Related papers: Encoding Turing Machines into the Deterministic La…
Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a…
Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
Leveraging the extraordinary phenomena of quantum superposition and quantum correlation, quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers. This paper tackles two pivotal…
In the companion to this paper, we described a generalization of the deterministic quantum cloning process, called enscription, which utilizes entanglement in order to achieve the "copying" of (certain) sets of distinct quantum states which…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
We introduce a multi-parameter generalization of the Lambda-determinant of Robbins and Rumsey, based on the cluster algebra with coefficients attached to a T-system recurrence. We express the result as a weighted sum over alternating sign…
This pedagogical article elucidates the fundamentals of trapped-ion quantum computing, which is one of the potential platforms for constructing a scalable quantum computer. The evaluation of a trapped-ion system's viability for quantum…
Infinite time Turing machines extend the classical Turing machine concept to transfinite ordinal time, thereby providing a natural model of infinitary computability that sheds light on the power and limitations of supertask algorithms.
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
In this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be…
A new, comprehensive approach to inhabitation problems in simply-typed lambda-calculus is shown, dealing with both decision and counting problems. This approach works by exploiting a representation of the search space generated by a given…
We present an encoding and hardware-independent formulation of optimization problems for quantum computing. Using this generalized approach, we present an extensive library of optimization problems and their various derived spin encodings.…