Role of single-qubit decoherence time in adiabatic quantum computation

Abstract

We have studied numerically the evolution of an adiabatic quantum computer in the presence of a Markovian ohmic environment by considering Ising spin glass systems with up to 20 qubits independently coupled to this environment via two conjugate degrees of freedom. The required computation time is demonstrated to be of the same order as that for an isolated system and is not limited by the single-qubit decoherence time T * 2 , even when the minimum gap is much smaller than the temperature and decoherence-induced level broadening. For small minimum gap, the system can be described by an effective two-state model coupled only longitudinally to environment.Adiabatic quantum computation [1] (AQC) is an attractive model of quantum computation (QC). It eliminates the need for precise timing of the qubit transformations required in the gate-model computation scheme, and also is expected to possess some degree of fault tolerance afforded by the energy gap separating the ground from excited states of the qubit Hamiltonian. AQC approach is particularly appealing in the context of superconducting qubits which in principle have the required flexibility for implementation of complicated interactions. In the AQC, a system starts from a readily accessible ground state of some initial Hamiltonian H i and slowly evolves into the ground state of the final Hamiltonian H f which encodes solution to the problem of interest:where s(t) ∈ [0, 1] is a monotonic function of time t. Here, we only consider a linear time sweep s(t) = t/t f , where t f is the total evolution time. Transitions out of the ground state can be caused by the Landau-Zener processes [2] at the anticrossing (s=s * ), where the gap g between the ground state |0 and first excited state |1 goes through a minimum: g m ≡ g(s * ). The probability of being in the ground state at the end of the adiabatic evolution is approximately (h = k B = 1)To ensure large P 0f , one needs t f > ∼ t a . The computation time is hence determined by t a and thus by g m .In the gate-model QC, there is no direct correspondence between the wavefunction and the instantaneous system Hamiltonian. The Hamiltonian is only applied at the time of gate operations and usually involves only a few qubits. The wavefunction, therefore, is strongly affected by the environment and is irreversibly altered after the decoherence time, which is typically smaller than the single-qubit dephasing time T * 2 . This means that T * 2 imposes an upper limit on the total computation time, unless some quantum error correction scheme (which requires significant resources) is utilized. This is not true for AQC, as the wavefunction is always very close to the instantaneous ground state of the system Hamiltonian and is consequently more stable against the decoherence. Qualitatively, one expects decoherence to drive the system's reduced density matrix towards being diagonal in the energy basis, which is not harmful for AQC but is detrimental for the gate-model QC. Such robustness has been demonstrated in previous studies [3,4,...

Thermally assisted quantum annealing of a 16-qubit problem

“…It is important to note that for a single, unbiased qubit near s*, we estimate a decoherence time that is millions of times shorter than t a (see Supplementary Note 2). The fact that P GM similar to that of a closed system can be reached in time t a , despite the significantly shorter decoherence time, supports theoretical predictions that QA can be performed in the presence of small environmental noise [4][5][6][7][8][9][10][11][12] .…”

“…As noted earlier, for the closed system (blue squares and dashed line), t total is independent of t f . For T40, t total decreases with decreasing t f , and can be almost three orders of magnitude smaller than that expected for the closed system with t f ¼ 0.01 ms. Clearly, in the case of a smallgap anticrossing, such as the one studied here, annealing an open system fast multiple times can have a significant performance advantage over annealing slowly once or annealing a closed system, as predicted 11 . Such an efficiency enhancement due to coupling to the environment has been predicted to have an important role in nature, for example, in photosynthetic quantum energy transfer 38 .…”

“…However, efforts to develop useful quantum computers have been blocked primarily due to environmental noise. Adiabatic quantum computation (AQC) 2,3 is a scheme of quantum computation that is theoretically predicted to be more robust against noise [4][5][6][7][8][9][10][11][12] .…”

Minor-embedding in adiabatic quantum computation: I. The parameter setting problem

“…The derivation is based on the penalty or multiplier method, in which a constrained optimization is reduced to an unconstrained one by replacing the corresponding expression into the objective function as a penalty term with a large multiplier. 4 For example, this was used in the reduction from general (higher-order) unconstrained binary optimization to the quadratic one (see [8]). Notice that by construction (i.e., G is a minor of G emb and h ′ i k s are chosen such that…”

“…It is believed that AQC is advantageous over standard (the gate model) quantum computation in that it is more robust against environmental noise [11,3,4]. In 2004, D-Wave Systems Inc. undertook the endeavor to build an adiabatic quantum computer for solving NP-hard problems.…”