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Fault-Tolerant Quantum Computation
- B. Reichardt
- PhysicsEncyclopedia of Algorithms
Fault tolerance techniques will be essential for achieving the considerable potential of quantum computers and will need to control high noise rates and do so with low overhead, since qubits are expensive.
Classical command of quantum systems
A scheme is described that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics, and makes it possible to test whether a claimed quantum computer is truly quantum.
The quantum adiabatic optimization algorithm and local minima
- B. Reichardt
- PhysicsSTOC '04
- 13 June 2004
It is proved that for a constant range of values for the transverse field, the spectral gap is exponentially small in the sector length, and there are exponentially many eigenvalues all exponentially close to the ground state energy.
Universal fault-tolerant quantum computation with only transversal gates and error correction.
This work shows that "triorthogonal" stabilizer codes, introduced for state distillation by Bravyi and Haah, admit transversal implementation of the controlled-controlled-Z gate, and constructs a universal set of fault-tolerant gates without statedistillation by using only transversAL controlled- controlled-Z, transversals Hadamard, and fault-Tolerant error correction.
Quantum Query Complexity of State Conversion
- Troy Lee, R. Mittal, B. Reichardt, R. Spalek, M. Szegedy
- Computer Science, MathematicsIEEE 52nd Annual Symposium on Foundations of…
- 12 November 2010
It is obtained that the general adversary bound characterizes the quantum query complexity of any function whatsoever, implying that discrete and continuous-time query models are equivalent in the bounded-error setting, even for the general state-conversion problem.
Span Programs and Quantum Query Complexity: The General Adversary Bound Is Nearly Tight for Every Boolean Function
- B. Reichardt
- Computer Science50th Annual IEEE Symposium on Foundations of…
- 17 April 2009
It is generally that properties of eigenvalue-zero eigenvectors in fact imply an "effective" spectral gap around zero, and a strong universality result for span programs follows.
A classical leash for a quantum system: command of quantum systems via rigidity of CHSH games
A rigidity theorem is proved for the famous Clauser-Horne-Shimony-Holt (CHSH) game and allows us to establish that a quantum interactive proof system with a classical verifier is as powerful as one with a quantum verifier, or QMIP = MIP*.
Quantum Error Correction with Only Two Extra Qubits.
Fault-tolerant error-correction procedures that use only two extra qubits are introduced, based on adding "flags" to catch the faults that can lead to correlated errors on the data.
Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code
This work provides two simplified circuits for fault-tolerant preparation of Golay code-encoded ancillas, reducing the overhead by roughly a factor of four compared to standard encoding circuits and proves a threshold above 1.32×10-3 noise per gate.