Abstract
It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, T, and controlled-not gates, and these gates are easily extended to multiqubit systems. For example, the T gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of 4. We also construct a generalized phase gate, of which Z, S, and T are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- A nd two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk.
| Original language | English (US) |
|---|---|
| Article number | 062325 |
| Journal | Physical Review A |
| Volume | 100 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 18 2019 |
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All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics
Cite this
Isolated vertices in continuous-time quantum walks on dynamic graphs. / Wong, Thomas G.
In: Physical Review A, Vol. 100, No. 6, 062325, 18.12.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Isolated vertices in continuous-time quantum walks on dynamic graphs
AU - Wong, Thomas G.
PY - 2019/12/18
Y1 - 2019/12/18
N2 - It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, T, and controlled-not gates, and these gates are easily extended to multiqubit systems. For example, the T gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of 4. We also construct a generalized phase gate, of which Z, S, and T are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- A nd two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk.
AB - It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, T, and controlled-not gates, and these gates are easily extended to multiqubit systems. For example, the T gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of 4. We also construct a generalized phase gate, of which Z, S, and T are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- A nd two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk.
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U2 - 10.1103/PhysRevA.100.062325
DO - 10.1103/PhysRevA.100.062325
M3 - Article
AN - SCOPUS:85077237433
VL - 100
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 6
M1 - 062325
ER -