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Decoherence in quantum computers is formulated within the semigroup approach. The error generators are identified with the generators of a Lie algebra. This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model. A generic condition is presented for errorless quantum computation: decoherence-free… (More)

Quantum technology is maturing to the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators may be built with capabilities exceeding classical computers. A quantum annealer, in particular, solves optimization problems by evolving a known initial configuration at non-zero temperature… (More)

- Sergio Boixo, Tameem Albash, Federico M Spedalieri, Nicholas Chancellor, Daniel A Lidar
- Nature communications
- 2013

Quantum annealing is a general strategy for solving difficult optimization problems with the aid of quantum adiabatic evolution. Both analytical and numerical evidence suggests that under idealized, closed system conditions, quantum annealing can outperform classical thermalization-based algorithms such as simulated annealing. Current engineered quantum… (More)

- Troels F. Rønnow, Zhihui Wang, +6 authors Matthias Troyer
- 2014

Troels F. Rønnow, Zhihui Wang, Joshua Job, Sergio Boixo, Sergei V. Isakov, David Wecker, John M. Martinis, Daniel A. Lidar, and Matthias Troyer∗1 Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland Department of Chemistry and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA… (More)

- David Biron, Ofer Biham, Eli Biham, Markus Grassl, Daniel A. Lidar
- QCQC
- 1998

Grover’s algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N − r unmarked states. These equations are solved exactly. An expression for the optimal measurement time T ∼ O( √ N/r) is… (More)

- D Bacon, J Kempe, D A Lidar, And K B Whaley, D P Divincenzo
- 2001

We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the intrinsic ability of a system to act as a universal quantum computer using only its naturally available interactions. A key… (More)

- Ari Mizel, Daniel A Lidar, Morgan Mitchell
- Physical review letters
- 2007

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.

Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the problem have been proposed. Here we provide a detailed a review of the theory of decoherence-free subspaces and subsystems,… (More)

- Kristen L Pudenz, Tameem Albash, Daniel A Lidar
- Nature communications
- 2014

Quantum information processing offers dramatic speedups, yet is susceptible to decoherence, whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their power. This makes the development of quantum error correction an essential aspect of quantum computing. So far, little is known about… (More)

- Alireza Shabani, Daniel A. Lidar
- 2005

Alireza Shabani* and Daniel A. Lidar Physics Department and Center for Quantum Information and Quantum Control, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7 Chemical Physics Theory Group, Chemistry Department, and Center for Quantum Information and Quantum Control, University of Toronto, 80 St. George Street, Toronto,… (More)