Contextuality as a resource for measurement-based quantum computation beyond qubits
Contextuality—the obstruction to describing quantum mechanics in a classical statistical way—has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2018-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aae3ad |
| _version_ | 1797750570281336832 |
|---|---|
| author | Markus Frembs Sam Roberts Stephen D Bartlett |
| author_facet | Markus Frembs Sam Roberts Stephen D Bartlett |
| author_sort | Markus Frembs |
| collection | DOAJ |
| description | Contextuality—the obstruction to describing quantum mechanics in a classical statistical way—has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate nonlinear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality—the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits , which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for state-independent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation (MBC) that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality , which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit MBC are of the same underlying nature, avoiding the pathologies associated with qubit contextuality. |
| first_indexed | 2024-03-12T16:35:42Z |
| format | Article |
| id | doaj.art-9c9375955a284b378d6a30197c599446 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:42Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-9c9375955a284b378d6a30197c5994462023-08-08T14:55:12ZengIOP PublishingNew Journal of Physics1367-26302018-01-01201010301110.1088/1367-2630/aae3adContextuality as a resource for measurement-based quantum computation beyond qubitsMarkus Frembs0Sam Roberts1Stephen D Bartlett2https://orcid.org/0000-0003-4387-670XDepartment of Physics, Imperial College London, London SW7 2AZ, United KingdomCentre for Engineered Quantum Systems, School of Physics, The University of Sydney , Sydney, AustraliaCentre for Engineered Quantum Systems, School of Physics, The University of Sydney , Sydney, AustraliaContextuality—the obstruction to describing quantum mechanics in a classical statistical way—has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate nonlinear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality—the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits , which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for state-independent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation (MBC) that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality , which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit MBC are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.https://doi.org/10.1088/1367-2630/aae3adquantum informationquantum computingcontextualityBell nonlocality |
| spellingShingle | Markus Frembs Sam Roberts Stephen D Bartlett Contextuality as a resource for measurement-based quantum computation beyond qubits New Journal of Physics quantum information quantum computing contextuality Bell nonlocality |
| title | Contextuality as a resource for measurement-based quantum computation beyond qubits |
| title_full | Contextuality as a resource for measurement-based quantum computation beyond qubits |
| title_fullStr | Contextuality as a resource for measurement-based quantum computation beyond qubits |
| title_full_unstemmed | Contextuality as a resource for measurement-based quantum computation beyond qubits |
| title_short | Contextuality as a resource for measurement-based quantum computation beyond qubits |
| title_sort | contextuality as a resource for measurement based quantum computation beyond qubits |
| topic | quantum information quantum computing contextuality Bell nonlocality |
| url | https://doi.org/10.1088/1367-2630/aae3ad |
| work_keys_str_mv | AT markusfrembs contextualityasaresourceformeasurementbasedquantumcomputationbeyondqubits AT samroberts contextualityasaresourceformeasurementbasedquantumcomputationbeyondqubits AT stephendbartlett contextualityasaresourceformeasurementbasedquantumcomputationbeyondqubits |