Universal resources for quantum computing

Abstract

Unravelling the source of quantum computing power has been a major goal in the field of quan tum information science. In recent years, the quantum resource theory (QRT) has been established to characterize various quantum resources, yet their roles in quantum computing tasks still require in vestigation. The so-called universal quantum computing model (UQCM), e.g., the circuit model, has been the main framework to guide the design of quantum algorithms, creation of real quantum com puters etc. In this work, we combine the study of UQCM together with QRT. We find, on one hand, using QRT can provide a resource-theoretic characterization of a UQCM, the relation among models and inspire new ones, and on the other hand, using UQCM offers a framework to apply resources, study relation among resources and classify them.

We develop the theory of universal resources in the setting of UQCM, and find a rich spectrum of
UQCMs and the corresponding universal resources. Depending on a hierarchical structure of resource
theories, we find models can be classified into families. In this work, we study three natural families
of UQCMs in details: the amplitude family, the quasi-probability family, and the Hamiltonian family.
They include some well known models, like the measurement-based model and adiabatic model, and
also inspire new models such as the contextual model we introduce. Each family contains at least
a triplet of models, and such a succinct structure of families of UQCMs offers a unifying picture to
investigate resources and design models. It also provides a rigorous framework to resolve puzzles,
such as the role of entanglement vs. interference, and unravel resource-theoretic features of quantum
algorithms.

A family of quantum von Neumann architecture

“…with a set of free states ℱ, a set of free operations 𝒪, a set of resource states ℛ, and a set of universal resources 𝒰 ⊂ ℛ. [13] We will see below the generations in the QvN family rely on different forms of programs and operations on them. For simplicity, we assume classical control and focus on operations on programs.…”

“…It is intriguing to compare the resource theory of quantum programs with that for coherence or entanglement, defined for the amplitude family based on the circuit model. [13] In the setting of QvN-I, the ebit ω as a program is used to propagate quantum coherence, while coherence itself (in a non-diagonal state [16] ) is created by measurement or unitary evolution. So quantum program (or memory) is different from coherence as universal resources.…”

“…[6,7] This serves as the framework to systematically explore various quantum advantages and design algorithms, [8] such as quantum machine learning based on quantum memory. [9][10][11] Meanwhile, an attempt to systematically unify various universal quantum computing models was carried out, [12,13] and the resource-theoretic framework [13] proves to be useful to classify them. In this work, we use the resource theory to characterize QvN and establish three models of QvN forming a family, each with distinguished features that apply to different practical settings.…”

“…A hierarchy of universal resources was employed to define a family of computing models, consisting of at least three generations. [13] Given the set of finite-dimensional Choi states as programs, we establish three generations of QvN, summarized in Table 1. This forms the anticipated evolution family ('e-family'), [13] and indeed, we can see a hierarchy of resources of programs from local to nonlocal ones.…”

“…[13] Given the set of finite-dimensional Choi states as programs, we establish three generations of QvN, summarized in Table 1. This forms the anticipated evolution family ('e-family'), [13] and indeed, we can see a hierarchy of resources of programs from local to nonlocal ones. It shall also be noted that here we mainly rely on the resource theory of quantum programs.…”