45,935 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
Topologically biased random walk with application for community finding in networks
We present a new approach of topology biased random walks for undirected
networks. We focus on a one parameter family of biases and by using a formal
analogy with perturbation theory in quantum mechanics we investigate the
features of biased random walks. This analogy is extended through the use of
parametric equations of motion (PEM) to study the features of random walks {\em
vs.} parameter values. Furthermore, we show an analysis of the spectral gap
maximum associated to the value of the second eigenvalue of the transition
matrix related to the relaxation rate to the stationary state. Applications of
these studies allow {\em ad hoc} algorithms for the exploration of complex
networks and their communities.Comment: 8 pages, 7 figure
Quantivine: A Visualization Approach for Large-scale Quantum Circuit Representation and Analysis
Quantum computing is a rapidly evolving field that enables exponential
speed-up over classical algorithms. At the heart of this revolutionary
technology are quantum circuits, which serve as vital tools for implementing,
analyzing, and optimizing quantum algorithms. Recent advancements in quantum
computing and the increasing capability of quantum devices have led to the
development of more complex quantum circuits. However, traditional quantum
circuit diagrams suffer from scalability and readability issues, which limit
the efficiency of analysis and optimization processes. In this research, we
propose a novel visualization approach for large-scale quantum circuits by
adopting semantic analysis to facilitate the comprehension of quantum circuits.
We first exploit meta-data and semantic information extracted from the
underlying code of quantum circuits to create component segmentations and
pattern abstractions, allowing for easier wrangling of massive circuit
diagrams. We then develop Quantivine, an interactive system for exploring and
understanding quantum circuits. A series of novel circuit visualizations are
designed to uncover contextual details such as qubit provenance, parallelism,
and entanglement. The effectiveness of Quantivine is demonstrated through two
usage scenarios of quantum circuits with up to 100 qubits and a formal user
evaluation with quantum experts. A free copy of this paper and all supplemental
materials are available at
https://osf.io/2m9yh/?view_only=0aa1618c97244f5093cd7ce15f1431f9.Comment: Accepted by IEEE VIS 202
A Copositive Framework for Analysis of Hybrid Ising-Classical Algorithms
Recent years have seen significant advances in quantum/quantum-inspired
technologies capable of approximately searching for the ground state of Ising
spin Hamiltonians. The promise of leveraging such technologies to accelerate
the solution of difficult optimization problems has spurred an increased
interest in exploring methods to integrate Ising problems as part of their
solution process, with existing approaches ranging from direct transcription to
hybrid quantum-classical approaches rooted in existing optimization algorithms.
While it is widely acknowledged that quantum computers should augment classical
computers, rather than replace them entirely, comparatively little attention
has been directed toward deriving analytical characterizations of their
interactions. In this paper, we present a formal analysis of hybrid algorithms
in the context of solving mixed-binary quadratic programs (MBQP) via Ising
solvers. We show the exactness of a convex copositive reformulation of MBQPs,
allowing the resulting reformulation to inherit the straightforward analysis of
convex optimization. We propose to solve this reformulation with a hybrid
quantum-classical cutting-plane algorithm. Using existing complexity results
for convex cutting-plane algorithms, we deduce that the classical portion of
this hybrid framework is guaranteed to be polynomial time. This suggests that
when applied to NP-hard problems, the complexity of the solution is shifted
onto the subroutine handled by the Ising solver
Verifying Fairness in Quantum Machine Learning
Due to the beyond-classical capability of quantum computing, quantum machine
learning is applied independently or embedded in classical models for decision
making, especially in the field of finance. Fairness and other ethical issues
are often one of the main concerns in decision making. In this work, we define
a formal framework for the fairness verification and analysis of quantum
machine learning decision models, where we adopt one of the most popular
notions of fairness in the literature based on the intuition -- any two similar
individuals must be treated similarly and are thus unbiased. We show that
quantum noise can improve fairness and develop an algorithm to check whether a
(noisy) quantum machine learning model is fair. In particular, this algorithm
can find bias kernels of quantum data (encoding individuals) during checking.
These bias kernels generate infinitely many bias pairs for investigating the
unfairness of the model. Our algorithm is designed based on a highly efficient
data structure -- Tensor Networks -- and implemented on Google's TensorFlow
Quantum. The utility and effectiveness of our algorithm are confirmed by the
experimental results, including income prediction and credit scoring on
real-world data, for a class of random (noisy) quantum decision models with 27
qubits (-dimensional state space) tripling ( times more than)
that of the state-of-the-art algorithms for verifying quantum machine learning
models
- …