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arXiv:quant-ph/0209069 · Physical Review A

Multi-output programmable quantum processor

Ya‐Fei Yu, Jian Feng, Mingsheng Zhan

Published Nov 19, 2002• 21 citations
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Abstract

By combining telecloning and the programmable quantum gate array presented by Nielsen and Chuang [Phys. Rev. Lett. 79, 321 (1997)], we propose a programmable quantum processor which can be programmed to implement a restricted set of operations with several identical data outputs. The outputs are approximately transformed versions of input data. The processor successes with certain probability.

DOI
10.1103/physreva.66.052310

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By combining telecloning and the programmable quantum gate array presented by Nielsen and Chuang [Phys. Rev. Lett. 79, 321 (1997)], we propose a programmable quantum processor which can be programmed to implement a restricted set of operations with several identical data outputs. The outputs are approximately transformed versions of input data. The processor successes with certain probability.
We present a probabilistic quantum processor for qubits. The processor itself is represented by a fixed array of gates. The input of the processor is constituted by two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor we present can perform any operation on a single qubit with a certain probability. If the operation is unitary, the probability is in general 1/4, but for more restricted sets of operators the probability can be higher.
A quantum processor (the programmable gate array) is a quantum network with a ˇxed structure. A space of states is represented as tensor product of data and program registers. Different unitary operations with the data register correspond to ®loaded ¯ programs without any changing or ®tuning¯ of network itself. Due to such property and undesirability of entanglement between program and data registers, universality of quantum processors is subject of rather strong restrictions. Universal ®stochastic¯ quantum gate arrays were developed by different authors. It was also proved, that ®deterministic¯ quantum processors with ˇnite-dimensional space of states may be universal only in approximate sense. In the present paper it is shown that, using hybrid system with continuous and discrete quantum variables, it is possible to suggest a design of strictly universal quantum processors. It is also shown that ®deterministic ¯ limit of speciˇc programmable ®stochastic ¯ U(1) gates (probability of success becomes unit for inˇnite program register), discussed by other authors, may be essentially the same kind of hybrid quantum systems used here.
A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.
A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's No-Programming Theorem ), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via teleportation simulation , which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately.
We propose two different implementations of an asymmetric two-output probabilistic quantum processor, which can implement a restricted set of one-qubit operations. One of them is constructed by combining asymmetric telecloning with a quantum gate array. We analyze the efficiency of this processor by evaluating the fidelities between the desired operation and the one generated by the processor and show that the two output states are the same as the ones produced by the optimal universal asymmetric Pauli cloning machine. The schemes require only local operations and classical communication, they have the advantage of transmitting the two output states directly to two spatially separated receivers but they have a success probability of 1/2. We show further that we can perform the same one-qubit operation with unity probability at the cost of using nonlocal operations. We finally generalize the two schemes for D-level systems and find that the local ones are successful with a probability of 1/D and the nonlocal generalized scheme is always successful.