Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Abstract

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.

Fast adiabatic qubit gates using onlyσzcontrol

“…A natural solution to this constraint is using smooth waveforms, which also seems to be a good strategy in terms of controlling many qubits, achieving low crosstalk, and simplifying the requirements of control electronics and their system calibration. We thus rule out pulse and refocussing type protocols common in nuclear magnetic resonance (NMR) [15,16], but welcome any theory making this a practical solution.…”

Erratum: Quantum Factorization of 143 on a Dipolar-Coupling Nuclear Magnetic Resonance System [Phys. Rev. Lett.108, 130501 (2012)]

“…Moreover, AQC shows a better robustness against error caused by dephasing, environmental noise and imperfection of unitary operations [8,9]. Thus it has grown up rapidly as an attractive field of quantum computation researches.Several computational hard problems have been formulated as optimization problems and solved in the architecture of AQC, for example the 3-SAT problem, Deutsch's problem and quantum database search [7,[10][11][12][13][14]. Recently Peng et al…”

“…Several computational hard problems have been formulated as optimization problems and solved in the architecture of AQC, for example the 3-SAT problem, Deutsch's problem and quantum database search [7,[10][11][12][13][14]. Recently Peng et al [15] have adopted a simple scheme to solve the factoring problem in AQC and implemented it on a liquid-state NMR system to factor the number 21.…”

“…Then one π 2 hard pulse was applied to ρ 0000 on the y-axis to obtain the ground state of H 0 , i.e., |− ⊗4 (|− = (|0 − |1 )/ √ 2). In the experiment, the adiabatic evolution was approximated by M discrete steps [13][14][15]21]. We utilized the linear interpolation s(t) = t/T , where T is the total evolution time.…”

Spin qubits for quantum simulations

“…Examples include the 3-SAT algorithm [72,74] and the unsorted databases search [75]. Some small-scale adiabatic algorithms have already been implemented experimentally, using NMR systems [76][77][78]. In comparison to the circuit model, AQC appears to offer some advantages:…”