5 research outputs found
Quantum computing on encrypted data
The ability to perform computations on encrypted data is a powerful tool for
protecting privacy. Recently, protocols to achieve this on classical computing
systems have been found. Here we present an efficient solution to the quantum
analogue of this problem that enables arbitrary quantum computations to be
carried out on encrypted quantum data. We prove that an untrusted server can
implement a universal set of quantum gates on encrypted quantum bits (qubits)
without learning any information about the inputs, while the client, knowing
the decryption key, can easily decrypt the results of the computation. We
experimentally demonstrate, using single photons and linear optics, the
encryption and decryption scheme on a set of gates sufficient for arbitrary
quantum computations. Because our protocol requires few extra resources
compared to other schemes it can be easily incorporated into the design of
future quantum servers. These results will play a key role in enabling the
development of secure distributed quantum systems
Quantum learning algorithms imply circuit lower bounds
We establish the first general connection between the design of quantum
algorithms and circuit lower bounds. Specifically, let be a
class of polynomial-size concepts, and suppose that can be
PAC-learned with membership queries under the uniform distribution with error
by a time quantum algorithm. We prove that if , then , where
is an exponential-time analogue of
. This result is optimal in both and , since it is
not hard to learn any class of functions in (classical) time (with no error), or in quantum time with error at
most via Fourier sampling. In other words, even a
marginal improvement on these generic learning algorithms would lead to major
consequences in complexity theory.
Our proof builds on several works in learning theory, pseudorandomness, and
computational complexity, and crucially, on a connection between non-trivial
classical learning algorithms and circuit lower bounds established by Oliveira
and Santhanam (CCC 2017). Extending their approach to quantum learning
algorithms turns out to create significant challenges. To achieve that, we show
among other results how pseudorandom generators imply learning-to-lower-bound
connections in a generic fashion, construct the first conditional pseudorandom
generator secure against uniform quantum computations, and extend the local
list-decoding algorithm of Impagliazzo, Jaiswal, Kabanets and Wigderson (SICOMP
2010) to quantum circuits via a delicate analysis. We believe that these
contributions are of independent interest and might find other applications
S.: Efficient universal quantum circuits
Abstract. We define and construct efficient depth-universal and almostsize-universal quantum circuits. Such circuits can be viewed as generalpurpose simulators for central classes of quantum circuits and can be used to capture the computational power of the circuit class being simulated. For depth we construct universal circuits whose depth is the same order as the circuits being simulated. For size, there is a log factor blow-up in the universal circuits constructed here. We prove that this construction is nearly optimal.