Quantum Measurements and Circuits

Roy J. Glauber

Sung Won Yun, Thi Ha Kyaw, Joonwoo Bae

In this work, we present constructions of quantum circuits to implement general measurements on quantum hardware. Firstly, we investigate a quantum circuit ansatz by following the Naimark extension with a universal set of gates, such as controlled-NOT and single-qubit gates; we call it a {\it Naimark measurement}. We present a circuit ansatz framed by the Naimark extension, leaving single-qubit gates with parameters, and apply a classical optimizer to determine their parameters to approximate a desired quantum measurement. Secondly, we relax the Naimark measurement with quantum neural-network (QNN) circuits, employing parameterized quantum circuits. We present hybrid Naimark-QNN measurements by incorporating QNN circuits into Naimark measurements. Thirdly, we also consider fully QNN measurements with shallow parameterized circuits. Then, we compare the constructed measurement circuits, Naimark, hybrid Naimark-QNN, and fully QNN measurements, for strategies of state discrimination, such as minimum-error and maximum-confidence measurements. We demonstrate that QNN circuits can efficiently and effectively achieve near-optimal quantum measurements with fewer training iterations.

Yanbin Chen, Innocenzo Fulginiti, Christian B. Mendl

Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms and will become more relevant as an essential building block for quantum error correction. However, mid-circuit measurements impose significant demands on the quantum hardware due to the required signal analysis and classical feedback loop. This work presents a static circuit optimization algorithm that can substitute some of these measurements with an equivalent circuit with stochastic applications of gates. Our method uses ideas from constant propagation to classically precompute measurement outcome probabilities. Our proposed optimization is efficient, as its runtime scales polynomially on the number of qubits and gates of the circuit.

Leonardo Vanni, Roberto Laura

Martin Lukac, Marek A. Perkowski

In this paper we introduce the new model for Quantum Logic Synthesis. The innovation consists in designing circuits with the measurement process together with the computing circuit. The Measurement is used as a part of the entire computational process. We demonstrate the method to synthesize quantum circuits from examples (examples are cares of the quantum truth table) such that the synthesis process converts the don't knows (minterms not given as examples) to the entangled quantum output values which are measurement dependent. We extended the logic synthesis approach to measurement-based quantum circuits synthesis from incompletely specified or completely specified function specifications.

Xi Zhengjun and Li Yongming