TY - JOUR

T1 - Controlling Qubit Networks in Polynomial Time

AU - Arenz, Christian

AU - Rabitz, Herschel

N1 - Funding Information:
C.A. acknowledges the NSF (Grant No.CHE-1464569) and fruitful discussion with Daniel Burgarth and Benjamin Russell. H.R. acknowledges the ARO (Grant No.W911NF-16-1-0014).

PY - 2018/5/30

Y1 - 2018/5/30

N2 - Future quantum devices often rely on favorable scaling with respect to the number of system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in a time that scales at most polynomial in the number of qubits. We develop an upper bound for the minimum time required to implement a unitary transformation on a generic qubit network in which each of the qubits is subject to local time dependent controls. Based on the developed upper bound, the set of gates is characterized that can be implemented polynomially in time. Furthermore, we show how qubit systems can be concatenated through controllable two body interactions, making it possible to implement the gate set efficiently on the combined system. Finally, a system is identified for which the gate set can be implemented with fewer controls.

AB - Future quantum devices often rely on favorable scaling with respect to the number of system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in a time that scales at most polynomial in the number of qubits. We develop an upper bound for the minimum time required to implement a unitary transformation on a generic qubit network in which each of the qubits is subject to local time dependent controls. Based on the developed upper bound, the set of gates is characterized that can be implemented polynomially in time. Furthermore, we show how qubit systems can be concatenated through controllable two body interactions, making it possible to implement the gate set efficiently on the combined system. Finally, a system is identified for which the gate set can be implemented with fewer controls.

UR - http://www.scopus.com/inward/record.url?scp=85047765100&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevLett.120.220503

DO - 10.1103/PhysRevLett.120.220503

M3 - Article

C2 - 29906136

AN - SCOPUS:85047765100

VL - 120

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 22

M1 - 220503

ER -