Related papers: Complexity Theory for Quantum Promise Problems
We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information…
The conditional disclosure of secrets (CDS) setting is among the most basic primitives studied in information-theoretic cryptography. Motivated by a connection to non-local quantum computation and position-based cryptography, CDS with…
In this article we introduce a new complexity class called PQMA_log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness which is polynomially close…
Communication games are one of the widely used tools that are designed to demonstrate quantum supremacy over classical resources. In that, two or more parties collaborate to perform an information processing task to achieve the highest…
In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first,…
Quantum inspired protocols e.g. [AAV13,AG17] attempt to achieve a single-prover interactive protocol where a classical machine can verify quantum computations in an information-theoretically secure manner. We define a family of protocols…
We show an unconditional classical oracle separation between the class of languages that can be verified using a quantum proof ($\mathsf{QMA}$) and the class of languages that can be verified with a classical proof ($\mathsf{QCMA}$).…
Quantum Machine Learning (QML) is becoming increasingly prevalent due to its potential to enhance classical machine learning (ML) tasks, such as classification. Although quantum noise is often viewed as a major challenge in quantum…
Complementarity is an essential feature of quantum mechanics. The preparation of an eigenstate of one observable implies complete randomness in its complementary observable. In quantum cryptography, complementarity allows us to formulate…
Composition is a cornerstone of classical differential privacy, enabling strong end-to-end guarantees for complex algorithms through composition theorems (e.g., basic and advanced). In the quantum setting, however, privacy is defined…
Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA),…
The most general examples of quantum learning advantages involve data labeled by cryptographic or intrinsically quantum functions, where classical learners are limited by the infeasibility of evaluating the labeling functions using…
There is growing interest in developing rigorous tests of quantumness that are feasible even before practical quantum advantages become a reality. Such tests not only aim to certify the quantum nature of a system but also serve as…
We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order…
In cryptography, secure Multi-Party Computation (MPC) protocols allow participants to compute a function jointly while keeping their inputs private. Recent breakthroughs are bringing MPC into practice, solving fundamental challenges for…
The recent proliferation of NISQ devices has made it imperative to understand their computational power. In this work, we define and study the complexity class $\textsf{NISQ} $, which is intended to encapsulate problems that can be…
We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many…
Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
We study the complexity of approximately evaluating the Ising and Tutte partition functions with complex parameters. Our results are partly motivated by the study of the quantum complexity classes BQP and IQP. Recent results show how to…