Source-linked AI summary
Schemes for Parallel Quantum Computation Without Local Control of Qubits
S. C. Benjamin
TL;DR
The procedures implement conditional quantum transformations using globally applied update sequences and auxiliary information. They allow a control unit to reach distant targets and support compact multi-control operations.
Problem
The procedures address how a control unit can reach target qubits across an array while updates are applied globally.
Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9Method
The method moves a control unit through intervening qubits, uses reversible update sequences, and conditions transformations on auxiliary bits or control-qubit states.
Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9Results
The control unit can cross any number of intervening qubits, while Control-Control-U applies U only when both control qubits are in state 1.
Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9Takeaways & Limitations
The procedures support remote targeting and compact conditional multi-control operations within the array.
Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9
Abstract
from arXiv · showhide
Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally applied transformations. Here we demonstrate the minimum physical requirements for such an approach: a one-dimensional array composed of two alternating 'types' of two-state system. Each system need be sensitive only to the net state of its nearest neighbors, i.e. the number in state 1 minus the number in state 2. Additionally, we show that all such arrays can perform quite general parallel operations. A broad range of physical systems and interactions are suitable: we highlight two potential implementations.
NOT INTENDED FOR JOURNAL PUBLICATION
The procedures move a control unit through the array and use auxiliary information to implement conditional transformations. They support remote targeting, reversible handling of neighbor disturbances, and a compact control-control-U operation.
- The described update sequence re-applies earlier updates in reverse order after the relevant update has been applied.Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9
- The control unit can cross any number of intervening qubits to reach its target without changing its form.Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9
- At minimum spacing, a neighboring qubit may be disturbed, but reverse application of preceding updates undoes that disturbance.Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9
- The delaying transformation applies or omits the control-unit transform according only to four auxiliary bits set by a preceding subcomputer calculation.Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9
- The compact Control-Control-U gate applies U to target qubit W only when both control qubits X and Y are in state 1.Source: NOT INTENDED FOR JOURNAL PUBLICATION · p. 9