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Hu'nan Shifan Daxue xuebao. Ziran kexue ban

Programmable Quantum Processor for d-Level Systems Based on Generalized Bell States Measurement

Hao San-Ru

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Generalized universal programmable quantum processor to the d-level quant um system and a explicit scheme to implement a universal gate array is given. Th i s universal gate array consists of a joint Bell measurement and three controlled -NOT gates. In order to complete the Bell measurement and the controlled-NOT o peration for the d-level quantum system, we have introduced the generalized Bel l bases and generalized controlled-NOT operation for qudits, and discussed the properties of the generalized Bell basis states and controlled-NOT gate.

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Generalized universal programmable quantum processor to the d-level quant um system and a explicit scheme to implement a universal gate array is given. Th i s universal gate array consists of a joint Bell measurement and three controlled -NOT gates. In order to complete the Bell measurement and the controlled-NOT o peration for the d-level quantum system, we have introduced the generalized Bel l bases and generalized controlled-NOT operation for qudits, and discussed the properties of the generalized Bell basis states and controlled-NOT gate.
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.
We show that it is possible to control the trade-off between information gain and disturbance in generalized measurements of qudits by utilizing a programmable quantum processor. This universal quantum machine allows us to perform a generalized measurement on the initial state of the input qudit to construct a Husimi function of this state. The trade-off between the gain and the disturbance of the qudit is controlled by the initial state of ancillary system that acts as a program for the quantum-information distributor. The trade-off fidelity does not depend on the initial state of the qudit.
Controlling and programming quantum devices to process quantum information by the unit of qudit shows great potential to enhance the capabilities of qubit-based quantum technologies. Here, we report a programmable qudit-based quantum processor in silicon-photonic integrated circuits and demonstrate its enhancement of quantum computational parallelism. The processor monolithically integrates all the key functionalities and capabilities of initialisation, manipulation, and measurement of the two-ququart states and multi-value quantum-controlled logic gates with high-level fidelities. We implemented the basic quantum Fourier transform algorithms to benchmark the enhancement of quantum parallelism using qudits, allowing the implementations of more than one million high-fidelity preparations, operations and projections of qudit states in the processor. Our work shows an integrated quantum technology for qudit-based quantum computing with enhanced capacity, accuracy, and efficiency.
In this paper is presented in abstract theory of quantum processors and controllers, special kind of quantum computational network defined on a composite quantum system with two parts: the controlling and controlled subsystems. Such approach formally differs from consideration of quantum control as some external influence on a system using some set of Hamiltonians or quantum gates. The model of programmed quantum controllers discussed in present paper is based on theory of universal deterministic quantum processors (programmable gate arrays). Such quantum devices may simulate arbitrary evolution of quantum system and so demonstrate an example of universal quantum control.
A quantum processor (the programmable gate array) is a quantum network with a fixed 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. By different authors was developed universal "stochastic" quantum gate arrays. It was proved also, that "deterministic" quantum processors with finite-dimensional space of states may be universal only in approximate sense. In present paper 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 shown also that "deterministic" limit of specific programmable "stochastic" U(1) gates (probability of success becomes unit for infinite program register), discussed by other authors, may be essentially same kind of hybrid quantum systems used here.
We present a probabilistic quantum processor for qudits on a single qudit of dimension N. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor can perform any operation on a single qudit of dimension N with a certain probability. For a general unitary operation, the probability is 1/N2,{1/N}^{2},1/N2, but for more restricted sets of operators the probability can be higher. In fact, this probability can be independent of the dimension of the qudit Hilbert space of the qudit under some conditions.