11 research outputs found
Detecting Violations of Differential Privacy for Quantum Algorithms
Quantum algorithms for solving a wide range of practical problems have been
proposed in the last ten years, such as data search and analysis, product
recommendation, and credit scoring. The concern about privacy and other ethical
issues in quantum computing naturally rises up. In this paper, we define a
formal framework for detecting violations of differential privacy for quantum
algorithms. A detection algorithm is developed to verify whether a (noisy)
quantum algorithm is differentially private and automatically generate bugging
information when the violation of differential privacy is reported. The
information consists of a pair of quantum states that violate the privacy, to
illustrate the cause of the violation. Our algorithm is equipped with Tensor
Networks, a highly efficient data structure, and executed both on TensorFlow
Quantum and TorchQuantum which are the quantum extensions of famous machine
learning platforms -- TensorFlow and PyTorch, respectively. The effectiveness
and efficiency of our algorithm are confirmed by the experimental results of
almost all types of quantum algorithms already implemented on realistic quantum
computers, including quantum supremacy algorithms (beyond the capability of
classical algorithms), quantum machine learning models, quantum approximate
optimization algorithms, and variational quantum eigensolvers with up to 21
quantum bits
Quantum differentially private sparse regression learning
Differentially private (DP) learning, which aims to accurately extract
patterns from the given dataset without exposing individual information, is an
important subfield in machine learning and has been extensively explored.
However, quantum algorithms that could preserve privacy, while outperform their
classical counterparts, are still lacking. The difficulty arises from the
distinct priorities in DP and quantum machine learning, i.e., the former
concerns a low utility bound while the latter pursues a low runtime cost. These
varied goals request that the proposed quantum DP algorithm should achieve the
runtime speedup over the best known classical results while preserving the
optimal utility bound.
The Lasso estimator is broadly employed to tackle the high dimensional sparse
linear regression tasks. The main contribution of this paper is devising a
quantum DP Lasso estimator to earn the runtime speedup with the privacy
preservation, i.e., the runtime complexity is with
a nearly optimal utility bound , where is the sample
size and is the data dimension with . Since the optimal classical
(private) Lasso takes runtime, our proposal achieves quantum
speedups when . There are two key components in our algorithm.
First, we extend the Frank-Wolfe algorithm from the classical Lasso to the
quantum scenario, {where the proposed quantum non-private Lasso achieves a
quadratic runtime speedup over the optimal classical Lasso.} Second, we develop
an adaptive privacy mechanism to ensure the privacy guarantee of the
non-private Lasso. Our proposal opens an avenue to design various learning
tasks with both the proven runtime speedups and the privacy preservation
Quantum R\'enyi and -divergences from integral representations
Smooth Csisz\'ar -divergences can be expressed as integrals over so-called
hockey stick divergences. This motivates a natural quantum generalization in
terms of quantum Hockey stick divergences, which we explore here. Using this
recipe, the Kullback-Leibler divergence generalises to the Umegaki relative
entropy, in the integral form recently found by Frenkel. We find that the
R\'enyi divergences defined via our new quantum -divergences are not
additive in general, but that their regularisations surprisingly yield the Petz
R\'enyi divergence for and the sandwiched R\'enyi divergence for
, unifying these two important families of quantum R\'enyi
divergences. Moreover, we find that the contraction coefficients for the new
quantum divergences collapse for all that are operator convex,
mimicking the classical behaviour and resolving some long-standing conjectures
by Lesniewski and Ruskai. We derive various inequalities, including new reverse
Pinsker inequalites with applications in differential privacy and also explore
various other applications of the new divergences.Comment: 44 pages. v2: improved results on reverse Pinsker inequalities +
minor clarification
Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems
We propose a versatile privacy framework for quantum systems, termed quantum
pufferfish privacy (QPP). Inspired by classical pufferfish privacy, our
formulation generalizes and addresses limitations of quantum differential
privacy by offering flexibility in specifying private information, feasible
measurements, and domain knowledge. We show that QPP can be equivalently
formulated in terms of the Datta-Leditzky information spectrum divergence, thus
providing the first operational interpretation thereof. We reformulate this
divergence as a semi-definite program and derive several properties of it,
which are then used to prove convexity, composability, and post-processing of
QPP mechanisms. Parameters that guarantee QPP of the depolarization mechanism
are also derived. We analyze the privacy-utility tradeoff of general QPP
mechanisms and, again, study the depolarization mechanism as an explicit
instance. The QPP framework is then applied to privacy auditing for identifying
privacy violations via a hypothesis testing pipeline that leverages quantum
algorithms. Connections to quantum fairness and other quantum divergences are
also explored and several variants of QPP are examined.Comment: 31 pages, 10 figure