Decoherence in adiabatic quantum computation

Abstract

We have studied the decoherence properties of adiabatic quantum computation (AQC) in the presence of in general non-Markovian, e.g., low-frequency, noise. The developed description of the incoherent Landau-Zener transitions shows that the global AQC maintains its properties even for decoherence larger than the minimum gap at the anticrossing of the two lowest energy levels. The more efficient local AQC, however, does not improve scaling of the computation time with the number of qubits n as in the decoherence-free case. The scaling improvement requires phase coherence throughout the computation, limiting the computation time and the problem size n.The adiabatic ground-state scheme of quantum computation [1,2] represents an important alternative to the gate-model approach. In adiabatic quantum computation (AQC) the Hamiltonian H S of the qubit register and its wave function |ψ undergo adiabatic evolution in such a way that, while the transformations of |ψ represent some meaningful computation, this state also remains close to the instantaneous ground state |ψ G of H S throughout the process. This is achieved by starting the evolution from a sufficiently simple initial Hamiltonian H i , the ground state of which can be reached directly (e.g., by energy relaxation), and evolving into a final Hamiltonian H f , whose ground state provides the solution to some complex computation problem:where s(t) changes from 0 to 1 between some initial (t i =0) and final (t f ) times.The advantage of performing a computation this way, besides its insensitivity to gate errors, is that the energy gap between the ground and excited states of the Hamiltonian H S ensures some measure of protection against decoherence. This protection, as partly demonstrated in this work, is not absolute. Nevertheless, it allows for the ground state to maintain its coherence properties in time far beyond what would be the single-qubit decoherence time in the absence of the ground-state protection. This feature of the AQC remains intact [3] even if the decoherence strength and/or temperature is much larger than the minimum gap.In general, the performance of an adiabatic algorithm depends on the structure of the energy spectrum of its Hamiltonian H S . Here we consider a situation, which is typical for complex search and optimization problems [3], when the performance is limited by the anticrossing of the two lowest energy states. The minimum gap g m between those states shrinks with an increasing number n of qubits in the algorithm, although the exact scaling relation is not known in general. In an isolated system with no decoherence, the limitation is due to the usual Landau-Zener tunneling at the anticrossing, which drives the system out of the ground state with the probability given by the "adiabatic theorem". Different formulations of the theorem all give the computation time as some power of the minimum gap: t f ∝ g that there exists a well-defined energy gap between the two lowest energy states of the system. In a more realistic case with decoherenc...

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] .…”

“…An open system with T ¼ 0 has been theoretically predicted to behave similarly to a closed system for such an anticrossing 10,[34][35][36] . In this experiment, it was infeasible to reduce T below B20 mK.…”

“…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] .…”

Performance of two different quantum annealing correction codes

“…In the closed system setting, starting in the ground state of H(0) and evolving adiabatically, the system is guaranteed to reach the ground state of H I with high probability [15][16][17]. Although adiabatic dynamics is robust against certain forms of decoherence appearing in the more realistic open system setting [10,[18][19][20][21][22][23], it remains susceptible to thermal noise and specification errors [24], which can jeopardize the efficiency of the quantum computation. Therefore, any scalable quantum annealing architecture will require quantum error correction [25].…”

Quantum gates with controlled adiabatic evolutions

“…This is in contrast with traditional AQC setups in which the ground state is uniquely defined. The distinction between these two cases is important mainly because it is this uniqueness that normally provides AQC with the attractive property of being robust (to the extent that it is) against the devastating effects of decoherence, unlike other paradigms of quantum computation [19,20]. The doubly-degenerate ground state manifolds of the adiabatic gates suggest that, while very versatile, they are likely to be more vulnerable to the effects of noise, similarly to the situation that arises in holonomic quantum computation [21,22] and adiabatic gate teleportation [23,24].…”