Adiabatic theorem in the presence of noise

We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee that the adiabatic approximation performs within a prescribed tolerance. Our results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results.

[1]  Ruedi Seiler,et al.  Adiabatic theorems and applications to the quantum hall effect , 1987 .

[2]  V. N. Bogaevski,et al.  Matrix Perturbation Theory , 1991 .

[3]  Seth Lloyd,et al.  Adiabatic quantum computation is equivalent to standard quantum computation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[4]  Lorenza Viola,et al.  Dynamical suppression of 1/f noise processes in qubit systems. , 2004, Physical review letters.

[5]  M. Klein,et al.  Power-law corrections to the Kubo formula vanish in quantum Hall systems , 1990 .

[6]  Ben Reichardt,et al.  The quantum adiabatic optimization algorithm and local minima , 2004, STOC '04.

[7]  N. Cerf,et al.  Noise resistance of adiabatic quantum computation using random matrix theory , 2004, quant-ph/0409127.

[8]  B. Sanders,et al.  Inconsistency in the application of the adiabatic theorem. , 2004, Physical Review Letters.

[9]  Seth Lloyd,et al.  Scalable Superconducting Architecture for Adiabatic Quantum Computation , 2004 .

[10]  L. Kwek,et al.  Adiabatic approximation in open systems: an alternative approach , 2007 .

[11]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

[12]  Seth Lloyd,et al.  Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation , 2007, SIAM J. Comput..

[13]  J. Clarke,et al.  Flicker (1∕f) noise in the critical current of Josephson junctions at 0.09–4.2K , 2004 .

[14]  J. J. Sakurai,et al.  Modern Quantum Mechanics , 1986 .

[15]  Seth Lloyd,et al.  Superconducting persistent-current qubit , 1999, cond-mat/9908283.

[16]  Remarks on the formulations of the adiabatic theorem , 1991 .

[18]  J. Pinel,et al.  Validity of the adiabatic approximation in quantum mechanics , 2007, 0706.0885.

[19]  Frank Gaitan.  Simulation of Quantum Adiabatic Search in the Presence of Noise , 2006 .

[20]  D. A. Lidar,et al.  Adiabatic approximation in open quantum systems , 2005 .

[21]  Andrew M. Childs,et al.  Robustness of adiabatic quantum computation , 2001, quant-ph/0108048.

[22]  M. Tiersch,et al.  Non-markovian decoherence in the adiabatic quantum search algorithm , 2006, quant-ph/0608123.

[23]  Seth Lloyd,et al.  Quantum process tomography of the quantum Fourier transform. , 2004, The Journal of chemical physics.

[24]  Adiabatic theorem for non-Hermitian time-dependent open systems (11 pages) , 2005, physics/0507166.

[25]  M. Ruskai,et al.  Bounds for the adiabatic approximation with applications to quantum computation , 2006, quant-ph/0603175.

[26]  C. H. Oh,et al.  Quantitative conditions do not guarantee the validity of the adiabatic approximation. , 2005, Physical review letters.