Decoherence induced deformation of the ground state in adiabatic quantum computation

Abstract

Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties.

Experimental Determination of Ramsey Numbers

“…4 contains the energy histograms for R(4, 2). Examining the inset histogram for N = 3 (4), we see that: (i) h min = 0 (1); (ii) the number of optimal graphs is 1 (7); and (iii) from the main histogram, the probability to find an optimal a a a-configuration is approximately 1.0 (0.97). The minimum energies h min = 0 and 1 for N = 3 and 4 agree exactly with the corresponding final ground-state energies E gs (t f ) found in Ref.…”

Error-corrected quantum annealing with hundreds of qubits

“…Provided B(t f )ck B T, the final state at the end of the annealing process is stable against thermal excitations when it is measured. If the evolution is adiabatic, that is, if H(t) is a smooth function of time and if the gap D: ¼ min t2 0;t f ½ E 1 (t) À E 0 (t) between the first excited-state energy E 1 (t) and the ground-state energy E 0 (t) is sufficiently large compared with both 1/t f and T, then the adiabatic approximation for open systems [42][43][44][45] guarantees that the desired ground state of H Ising will be reached with high fidelity at t f . However, hard problems are characterized by gaps that close superpolynomially or even exponentially with increasing problem size 10,11,46 .…”

Thermally assisted quantum annealing of a 16-qubit problem

“…Unless there are an exponential number of states within the energy k B T (k B is Boltzmann's constant) from the ground state, the thermal reduction of the ground-state probability will not significantly affect the performance. This picture changes in the strong coupling limit wherein it may no longer be possible to identify well-defined eigenstates of the system Hamiltonian independent of the environment 27 . It should be noted that, even if the environment is weakly coupled to the system and the equilibrium probability of the ground state is not vanishingly small, the time to reach such a probability is a concern for practical computation.…”