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  • Crypto
    Verifiable Quantum Computation
    Much of the research of my group is focused on developing novel methods for certifying the correctness of computations performed on quantum information processing devices.

    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.

  • Crypto
    Blind Quantum Computation
    Blind quantum computation is a form of secure delegated computation in which a user delegates a quantum computation to a remote server, but wishes to keep the computation itself hidden from the server.

    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.

  • Crypto
    Quantum Homomorphic Encryption
    One of my most recent interests is whether quantum mechanics allows for new approaches to homomorphic encryption. Homomorphic encryption is a form of encryption which allows for computation to be performed on encrypted data even without access to the secret key. The existence of even computationally secure fully homomorphic encryption schemes, schemes which allow for arbitrary processing of encrypted data, remained an open question until very recently. My interest lies in finding new quantum approaches to this problem which can provide some form of information theoretic security, and in determining the limits of what is possible.

    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).

  • Physics
    Quantum Computer Architectures
    The main motivation for my research is that I truly want to see quantum technologies become a reality as soon as possible. As such, I have an active interest in the using theory to lower the barriers to scalable devices.

    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).

  • Physics
    Quantum Enhanced Metrology
    The use of entangled states allows for a significant improvement in precision for a range of metrology applications, including measurements of magnetic field strength and of optical phase.

    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).

  • CS
    Computational Complexity
    Computational complexity theory seeks to establish relationships between the hardness of computational problems. I am interested in a number of complexity questions which arise from physics, including the hardness of simulating physically motivated models of computation, as well as questions relating to the computational hardness of computing (for example see Physical Review Letters 112, no. 13 (2014): 130502) or approximating ground states to physical Hamiltonians (see arXiv:1409.0260).