Instantaneous nonlocal quantum computation and circuit depth reduction
- URL: http://arxiv.org/abs/2306.09326v2
- Date: Thu, 22 Jun 2023 17:42:16 GMT
- Title: Instantaneous nonlocal quantum computation and circuit depth reduction
- Authors: Li Yu, Jie Xu, Fuqun Wang, Chui-Ping Yang
- Abstract summary: Two-party quantum computation is a computation process with bipartite input and output, in which there are initial shared entanglement.
In the first part, we show that a particular simplified subprocedure, known as a garden-hose gadget, cannot significantly reduce the entanglement cost.
In the second part, we show that any unitary circuit consisting of layers of Clifford gates and T gates can be implemented using a circuit with measurements of depth proportional to the T-depth of the original circuit.
- Score: 7.148511452018054
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Instantaneous two-party quantum computation is a computation process with
bipartite input and output, in which there are initial shared entanglement, and
the nonlocal interactions are limited to simultaneous classical communication
in both directions. It is almost equivalent to the problem of instantaneous
measurements, and is related to some topics in quantum foundations and
position-based quantum cryptography. In the first part of this work, we show
that a particular simplified subprocedure, known as a garden-hose gadget,
cannot significantly reduce the entanglement cost in instantaneous two-party
quantum computation. In the second part, we show that any unitary circuit
consisting of layers of Clifford gates and T gates can be implemented using a
circuit with measurements (or a unitary circuit) of depth proportional to the
T-depth of the original circuit. This result has some similarity with and also
some difference from a result in measurement-based quantum computation. It is
of limited use since interesting quantum algorithms often require a high ratio
of T gates, but still we discuss its extensions and applications.
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