Quantum computers offer fundamental algorithmic advantages over classical computers and building a quantum computer would fundamentally change the power of our computers. Large scale quantum computers, however, are difficult to build in large part due to the fact that quantum systems interact with their environment and quickly lose their quantum nature. The solution to this problem, at least in theory, was provided by the theory of fault-tolerant quantum computation. The theory of fault-tolerant quantum computation, while providing an in principle demonstration of viability of quantum computers, suffers from requiring protocols that have a severe complexity overhead. As a result of these difficulties, an alternative approach toward building a robust quantum computer has been pursued in which many-body quantum systems protect quantum information by encoding this information in suitable protected degrees of freedom. In this approach the natural physics of the system helps protect the quantum information. A difficulty arises, however, due in part to the complexity required of the engineered quantum system. The research being performed here seeks to overcome this obstacle and open the path for constructing the equivalent of a transistor for quantum computers.
Here the investigators study three approaches to engineering effective many-body interactions suitable for protecting quantum information. The first approach involves the construction of fault-tolerant perturbation gadgets. This research involves studying the robustness of the perturbation gadgets. The second approach involves the use of quantum circuits to simulate Hamiltonian dynamics. In this technique, research is performed on new methods for fault-tolerant simulation. A final technique involves the use of time-dependent Hamiltonians and the research involves a detailed study of the errors in this time-dependent construction.
During the first year we began the study of the novel methods for implementing self-correcting quantum systems. The first method we chose to study was the fault-tolerant stabilizer simulations. These are quantum circuits which simulate infinitesimal evolution of a Hamiltonian in such a way that errors are not propagated among qubits during the evolution. We developed a general method for building such circuits and investigated how a realistic decoherence method will affect these evolutions. The second work where we made progress is in the time dependent simulation of perturbation theory gadgets. We performed a basic analysis of the errors in this construction and shown them to be relatively small. We also begun an analysis of the robustness of perturbation theory gadgets during the first year, but this work is still in preliminary form. Finally, in thinking about the implementations of quantum concatenated code Hamiltonians and other self-correcting quantum systems, we discovered a new way to perform universal quantum computation. In joint work with personnel from the Perimeter Institute, we have shown a basic primitive, adiabatic gate teleportation can be used to adiabatically perform universal quantum computation. When applied to physically robust quantum systems, such as those considered in this grant, this leads to an entirely new way to perform universal quantum computation, which is very much in sync with how these system protect themselves from errors. This work was published in Physical Review Letters. During the second year we continued our investigations of method for implementing self-correcting quantum computers. We developed a framework for understanding how to build an error model for the circuits we described in the previous years work. This later work was at the bequest of criticism of our first year results, and we finished the combined result of this work. We further continued our work resulting from the first year’s discovery of adiabatic gate teleportation. In particular we were able to demonstrate how to perform measurement based quantum computing using only adiabatic deformations of Hamiltonians. This work has been published in Physical Review A. We further extended this work to topological quantum computing, demonstrating how to adibiatically enact universal quantum computing on these systems. In the third year of the grant we continued to study the bang-bang simulation of self-correcting systems. We obtained, unfortunately, a no-go theorem for this approach. We believe that this theorem will be a great relevance to other proposals to achieve simulation of fault-tolerant self-correcting systems. On a more positive note we realized that our constructions of universal adiabatic cluster state computing leads to a new set of quantum error correcting codes. With an REU student, we were able to show how to take any stabilizer code and convert it into a stabilizer code with spatially local, low-weight error check operators. This was motivated by our work on trying to understand how to simulate effective Hamiltonians with perturbation theory gadgets and our discovery that one needed to use ancillas more directly in these constructions. The new codes we have discovered are likely to open an entirely new path toward naturally fault-tolerant quantum computation. Website: http://quantum.cs.washington.edu/ The results of our research are collected on the group's website. Our group's website contains discussions of various research, publications, and group info. Further, the results were communicated on the blog, "The Quantum Pontiff" at http://dabacon.org/pontiff/.
