Advanced Topics in Quantum Fault Tolerance: CS 798 (Winter 2010)

Announcements

Lecture notes

Recommended reading

Codes: collection

General:

• arXiv: link
• John Preskill's Quantum Computation course at Caltech: link

Project Guidelines

• Fault-tolerance schemes:
  • "Effective fault-tolerant quantum computation with slow measurements" - DiVincenzo & Aliferis (quant-ph/0607047)
  • "A comparative code study for quantum fault tolerance" - Cross, DiVincenzo & Terhal (QIC 2009)
  • "Subsystem fault tolerance with the Bacon-Shor code" - Aliferis & Cross (quant-ph/0610063v3)
  • "Overhead & noise threshold of fault-tolerant quantum error correction" - Steane (quant-ph/0207119)
  • Postselection-based schemes:
    • "Quantum computing with realistically noisy devices" - Knill (Nature, 2005)
    • "Scalable quantum computation in the presence of large detected-error rates" - Knill (quant-ph/0312190)
    • "Thresholds for linear optics quantum computation" - Knill, Laflamme & Milburn (quant-ph/0006120)
    • "Erasure thresholds for efficient linear optics quantum computation" - Silva (quant-ph/0405112)
  • Surface codes:
    • "Fault-tolerant quantum computation with high threshold in two dimensions" - Raussendorf & Harrington (quant-ph/0610082)
    • "Topological fault-tolerance in cluster state quantum computation" - Raussendorf, Harrington & Goyal (quant-ph/0703143)
• Threshold estimates and proofs:
  • "Fault-tolerant quantum computation with long-range correlated noise" - Aharonov, Kitaev & Preskill (quant-ph/0510231)
  • "Fault-tolerant quantum computation versus Gaussian noise" - Ng & Preskill (0810.4953)
  • "Fault-tolerant quantum computation for local non-Markovian noise" - Terhal & Burkard (quant-ph/0402104)
  • Locality constraints:
    • "Local fault-tolerant quantum computation" - Svore, Terhal & DiVincenzo (quant-ph/0410047)
    • "Threshold error penalty.. nearest neighbour communication" - Szkopek et al (quant-ph/0411111)
    • "Fault-tolerant quantum computation with local gates" - Gottesman (quant-ph/9903099)
• Quantum computer architectures:
  • "A fault tolerant, area efficient architecture for Shor's factoring algorithm" - Whitney et al (0909.2188)
  • "Running a quantum circuit at the speed of data" - Isailovic, Whitney, Patel & Kubiatowicz (0804.4725)
  • "Architectural implications of quantum computing technologies" - Van Meter & Oskin (JETC 2006)
  • "Quantum computer architecture for fast entropy extraction" - Steane (quant-ph/0203047)
  • "Quantum computing for computer architects" - Metodi & Chong (2006)
  • "Quantum Memory Hierarchies- Efficient Designs to Match Available Parallelism in Quantum Computing" (quant-ph/0604070)
  • "Scalable Error Correction in Distributed Ion Trap Computers" (quant-ph/0606226)
  • "Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins" - Taylor et al (Nature Physics, 2005)
  • "Scalability of quantum computation with addressable optical lattices" - Beals, Vala & Whaley (0804.1971)
  • "The impact of classical electronics on a solid-state logical qubit memory" - Levy et al (0904.0003)
• Fault-tolerance threshold upper bounds:
  • All-unitary control:
    • "Polynomial simulations of decohered quantum computers" - Aharonov & Ben-Or (1996)
    • "An upper bound on the threshold quantum decoherence rate - Razborov (quant-ph/0310136)
    • "Upper bounds on the noise threshold for fault-tolerant quantum computing" - Kempe, Regev, Unger & de Wolf (0802.1464)
  • Allowing classical control:
    • "Classical simulability, entanglement breaking, & quantum computation thresholds" - Virmani et al (quant-ph/0408076)
    • "New limits on fault-tolerant quantum computation" - Buhrman, Cleve, Laurant, Linden, Schrijver & Unger (STOC 2006)
  • Heuristic bounds:
    • "Error channels and the threshold for fault-tolerant quantum computation" - Eastin (0710.2560)
    • "Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers" - Plenio & Virmani (0810.4340)
• More physical considerations:
  • "Combining dynamical decoupling with fault-tolerant quantum computation" - Ng, Lidar & Preskill (0911.3202)
  • "Equivalence of decoupling schemes & orthogonal arrays" - Roetteler et al (quant-ph/0409135)
  • "Fault-tolerant computing with biased-noise superconducting qubits" - Aliferis, Brito, DiVincenzo, Preskill, Steffen & Terhal (0806.0383)
  • "Fault-tolerant quantum computation against biased noise" - Aliferis & Preskill (0710.1301)
• Quantum coding theory:
  • "Generalized concatenation for quantum codes" - Grassl, Shor & Zeng (0905.0428)
  • "Catalytic quantum error correction" - Brun, Devetak & Hsieh (quant-ph/0608027)
  • Surface codes:
    • "Fast decoders for topological quantum codes" - Duclos-Cianci & Poulin (0911.0581)
    • "Topological quantum memory" - Dennis, Kitaev, Landahl & Preskill (quant-ph/0110143)
    • "Topological color codes & two-body quantum lattice Hamiltonians" - Kargarian, Bombin & Martin-Delgado (0906.4127)
    • "Topological subsystem codes" - Bombin (0908.4246)
  • Channel-specialized codes:
    • "High performance single-error-correcting quantum codes for amplitude damping" - Shor, Smith, Smolin & Zeng (0907.5149)
    • "Structured near-optimal channel-adapted quantum error correction" - Fletcher, Shor & Win (0708.3658v2)
  • Self-correcting codes:
    • "Thermodynamic stability criteria for a quantum memory based on stabilizer & subsystem codes" - Chesi, Loss, Bravyi & Terhal (0907.2807)
    • "Operator quantum error correcting subsystems for self-correction quantum memories" - Bacon (quant-ph/0506023)
    • "A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes" - Bravyi & Terhal (0810.1983)
  • Coding limitations:
    • "Tradeoffs for reliable quantum information storage in 2D systems" - Bravyi, Poulin & Terhal (0909.5200)
    • "Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit" - Chen, Chung, Cross, Zeng & Chuang (0801.2360)
    • "Transversality versus universality for additive quantum codes" - Zeng, Cross & Chuang (0706.1382)
    • "Restrictions on Transversal Encoded Quantum Gate Sets" - Eastin & Knill
    • "Qu shadow enumerators" - Rains (quant-ph/9611001v2)