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Control barrier functions (CBFs) have become a popular tool to enforce safety of a control system. CBFs are commonly utilized in a quadratic program formulation (CBF-QP) as safety-critical constraints. A class $\mathcal{K}$ function in CBFs…
How to implement multi-qubit gates efficiently with high precision is essential for realizing universal fault tolerant computing. For a physical system with some external controllable parameters, it is a great challenge to control the time…
Deep learning has become a promising programming paradigm in software development, owing to its surprising performance in solving many challenging tasks. Deep neural networks (DNNs) are increasingly being deployed in practice, but are…
We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such…
The preparation and certification of quantum states is a fundamental challenge across quantum information technology. We introduce a tomography-free state certification method that lower-bounds the fidelity by estimating expectation values…
We introduce a quadrature scheme--QBKIX--for the high-order accurate evaluation of layer potentials associated with general elliptic PDEs near to and on the domain boundary. Relying solely on point evaluations of the underlying kernel, our…
It has become standard that, when a SAT solver decides that a CNF $\Gamma$ is unsatisfiable, it produces a certificate of unsatisfiability in the form of a refutation of $\Gamma$ in some proof system. The system typically used is DRAT,…
Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive…
We introduce new semi-algebraic proof systems for Quantified Boolean Formulas (QBF) analogous to the propositional systems Nullstellensatz, Sherali-Adams and Sum-of-Squares. We transfer to this setting techniques both from the QBF…
As progress on experimental quantum processors continues to advance, the problem of verifying the correct operation of such devices is becoming a pressing concern. The recent discovery of protocols for verifying computation performed by…
In device-independent quantum key distribution (DIQKD), the violation of a Bell inequality is exploited to establish a shared key that is secure independently of the internal workings of the QKD devices. An experimental implementation of…
In a functional encryption (FE) scheme, a user that holds a ciphertext and a function key can learn the result of applying the function to the plaintext message. Security requires that the user does not learn anything beyond the function…
Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…
Various techniques have been used in recent years for verifying quantum computers, that is, for determining whether a quantum computer/system satisfies a given formal specification of correctness. Barrier certificates are a recent novel…
We introduce a novel generalization of Counterexample-Guided Inductive Synthesis (CEGIS) and instantiate it to yield a novel, competitive algorithm for solving Quantified Boolean Formulas (QBF). Current QBF solvers based on…
We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4. Key to our approach is reflection: a Boolean checker function whose soundness is fully proved in Lean and executed as compiled native code.…
We introduce a new class of methods for finite-sample false discovery rate (FDR) control in multiple testing problems with dependent test statistics where the dependence is fully or partially known. Our approach separately calibrates a…
Finite-sample analyses of deep Q-learning typically treat replayed data as independent, even though it is sampled from temporally dependent state-action trajectories. We study the Deep Q-networks (DQN) algorithm under explicit dependence by…
We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…
In a recent work by Maitra et al. (Phys. Rev. A, 2017), it was shown that the existing Quantum Private Query (QPQ) protocols fail to maintain the database security if the entangled states shared between Alice and Bob are not of a certain…