Vol.20 No.3&4, March
5, 2020
Research Articles:
Rational proofs for quantum
computing
(pp181-193)
Tomoyuki Morimae and Harumichi Nishimura
It is an open problem whether a
classical client can delegate quantum computing to an efficient remote
quantum server in such a way that the correctness of quantum computing
is somehow guaranteed. Several protocols for verifiable delegated
quantum computing have been proposed, but the client is not completely
free from any quantum technology: the client has to generate or measure
single-qubit
states. In this paper, we show that the client can be completely
classical if the server is rational (i.e., economically motivated),
following the ``rational proofs" framework of
Azar
and
Micali. More precisely, we consider
the following protocol. The server first sends the client a message
allegedly equal to the solution of the problem that the client wants to
solve. The client then gives the server a monetary reward whose amount
is calculated in classical probabilistic polynomial-time by using the
server's message as an input. The reward function is constructed in such
a way that the expectation value of the reward (the expectation over the
client's probabilistic computing) is maximum when the server's message
is the correct solution to the problem. The rational server who wants to
maximize his/her profit therefore has to send the correct solution to
the client.
A method of mapping and
nearest neighbor optimization for 2-D quantum circuits
(pp194-212)
Yuxin Zhang, Zhijin. Guan, Longyong Ji, Qin Fang Luan and
Yizhen Wang
In some practical quantum
physical architectures, the
qubits
need to be distributed on 2-dimensional (2-D) grid structure to
implement quantum computation. In order to map an 1-dimensional
(1-D) quantum circuit into a 2-D grid structure and satisfy the nearest
neighbor constraint of
qubit
interaction in the grid structure, a mapping method from 1-D quantum
circuit to 2-D grid structure is proposed in this paper. This method
firstly determines the order of placing
qubits,
and then presents the layout strategy of
qubits
in 2-D grid. We also proposed an algorithm for establishing
interaction paths between non-adjacent
qubits
in 2-D grid structure, which can satisfy the physical constraints of the
interaction of quantum bits in the grid in the process of mapping an 1-D
quantum circuit to a 2-D grid structure. For some benchmark circuits,
after using the method of this paper to place
qubits,
it is possible to make every 2-qubit
gate in the circuit have a nearest neighbor, so that there is no need to
use SWAP gate to establish channel routing. Compared with the latest
available methods, the average optimization rate is 82.38\%.
A local model of quantum
Turing machines
(pp213-229)
Dong-Sheng
Wang
The model of local Turing
machines is introduced, including classical and quantum ones, in the
framework of matrix-product states. The locality refers to the fact that
at any instance of the computation the heads of a Turing machine have
definite locations. The local Turing machines are shown to be equivalent
to the corresponding circuit models and standard models of Turing
machines by simulation methods. This work reveals the fundamental
connection between tensor-network states and information processing.
Quantum walks as mathematical
foundation for quantum gates
(pp230-258)
Dmitry Solenov
It is demonstrated that in
gate-based quantum computing architectures quantum walk is a natural
mathematical description of quantum gates. It originates from
field-matter interaction driving the system, but is not attached to
specific
qubit
designs and can be formulated for very general field-matter
interactions. It is shown that, most generally, gates are described by a
set of coined quantum walks. Rotating wave and resonant approximations
for field-matter interaction simplify the walks, factorizing the coin,
and leading to pure continuous time quantum walk description. The walks
reside on a graph formed by the Hilbert space of all involved
qubits
and auxiliary states, if present. Physical interactions between
different parts of the system necessary to propagate entanglement
through such graph---quantum network---enter via reduction of symmetries
in graph edges. Description for several single- and two-qubit
gates are given as examples.
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