## Profile
Quantum Chaos
## Outputs
Title | Category | Date | Authors |
Quantum mechanics of Hyperion University of Calgary | Publication | 2005-08-01 | N. Wiebe, L. E. Ballentine | Improved error-scaling for adiabatic quantum evolutions University of Calgary | Publication | 2012-01-01 | N. Wiebe, N. S. Babcock | Quantum computer simulations of time dependent HamiltoniansIn 1982, Feynman suggested a quantum computer would efficiently simulate quantum systems and illustrated this concept with Heisenberg chains (Int. J. Theor. Phys, 21, 467), which are difficult to solve on a classical computer. Since then a number of sophisticated quantum simulation schemes have been created to simulate time independent Hamiltonians, but to date only simplistic simulation schemes have been proposed for simulating time dependent Hamiltonians.
In this talk I will present a sophisticated quantum algorithm that can simulate the evolution of a sufficiently smooth and sparse time dependent Hamiltonian, which uses a number of gate operations that is comparable to the best known simulation schemes for time independent Hamiltonians. Applications of this algorithm to simulating Hamiltonian based quantum computing schemes in the circuit model (such as adiabatic quantum computing) will also be discussed. University of Calgary | Presentation | 2008-02-15 | N. Wiebe | Computing time ordered operator exponentials efficiently and accurately University of Calgary | Presentation | 2008-11-17 | N. Wiebe, W. D. Berry, P. Høyer, B. C. Sanders | Simulating quantum dynamics on a quantum computerWe develop an efficient quantum algorithm for simulating time-dependent Hamiltonian evolution of general input states on a quantum computer. Given conditions on the smoothness of the Hamiltonian, the complexity of the algorithm is close to linear in the evolution time, and therefore is comparable to algorithms for time-independent Hamiltonians. In addition, we show how the complexity can be reduced by optimizing the time steps. The complexity of the algorithm is quantified by calls to an oracle, which yields information about the Hamiltonian, and accounts for all computational resources. In contrast to previous work, which allowed an oracle query to yield an arbitrary number of bits or qubits, we assign a cost for each bit or qubit accessed. This per-bit or per-qubit costing of oracle calls reveals hitherto unnoticed simulation costs. We also account for discretization errors in the time and the representation of the Hamiltonian. We generalize the requirement of sparse Hamiltonians to being a sum of sparse Hamiltonians in various bases for which the transformation to a sparse Hamiltonian may be performed efficiently. University of Calgary | Presentation | 2011-03-24 | N. Wiebe, W. D. Berry, P. Høyer, B. C. Sanders | Quantum-circuit design for efficient simulations of many-body quantum dynamics University of Calgary | Publication | 2012-01-01 | S. Raeisi, N. Wiebe, B. C. Sanders | A path integral approach to the quantum adiabatic approximation University of Calgary | Presentation | 2010-07-16 | D. Cheung, P. Høyer, N. Wiebe |
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