Abstract
We provide a new approach to adiabatic state preparation that uses coherent control and measurement to average different adiabatic evolutions in ways that cause their diabatic errors to cancel, allowing highly accurate state preparations using less time than conventional approaches. We show that this new model for adiabatic state preparation is polynomially equivalent to conventional adiabatic quantum computation by providing upper bounds on the cost of simulating such evolutions on a circuit-based quantum computer. Finally, we show that this approach is robust to small errors in the quantum control register and that the system remains protected against noise on the adiabatic register by the spectral gap.
Highlights
Nathan Wiebe Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA and Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, 200 University Ave., West, Waterloo, Ontario, Canada (Dated: October 3, 2018)
Local adiabatic evolution [8, 9] (LAE) minimizes the time to reach the adiabatic regime by choosing the evolution speed such that the adiabatic condition is satisfied at each instant throughout the evolution
In a typical scenario of LAE, the rate at which the Hamiltonian changes is fast in the beginning and the end of evolution, when the distance between the ground state and the first excited state is large, and small in the middle around the minimal gap. This approach optimizes the scaling of the evolution time with the size of the system and works best to reduce diabatic errors in the short time or “Landau–Zener” regime
Summary
It is not possible to provide a closed form solution to the Schrodinger equation for the case of time–dependent Hamiltonians in general. Since the adiabatic approximation requires slow evolution, it is useful to consider how the approximation error scales as the speed of the transition from the initial to the final Hamiltonian decreases. This makes it natural to parameterize time via the variable s where s = t/T,. It is necessary for us to use a first order adiabatic approximation, which provides us with the error in the adiabatic approximation correct to O(1/T 2) [20]: This result can be found by using path integral methods using techniques discussed in [24,25,26] and upper bounds on the magnitude of the sum of all O(1/T 2) terms are given in [20]. Our work provides a way to achieve this, thereby illustrating that controlled adiabatic evolution affords greater power than conventional adiabatic evolution
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