# Gapped Frustration-Free Local Spin Chains

In addition to many other challenges, standard qubit designs require rapid pulses of laser light, electrical currents, or similar control signals. Adiabatic quantum computation is an alternative vision that obviates the need for rapid pulses. It is known that adiabatic quantum computation can be just as powerful as the standard designs for a computer held at zero temperature. Unfortunately, if the temperature rises above absolute zero, adiabatic quantum computation tends to get ruined. Is there a way, even in principle, to fix this problem? Since no computer in the real world is actually held at zero temperature, the viability of adiabatic quantum computation hinges on finding such a fix.

The Mizel group has held a long-standing interest in the adiabatic quantum computation paradigm [1] and in the technical issues surrounding temperature. Recently, the group published a paper in Journal of Physics: Condensed Matter proposing a model system [2] that performs a trivial computation — a series of approximate identity gates applied to a single quantum bit. Subtle numerical calculations suggested the proposed system would be robust against non- zero temperature as a result of an energy gap. This finding was followed by collaborative work with Dr. Van Molino [3] that proved the system indeed possesses an energy gap. The proof required the development of a new mathematical technique of interest in its own right.

While this proposed model system only performs a trivial computation, it sheds light on how one might generalize to non-trivial computations. If adiabatic quantum computation does turn out to be viable at non-zero temperature, the potential exists for a different — and possibly easier — way to build a quantum computer.

References

[1] A. Mizel, M. W. Mitchell, and M. L. Cohen, “Energy Barrier to Decoherence,’’ Phys. Rev. A. Rapid Comm. 63, 40302 (2001)

[2] A. Mizel, “Entanglement versus gap, quantum teleportation, and the AKLT model,” J. Phys.: Condens. Matter 33 315801 (2021)

[3] A. Mizel and V. Molino, “Renormalization method for proving frustration-free local spin chains are gapped,” arXiv:2111.09358 (2021)