Related papers: A lambda calculus for density matrices with classi…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol.…
We work with reference to a well-known semiclassical model, in which quantum degrees of freedom interact with classical ones. We show that, in the classical limit, it is possible to represent classical results (e.g., classical chaos) by…
Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized.…
The primary focus of this work is to investigate how the most emblematic classical probability density, namely a Gaussian, can be mapped to a valid quantum states. To explore this issue, we consider a Gaussian whose squared variance depends…
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
We define a map which relates four dimensional classical stochastic matrices to qubit quantum channels. The map preserves the spectrum and the composition of processes. To do this we introduce the concept of Bloch tetrahedron which plays…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalised in the basis of the controller variable that is coupled to the…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the…
A density matrix approach is developped for the control of a mixed-state quantum system using a time-dependent external field such as a train of pulses. This leads to the definition of a target density matrix constructed in a reduced…
A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to…
This research explores the integration of quantum data embedding techniques into classical machine learning (ML) algorithms, aiming to assess the performance enhancements and computational implications across a spectrum of models. We…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum…
No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is neccessarily one with partial observations, and can generally be converted into a completely observed control…