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arXiv:quant-ph/0311172 · Physical Review A

Generalized measurements via a programmable quantum processor

Marián Roško, Vladimír Bužek, Paul Robert Chouha, Mark S. Hillery

Published Dec 2, 2003• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.68.062302

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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.
We analyze probabilistic realizations of programmable quantum processors that allow us to realize unitary operations on qubits as well as on qudits. Programmable processors are composed of two inputs — the data register and the program register. In the input state of the program register information about the operation that is supposed to be performed on the data is encoded. At the output of the probabilistic processor a measurement over the program register is performed. An intrinsic property of probabilistic processors is that they sometimes fail, but we know when this happens. We present a complete analysis of two processors: (1) The so-called [Formula: see text] processor that is based on a simple controlled-NOT gate. (2) The so-called [Formula: see text] processor that utilizes the quantum-information-distributor circuit.
Programmable photonic quantum processors face a critical challenge: despite significant advances in quantum state preparation and manipulation, measurements remain limited to projective techniques. Here, we demonstrate a programmable measurement processor that overcomes this limitation by enabling arbitrary quantum measurements within a scalable circuit framework. Our large-scale integrated photonic architecture achieves precise coherent control of ancillary quantum systems, realizing a universal four-dimensional quantum measurement device. We benchmark the processor by performing measurement tomography on 100 randomly selected measurements, achieving an average fidelity of 97.7%. The processor's performance exceeds the theoretical limits of projective measurements in three key quantum information tasks: state discrimination (with 23 times lower error), state estimation (with 10.6% higher fidelity), and randomness generation (with 37% more randomness yield), demonstrating its high operational quality. This work establishes a fully programmable quantum measurement processor, advancing the development of universal quantum operations for photonic quantum information processing by providing the key missing component.
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.
Controlling and programming quantum devices to process quantum information by the unit of quantum dit, i.e., qudit, provides the possibilities for noise-resilient quantum communications, delicate quantum molecular simulations, and efficient quantum computations, showing 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 quantum quart (ququart) states and multi-value quantum-controlled logic gates with high-level fidelities. By reprogramming the configuration of the processor, we implemented the most basic quantum Fourier transform algorithms, all in quaternary, to benchmark the enhancement of quantum parallelism using qudits, which include generalised Deutsch-Jozsa and Bernstein-Vazirani algorithms, quaternary phase estimation and fast factorization algorithms. The monolithic integration and high programmability have allowed the implementations of more than one million high-fidelity preparations, operations and projections of qudit states in the processor. Our work shows an integrated photonic quantum technology for qudit-based quantum computing with enhanced capacity, accuracy, and efficiency, which could lead to the acceleration of building a large-scale quantum computer.