Related papers: Representation of Boolean Quantum Circuits as Reed…
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the…
A rotation-based synthesis framework for reversible logic is proposed. We develop a canonical representation based on binary decision diagrams and introduce operators to manipulate the developed representation model. Furthermore, a…
This paper proposes a new logic optimization paradigm based on circuit simulation, which reduces the need for Boolean computations such as SAT-solving or constructing BDDs. The paper develops a Boolean resubstitution framework to…
The use of $d$-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Molecular Nanomagnets are ideal spin systems to…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the…
Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement,…
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for…
We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires…
We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly-coupled to a resonator field mode can be used to…
We demonstrate that a classical emulation of quantum gate operations, here represented by an actual analog electronic device, can be modeled accurately as a quantum operation in terms of a universal set of Pauli operators. This observation…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
We show how to implement a Rindler transformation of coordinates with an embedded quantum simulator. A suitable mapping allows to realise the unphysical operation in the simulated dynamics by implementing a quantum gate on an enlarged…
Our primary purpose is to isolate the abstract, mathematical properties of circuits -- both classical Boolean circuits and quantum circuits -- that are essential for their computational interpretation. A secondary purpose is to clarify the…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
The interpretation of quantum mechanics continues to be debated, and quantum nonlocality accentuates the puzzle. Quantum interpretations can be classified broadly into two types: realist interpretations, which assert that quantum states…
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various…