation is possible. not all physical systems are equally good for computation: there exist systems whose PHYSICS guarantees their ability to enact robust classical computation.

  14. In Practice Hard Drive Integrated Circuit Coding: majority vote of magnetism Coding: majority vote of current Error correction: local energy minimization Error correction: amplification fault-tolerance guaranteed by conducting-insulating phase transition

  15. Rant mode ON The Physics Guarantee What is the phase of matter corresponding to the computer? There are distinct PHYSICAL and DYNAMICAL reasons why robust classical computation is possible. not all physical systems are equally good for computation: there exist systems whose PHYSICS guarantees their ability to enact robust classical computation. What is the phase of matter corresponding to the quantum computer? Are there (or can we engineer) physical systems whose PHYSICS guarantees robust quantum computation?

  16. Rant mode shutting down The Quantum Hard Drive? Do there exist (or can we engineer) quantum systems whose physics guarantees fault-tolerant quantum computation? 1. Coherence preserving. 2. Accessible Fault-Tolerant Operations “self-correcting” 3. Universality Kitaev’s Codes hint that this is possible (in <4D!)

  17. Rant mode OFF What Will a QC Look Like? CuBits concatenation Engineering? local codes Physics?

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