Quantum Computation and Quantum Operations

Marcelo Serrano Zanetti

This work presents a new protocol for simulating quantum systems based on quantum state preparation, with various applications such as the simulation of quantum channels and the implementation of general measurements. In general, these applications are modeled by quantum operations and involve completely positive trace-preserving (CPTP) maps. These maps correspond to sets of operators known as Kraus operators, when applied to the simulation of quantum channels, and general measurement operators, when applied to the implementation of non-selective measurements. In the literature, especially when the experimental platform is circuit-based quantum computing, these operators are employed to adjust the parameters of unitary matrices, which are the ones that actually operate in the experiment. To do this, it is necessary to solve a system of nonlinear equations numerically. The new protocol avoids these complications by applying the operators directly over the analytical description of the quantum systems to be simulated. Through the use of isometries and purifications, it models the quantum operations of interest to the experimentalist, whether they are quantum channels or general measurements, enabling the use of software libraries for symbolic algebra to perform exact and automated manipulation of the state vector, with complex amplitudes, to be prepared for simulation. The algebraic manipulation of the state vector provides greater flexibility in experimental planning, as it can be used on any quantum simulation platform. More specifically, it is not restricted to circuit-based quantum computing. Finally, the use of the new protocol is illustrated in the simulation of one-qubit channels, qudits, Lorentz transformations, mixed-state simulations, POVM implementation, and the certification of quantum contextuality via POVMs.

Héctor Freytes, Roberto Giuntini, Giuseppe Sergioli +1 more

In this work we introduce a particular kind of quantum operations called polynomial quantum operations that allow us to represent the basic operations of the standard Product MV -algebra. Consequently, these operations can be treated as quantum computational gates in the powerful model of quantum computation given by “quantum operations - density operators”.

Kamil A. Valiev

Vasily Evgenevich Tarasov

Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of $4^{n}$-dimensional operator Hilbert space. Unitary quantum gates and nonunitary quantum operations for n-qubit system are considered as generalized quantum gates acting on mixed state. In this paper we study universality for quantum computations by quantum operations on mixed states.

Joseph M. Landsberg