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Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but it is useful only if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors—“bugs.” Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal methods to quantum programming. With such methods, a programmer writes a mathematical specification alongside the program and semiautomatically proves the program correct with respect to it. The proof’s validity is automatically confirmed—certified—by a “proof assistant.” Formal methods have successfully yielded high-assurance classical software artifacts, and the underlying technology has produced certified proofs of major mathematical theorems. As a demonstration of the feasibility of applying formal methods to quantum programming, we present a formally certified end-to-end implementation of Shor’s prime factorization algorithm, developed as part of a framework for applying the certified approach to general applications. By leveraging our framework, one can significantly reduce the effects of human errors and obtain a high-assurance implementation of large-scale quantum applications in a principled way. 

We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and classical effects. For example, one can use sum types to implement the direct sum of linear operators, exception-handling syntax to implement projective measurements, and aliasing to induce entanglement. Further, Qunity takes advantage of the overlooked BQP subroutine theorem, allowing one to construct reversible subroutines from irreversible quantum algorithms through the uncomputation of "garbage" outputs. Unlike existing languages that enable quantum aspects with separate add-ons (like a classical language with quantum gates bolted on), Qunity provides a unified syntax and a novel denotational semantics that guarantees that programs are quantum mechanically valid. We present Qunity's syntax, type system, and denotational semantics, showing how it can cleanly express several quantum algorithms. We also detail how Qunity can be compiled into a low-level qubit circuit language like OpenQASM, proving the realizability of our design. 

We present a formal model of Checked C, a dialect of C that aims to enforce spatial memory safety. Our model pays particular attention to the semantics of dynamically sized, potentially null-terminated arrays. We formalize this model in Coq, and prove that any spatial memory safety errors can be blamed on portions of the program labeled unchecked; this is a Checked C feature that supports incremental porting and backward compatibility. While our model's operational semantics uses annotated (“fat”) pointers to enforce spatial safety, we show that such annotations can be safely erased. Using PLT Redex we formalize an executable version of our model and a compilation procedure to an untyped C-like language, as well as use randomized testing to validate that generated code faithfully simulates the original. Finally, we develop a custom random generator for well-typed and almost-well-typed terms in our Redex model, and use it to search for inconsistencies between our model and the Clang Checked C implementation. We find these steps to be a useful way to co-develop a language (Checked C is still in development) and a core model of it. 

As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of mechanized proof to the domain of quantum programming in the context of the SQIR development. It verifies the correctness of a range of a quantum algorithms including Grover’s algorithm and quantum phase estimation, a key component of Shor’s algorithm. In doing so, it aims to highlight both the successes and challenges of formal verification in the quantum context and motivate the theorem proving community to target quantum computing as an application domain. 

The role of interfacial nonidealities and disorder on thermal transport across interfaces is traditionally assumed to add resistance to heat transfer, decreasing the thermal boundary conductance (TBC). However, recent computational studies have suggested that interfacial defects can enhance this thermal boundary conductance through the emergence of unique vibrational modes intrinsic to the material interface and defect atoms, a finding that contradicts traditional theory and conventional understanding. By manipulating the local heat flux of atomic vibrations that comprise these interfacial modes, in principle, the TBC can be increased. In this work, experimental evidence is provided that interfacial defects can enhance the TBC across interfaces through the emergence of unique high‐frequency vibrational modes that arise from atomic mass defects at the interface with relatively small masses. Ultrahigh TBC is demonstrated at amorphous SiOC:H/SiC:H interfaces, approaching 1 GW m⁻²K⁻¹and are further increased through the introduction of nitrogen defects. The fact that disordered interfaces can exhibit such high conductances, which can be further increased with additional defects, offers a unique direction to manipulate heat transfer across materials with high densities of interfaces by controlling and enhancing interfacial thermal transport.