Related papers: The Zeta Calculus
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
The use of programming languages can wax and wane across the decades. We examine the split-apply- combine pattern that is common in statistical computing, and consider how its invocation or implementation in languages like MATLAB and APL…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based…
Quantum computing is an emerging technology in which quantum mechanical properties are suitably utilized to perform certain compute-intensive operations faster than classical computers. Quantum algorithms are designed as a combination of…
The present work points out that the Deutsch-Jozsa algorithm was the first formal description of a quantum decider. In particular, it is studied here the class of languages whose indicator functions allow the Deutsch-Jozsa algorithm to…
A scheme of universal quantum computation on a chain of qubits is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
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,…
ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain…
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. A simulator for quantum algorithms must be capable of performing heavy mathematical matrix transforms. The design of the simulator…
In this paper, we show that a qutrit version of ZX-calculus, with rules significantly different from that of the qubit version, is complete for pure qutrit stabilizer quantum mechanics, where state preparations and measurements are based on…
Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax…
The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the…
We propose a hybrid quantum computing scheme where qubit degrees of freedom for computation are combined with quantum continuous variables for communication. In particular, universal two-qubit gates can be implemented deterministically…
An implementation method of a gate in a quantum computer is studied in terms of a finite number of steps evolving in time according to a finite number of basic Hamiltonians, which are controlled by on-off switches. As a working example, the…
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
Certain types of quantum computing platforms, such as those realized using Rydberg atoms or Kerr-cat qubits, are natively more susceptible to Pauli-Z noise than Pauli-X noise, or vice versa. On such hardware, it is useful to ensure that…
Jacobi's $\theta$ function has numerous applications in mathematics and computer science; a naive algorithm allows the computation of $\theta(z,\tau)$, for $z, \tau$ verifying certain conditions, with precision $P$ in $O(\mathcal{M}(P)…