Related papers: Minimal Equational Theories for Quantum Circuits

Minimal Equational Theories for Quantum Circuits

URL: http://arxiv.org/abs/2311.07476v2
Date: Fri, 17 May 2024 14:48:46 GMT
Title: Minimal Equational Theories for Quantum Circuits
Authors: Alexandre Clément, Noé Delorme, Simon Perdrix,
Abstract summary: We show that any true equation on quantum circuits can be derived from simple rules. One of our main contributions is to prove the minimality of the equational theory.
Score: 44.99833362998488
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one which states that a multi-control $2\pi$ rotation is nothing but the identity. Our work improves on the recent complete equational theories for quantum circuits, by getting rid of several rules including a fairly impractical one. One of our main contributions is to prove the minimality of the equational theory, i.e. none of the rules can be derived from the other ones. More generally, we demonstrate that any complete equational theory on quantum circuits (when all gates are unitary) requires rules acting on an unbounded number of qubits. Finally, we also simplify the complete equational theories for quantum circuits with ancillary qubits and/or qubit discarding.

Related papers

Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory [0.058331173224054456]
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. We show that the non-semisimple theory introduces new anyon types that extend the Ising framework.
arXiv Detail & Related papers (2024-10-18T21:03:07Z)
Quantum Circuit Completeness: Extensions and Simplifications [44.99833362998488]
The first complete equational theory for quantum circuits has only recently been introduced. We simplify the equational theory by proving that several rules can be derived from the remaining ones. The complete equational theory can be extended to quantum circuits with ancillae or qubit discarding.
arXiv Detail & Related papers (2023-03-06T13:31:27Z)
Is there a finite complete set of monotones in any quantum resource theory? [39.58317527488534]
We show that there does not exist a finite set of resource monotones which completely determines all state transformations. We show that totally ordered theories allow for free transformations between all pure states.
arXiv Detail & Related papers (2022-12-05T18:28:36Z)
Quantum mechanics? It's all fun and games until someone loses an $i$ [0.0]
QBism regards quantum mechanics as an addition to probability theory. Recent work has demonstrated that reference devices employing symmetric informationally complete POVMs (or SICs) achieve a minimal quantumness. We attempt to identify the optimal reference device in the first real dimension without a SIC.
arXiv Detail & Related papers (2022-06-30T15:15:16Z)
A Complete Equational Theory for Quantum Circuits [58.720142291102135]
We introduce the first complete equational theory for quantum circuits. Two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations.
arXiv Detail & Related papers (2022-06-21T17:56:31Z)
Gaussian initializations help deep variational quantum circuits escape from the barren plateau [87.04438831673063]
Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
arXiv Detail & Related papers (2022-03-17T15:06:40Z)
The principle of majorization: application to random quantum circuits [68.8204255655161]
Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. We verified that all the families of circuits satisfy on average the principle of majorization. Clear differences appear in the fluctuations of the Lorenz curves associated to states.
arXiv Detail & Related papers (2021-02-19T16:07:09Z)
Operational Resource Theory of Imaginarity [48.7576911714538]
We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
arXiv Detail & Related papers (2020-07-29T14:03:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.