Related papers: On Lagrangian Formalism of Quantum Computation
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum…
We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of…
The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…
We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we…
The ZX-calculus is an algebraic formalism that allows quantum computations to be simplified via a small number of simple graphical rewrite rules. Recently, it was shown that, when combined with a family of "sum-over-Cliffords" techniques,…
Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
We introduce a novel scheme of quantum recursive programming, in which large unitary transformations, i.e. quantum gates, can be recursively defined using quantum case statements, which are quantum counterparts of conditionals and case…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this paper, we comment on…