Together with Elham Kashefi, I proposed a method for using traps hidden using a blind quantum computing protocol to verify the correctness of a quantum computation with exponentially small probability of error (see arXiv:1203.5217). We worked with the group of Philip Walther to experimentally demonstrate this approach in a photonic system (see Nature Physics 9 (2013): 727–731).
My research focus at present is in removing the need for the user to trust the device they use to probe the computation and developing techniques to provide reliable testing while correcting minor errors. I am also interested in developing verification techniques which do not require quantum communication or pre-shared entanglement.
Together with Anne Broadbent and Elham Kashefi, I introduced a protocol for accomplishing this task with perfect security: no information other than inevitable upper bounds on circuit complexity is leaked to the server, even if it deviates from the protocol. Our results were initially reported in FOCS’09, pp. 517-526. We worked with the group of Philip Walther to experimentally demonstrate our scheme, with an initial demonstration using four photonics qubits reported in Science 335, no. 6066 (2012): 303-308.
Since then my work in the area has mainly focused on increasing the efficiency of blind computation, establishing composable security for such protocols and extending the blind computation approach to other settings, such as verifiable computing.
Recent research from my group has shown that perfect security is unobtainable for any scheme with a compact encoding (see Physical Review A 90, no. 5 (2014): 050303).
Most recently we have proposed a scheme for quantum homomorphic encryption which does offer information theoretic security and allows for the evolution of quantum circuits with a constant number of non-Clifford group gates (see arXiv:1508.00938).
My prior work in this area has included development of techniques for performing computation in the absence of local control (see for example Physical Review Letters 97, no. 9 (2006): 090502) and for achieving long range entanglement between systems such as nitrogen vacancy defects in diamond (see New Journal of Physics 8, no. 8 (2006): 141) and ion traps (see arXiv:1406.0880).
I am interested in the ultimate limits of quantum enhancements, particularly in the presence of environmental noise. In particular, I have worked on techniques for mitigating the effect of noise which suggest an intermediate scaling in the presence of noise which is well separated from both the classical and quantum limits, falling between the two (see Science 324, no. 5931 (2009): 1166-1168).