Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis

Abstract

Cryptanalysis on standard quantum cryptographic systems generally involves finding optimal adversarial attack strategies on the underlying protocols. The core principle of modelling quantum attacks in many cases reduces to the adversary's ability to clone unknown quantum states which facilitates the extraction of some meaningful secret information. Explicit optimal attack strategies typically require high computational resources due to large circuit depths or, in many cases, are unknown. In this work, we propose variational quantum cloning (VQC), a quantum machine learning based cryptanalysis algorithm which allows an adversary to obtain optimal (approximate) cloning strategies with short depth quantum circuits, trained using hybrid classical-quantum techniques. The algorithm contains operationally meaningful cost functions with theoretical guarantees, quantum circuit structure learning and gradient descent based optimisation. Our approach enables the end-to-end discovery of hardware efficient quantum circuits to clone specific families of quantum states, which in turn leads to an improvement in cloning fidelites when implemented on quantum hardware: the Rigetti Aspen chip. Finally, we connect these results to quantum cryptographic primitives, in particular quantum coin flipping. We derive attacks on two protocols as examples, based on quantum cloning and facilitated by VQC. As a result, our algorithm can improve near term attacks on these protocols, using approximate quantum cloning as a resource.

arXiv comment16 pages main text, 25 pages supplementary material, 20 figures. Comments welcome

References in corpus (101)

• Deep Learning in Neural Networks: An Overview
• Quantum Computing in the NISQ era and beyond
• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Quantum cryptography: Public key distribution and coin tossing
• Variational Quantum Algorithms
• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Advances in Quantum Cryptography
• A Quantum Approximate Optimization Algorithm
• Quantum Circuit Learning
• Quantum Convolutional Neural Networks
• Quantum fingerprinting
• Parameterized quantum circuits as machine learning models
• Quantum Copying: Beyond the No-Cloning Theorem
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Ground-to-satellite quantum teleportation
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Quantum Error Correction for Beginners
• Towards Practical Quantum Variational Algorithms
• Optimal Quantum Cloning Machines
• Noncommuting mixed states cannot be broadcast
• Quantum cloning
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• Hybrid quantum-classical algorithms and quantum error mitigation
• Probabilistic cloning and identification of linearly independent quantum states
• Quantum Natural Gradient
• Robust determination of molecular spectra on a quantum processor
• Continuous-variable quantum neural networks
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Quantum-assisted quantum compiling
• Robust data encodings for quantum classifiers
• Quantum state discrimination and its applications
• Hierarchical quantum classifiers
• Active learning machine learns to create new quantum experiments
• Phase covariant quantum cloning
• Optimal universal quantum cloning and state estimation
• Experimental Quantum Cloning of Single Photons
• Automated Machine Learning: From Principles to Practices
• Learning the quantum algorithm for state overlap
• Automated Search for new Quantum Experiments
• Effect of barren plateaus on gradient-free optimization
• Optimal Cloning of Pure States, Judging Single Clones
• Structure optimization for parameterized quantum circuits
• Variational Quantum State Diagonalization
• Towards the Science of Security and Privacy in Machine Learning
• Noise Resilience of Variational Quantum Compiling
• Variational algorithms for linear algebra
• Quantum copying: A network
• Quantum protocols for anonymous voting and surveying
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Why Quantum Bit Commitment And Ideal Quantum Coin Tossing Are Impossible
• Variational Quantum State Eigensolver
• Overview and Comparison of Gate Level Quantum Software Platforms
• Two qubit copying machine for economical quantum eavesdropping
• Quantum cloning machines for equatorial qubits
• Quantum Cloning Machines and the Applications
• Experimental Quantum Cloning with Prior Partial Information
• Variational Quantum Fidelity Estimation
• Machine learning for long-distance quantum communication
• Machine learning of noise-resilient quantum circuits
• Quantum Optimization with a Novel Gibbs Objective Function and Ansatz Architecture Search
• Universal Variational Quantum Computation
• Alternative fidelity measure for quantum states
• Variational Quantum Unsampling on a Quantum Photonic Processor
• Symmetries in Quantum Key Distribution and the Connection between Optimal Attacks and Optimal Cloning
• Experimental Realization of $1\to 2$ Asymmetric Phase-Covariant Quantum Cloning
• Quantum Singular Value Decomposer
• Variational Consistent Histories as a Hybrid Algorithm for Quantum Foundations
• Quantum Key Distribution between N partners: optimal eavesdropping and Bell's inequalities
• Quantum machine learning for data scientists
• Near-term quantum algorithms for linear systems of equations
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Variationally Learning Grover's Quantum Search Algorithm
• Robust quantum compilation and circuit optimisation via energy minimisation
• Experimental Eavesdropping Based on Optimal Quantum Cloning
• Contextual advantage for state-dependent cloning
• A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver
• MoG-VQE: Multiobjective genetic variational quantum eigensolver
• Designing quantum experiments with a genetic algorithm
• Experimental quantum forgery of quantum optical money
• Fair Loss-Tolerant Quantum Coin Flipping
• Optimal mirror phase-covariant cloning
• Bound on trace distance based on superfidelity
• Cloning and Cryptography with Quantum Continuous Variables
• Experimental demonstration of quantum advantage for NP verification with limited information
• Unconditionally Secure Quantum Coin Tossing
• General Quantum Key Distribution in Higher Dimension
• Quantum statistical zero-knowledge
• Optimal Broadcasting of Mixed States
• Mixed Qubit Cannot Be Universally Broadcast
• Quantum Cryptography: Security Criteria Reexamined
• Experimental hybrid quantum-classical reinforcement learning by boson sampling: how to train a quantum cloner
• Optimally Stopped Variational Quantum Algorithms

Cited by in corpus (6)

• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Quantum cryptography beyond key distribution: theory and experiment
• Variational approach to photonic quantum circuits via the parameter shift rule
• Probing Quantum Telecloning on Superconducting Quantum Processors
• Variational quantum cloning machine on an integrated photonic interferometer
• Optical Quantum Computing