Growing interest in the field of quantum computing is fueled by quantum computers projected ”quantum supremacy” in speed and security. The potential for ultra-high speeds may produce a dramatic change in data science, machine learning, analytics, and information processing. This research study will focus on encryption algorithms where quantum computing may affect protocols and deciphering codes. Specifically, homomorphic encryption (HE) enables mathematical operations to be performed on encrypted data without having to decrypt the data in the process. Quantum homomorphic encryption (QHE) enables quantum circuits to be performed on encrypted qubits. In this research experience for undergraduates (REU) study, we design quantum circuits to implement QHE on a quantum teleportation circuit. The teleportation algorithm is profiled in terms of performance and complexity and comparative results are provided for encoded versus unencoded circuits. This work serves as a building block for encrypting more complex quantum algorithms such as Quantum Neural Networks (QNN).
Growing interest in the field of quantum computing is fueled by quantum computers projected ”quantum supremacy” in speed and security. The potential for ultra-high speeds may produce a dramatic change in data science, machine learning, analytics, and information processing. This research study will focus on encryption algorithms where quantum computing may affect protocols and deciphering codes. Specifically, homomorphic encryption (HE) enables mathematical operations to be performed on encrypted data without having to decrypt the data in the process. Quantum homomorphic encryption (QHE) enables quantum circuits to be performed on encrypted qubits. In this research experience for undergraduates (REU) study, we design quantum circuits to implement QHE on a quantum teleportation circuit. The teleportation algorithm is profiled in terms of performance and complexity and comparative results are provided for encoded versus unencoded circuits. This work serves as a building block for encrypting more complex quantum algorithms such as Quantum Neural Networks (QNN).
Cloud computing allows clients with limited computational resources to offload computations to more powerful remote servers. In this paradigm, homomorphic encryption (HE) schemes enable a server to run any computation on a client's encrypted data. These schemes are widely used in cloud computing protocols such as delegated computing, two-party secure computation, and zero-knowledge proofs. Quantum homomorphic encryption (QHE) aims to achieve the objectives of HE with quantum data and quantum circuits, enabling cloud quantum servers to compute on encrypted quantum data uploaded by clients. In this work, we consider a scenario where a client has access to a quantum “encryption/decryption device”, which allows the encryption, transmission, reception, and decryption of quantum states, but not universal quantum computation. In this setting, we provide a proof-of-concept software simulation of quantum homomorphic encryption. Our code implements the “EPR scheme” of Broadbent and Jeffery, which allows for the execution of universal quantum circuits by the server at the cost of requiring shared EPR pairs between the client and server. Our implementation explores the near-term viability of the EPR scheme. Perhaps unsurprisingly, our experiments indicate that the additional cost of homomorphic circuit evaluation is minor in comparison to the simulation cost of the quantum operations. Our simulation toolkit is implemented in Python and is open-source.
We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of T + T † gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains three qubits. The T + T † -gate complexity of Grover's algorithm is also analyzed in order to show that any Grover circuit can be evaluated homomorphically in an efficient manner. We discuss how to apply these QHE schemes to allow for the efficient homomorphic evaluation of any Grover circuit composed of n qubits using n − 2 extra ancilla qubits. We also show how the homomorphic evaluation of the special case where there is only one marked item can be implemented using an algorithm that makes the decryption process more efficient compared with the standard Grover algorithm. Published by the American Physical Society 2024
Homomorphic encryption is a cryptographic primitive that enables information processing on encrypted data. Such primitives are useful in a delegated computing setting in which a client delegates processing to a server, but does not trust the server fully with her information. Here, I discuss a way of performing quantum homomorphic encryption. A homomorphic encryption protocol comprises of four algorithms: random key generation, encryption, evaluation, and decryption. Our technique requires that a pair of commuting operators be used to implement the encryption and evaluation. The client randomly selects the former, while the server implements the latter. Then post-evaluation, if the client decrypts using the inverse of the encryption, he retrieves the input state with the desired computation implemented. The code space has to be chosen carefully so that non-trivial evaluations can be performed on the logical qubits. Since the encryption key is not known to the server, the randomness introduced by key generation hides some information about the encoded data despite it being put into the hands of the server. This framework is powerful because it gives a general description for implementing quantum homomorphic encryption. For example, families of commuting groups of operators are known to exist via the Schur-Weyl duality. However, it is limited by a no-go theorem that states that an exponential overhead is needed if arbitrary computation and perfect security are desired. Nonetheless, our protocols are still interesting as an application for near-term quantum computers, especially when the computational tasks require only low-depth circuits.
Homomorphic encryption (HE) is a groundbreaking cryptographic method that allows calculations on encrypted data without the need for decryption, thus safeguarding privacy and security. This article investigates how to implement homomorphic encryption with QISKIT, a free-to-use quantum computing framework. The research investigates the theoretical underpinnings of HE, its use in quantum computing, and its importance for privacy-preserving calculations. Moreover, the study covers adder circuits based on quantum logic gates, their realization with QISKIT, and the prospects for improving computational security in cloud environments. The results stress the practical viability of HE in quantum environments, underscoring its possible uses in secure data processing and privacy-enhancing technologies.
Quantum homomorphic encryption (QHE), allows a quantum cloud server to compute on private data as uploaded by a client. We provide a proof-of-concept software simulation for QHE, according to the "EPR" scheme of Broadbent and Jeffery, for universal quantum circuits. We demonstrate the near-term viability of this scheme and provide verification that the additional cost of homomorphic circuit evaluation is minor when compared to the simulation cost of the quantum operations. Our simulation toolkit, py−qhe−epr package, is an open-source Python implementation, that serves as a step towards further hardware applications of quantum homomorphic encryption between networked quantum devices.
Abstract As cloud services continue to expand, the security of private data stored and processed in these environments has become paramount. This work delves into quantum homomorphic encryption (QHE), an emerging technology that facilitates secure computation on encrypted quantum data without revealing the underlying information. We reinterpret QHE schemes through classical-quantum circuits (CQC), enhancing efficiency and addressing previous limitations related to key computations. Our approach eliminates the need for exponential key preparation by calculating keys in real-time during simulation, leading to a linear complexity in classically controlled gates. We also investigate the T / T † -gate complexity associated with various quantum walks, particularly Szegedy quantum and semiclassical algorithms, demonstrating efficient homomorphic implementations across different graph structures. Our simulations, conducted in Qiskit, validate the effectiveness of QHE for both standard and semiclassical walks. The rules for the homomorphic evaluation of the reset and intermediate measurement operations have also been included to perform the QHE of semiclassical walks. Additionally, we introduce the CQC-QHE library, a comprehensive tool that simplifies the construction and simulation of CQC tailored for QHE. Future work will focus on optimizing classical functions within this framework and exploring broader graph types to enhance QHE applications in practical scenarios.