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IFAC-PapersOnLine

One Port Impedance Quantization For a Class of Annihilation Operator Linear Quantum Systems

Aline I. Maalouf, Ian R. Petersen

Published Jan 1, 2020• 2 citations
Publisher

Abstract

This paper provides a procedure for building a one port impedance quantization involving annihilation operators only for a class of linear quantum systems having a positive real impedance transfer function matrix. Based on the positive real properties of these quantum systems, it is shown that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, illustrated for one-port circuits may be useful for the implementation of superconducting microwave circuits used in quantum filters found in the field of quantum computing.

DOI
10.1016/j.ifacol.2020.12.137

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This paper provides a procedure for building a one port impedance quantization involving annihilation operators only for a class of linear quantum systems having a positive real impedance transfer function matrix. Based on the positive real properties of these quantum systems, it is shown that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, illustrated for one-port circuits may be useful for the implementation of superconducting microwave circuits used in quantum filters found in the field of quantum computing.
This paper provides a procedure for building a multiport impedance quantization involving annihilation operators only for a class of linear quantum systems having a positive real impedance transfer function matrix. Based on the positive real properties of these quantum systems, it is shown that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, illustrated for multiport circuits may be useful for the implementation of superconducting microwave circuits used in quantum filters found in the field of quantum computing.
Theoretical developments in the field of quantum optics and quantum superconducting electrical circuits involving continuous measurement based feedback control as well as coherent control are an important prerequisites for advances in the domain of quantum technology. Within these perspectives, this paper considers positive real properties for a class of quantum systems whose quantum stochastic differential equation model involves annihilation operators only and then relates them to corresponding bounded real properties and consequently to physical realizability conditions developed earlier by the authors. Based on the positive real properties of these quantum systems, it is anticipated that it is possible to use the Brune algorithm in order to find an electrical circuit that can physically implement these quantum systems. This theory, in the case of one-port circuits, may be useful for the implementation of microwave circuits related to quantum filters found in the field of quantum computing.
We propose a new quantization method for superconducting electronic circuits involving a Josephson-junction device coupled to a linear microwave environment. The method is based on an exact impedance synthesis of the microwave environment considered as a blackbox with impedance function Z(s)Z(s)Z(s). The synthesized circuit captures dissipative dynamics of the system with resistors coupled to the reactive part of the circuit in a nontrivial way. We quantize the circuit and compute relaxation rates following previous formalisms for lumped element circuit quantization. Up to the errors in the fit our method gives an exact description of the system and its losses.
In this thesis we propose new methods in multi-qubit multi-mode circuit quantum electrodynamics (circuit-QED) architectures. In Chapter 2 we describe a direct parity measurement method for three qubits, which can be realized in 2D circuit-QED with a possible extension to four qubits in a 3D circuit-QED setup for the implementation of the surface code. In Chapter 3 we show how to derive Hamiltonians and compute relaxation rates of the multi-mode superconducting microwave circuits consisting of single Josephson junctions using an exact impedance synthesis technique (the Brune synthesis) and applying previous formalisms for lumped element circuit quantization. In the rest of the thesis we extend our method in Chapter 3 to multi-junction (multi-qubit) multi-mode circuits through the use of state-space descriptions which allows us to quantize any multiport microwave superconducting circuit with a reciprocal lossy impedance response.
This paper considers the bounded real properties for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. The paper considers complex quantum versions of the Bounded Real Lemma, the Strict Bounded Real Lemma and the Lossless Bounded Real Lemma. For the class of quantum systems under consideration, it is shown that the question of physical realizability is related to the Bounded Real and Lossless Bounded Real properties.