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Quantum Information Processing

Quantum measurement detection algorithms

Guillermo Lugilde Fernández, Elías F. Combarro, I. F. Rúa

Published Aug 13, 2022• 1 citation
Publisher

Abstract

Abstract In this paper, we introduce and study the quantum measurement detection algorithms (QMDA), whose objective is to detect whether unwanted measurements are being taken in a quantum circuit or not by applying the Zeno effect. A QMDA is a quantum circuit that includes three unitary matrices, one of them being applied numerous times consecutively, and whose initial state is fixed when no foreign measurements occur. One example is the Elitzur–Vaidman bomb tester, which is generalized by the QMDA definition, allowing the detection of measurements that are taken in an unknown basis and in circuits with an arbitrary number of qubits. We prove some key properties and limitations of these algorithms, as well as studying the performance of the Elitzur–Vaidman bomb tester and its possible improvements. Some extensions of the definition would lead to algorithms such as the counterfactual communication one.

DOI
10.1007/s11128-022-03614-6

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Abstract In this paper, we introduce and study the quantum measurement detection algorithms (QMDA), whose objective is to detect whether unwanted measurements are being taken in a quantum circuit or not by applying the Zeno effect. A QMDA is a quantum circuit that includes three unitary matrices, one of them being applied numerous times consecutively, and whose initial state is fixed when no foreign measurements occur. One example is the Elitzur–Vaidman bomb tester, which is generalized by the QMDA definition, allowing the detection of measurements that are taken in an unknown basis and in circuits with an arbitrary number of qubits. We prove some key properties and limitations of these algorithms, as well as studying the performance of the Elitzur–Vaidman bomb tester and its possible improvements. Some extensions of the definition would lead to algorithms such as the counterfactual communication one.
The aim of this paper is to carry out a critical analysis of the uses of the material conditionals employed to represent the counterfactual detections taking place inside Elitzur-Vaidman quantum bomb detectors in so-called quantum interaction free measurements (IFMs). We provide an exhaustive philosophical study of this classical approach focusing on its limitations. To do so, we formulate atomic propositions corresponding to the observable events of the experiments, to overcome the shortcomings of the conditional expression. Finally, we show that the standard definition ofcounterfactuality in quantum contexts based on classical logic is epistemologically too limited, presenting quantum logics as the most promising possible approach to address this type of quantum counterfactuality.
An Elitzur–Vaidman bomb tester demonstrates interaction-free sensing: detecting an object without absorbing a photon. The original protocol, however, has a success probability capped at 25%. We present a scalable quantum circuit that harnesses the quantum Zeno effect to overcome this limit. A single probe qubit undergoes repeated cycles of a small rotation followed by a controlled-NOT (CNOT) with an ancilla qubit representing the obstacle. The circuit requires only two qubits, regardless of the number of cycles N and has depth linear in N, compatible with near-term processors that support mid-circuit measurement and conditional reset. We simulate the circuit under ideal conditions and under a depolarizing noise model with gate errors typical of superconducting qubits (CNOT error 2% and single-qubit gate error rate 0.1%). Under noise, the success probability peaks around N=14 (reaching 72.0%), outperforming the original 25% limit by nearly a factor of three, with a well-defined optimal region. The protocol requires approximately 4.4 times fewer photons than the original Elitzur–Vaidman scheme to achieve 99.9% confidence. Its simple repetitive structure and well-defined optimal regime make it a practical benchmark for quantifying gate errors and decoherence on noisy intermediate-scale quantum hardware for quantum sensing applications.
Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a selected set of their applications in quantum algorithms. Our goal is to provide one of the first algorithmic overviews of measurement processes in quantum computing. From the quantum information-theoretical perspective, measurements are either a method to access the result of a quantum computation or a technique to modify a quantum state. We also identify measurement-based methods to solve quantum computational challenges, such as error mitigation and circuit cutting. We discuss three main categories of measurements: performing measurements in static quantum circuits, modifying the quantum state in dynamic quantum circuits via measurements, and addressing challenges in quantum computing with measurements. Based on the reviewed topics, the measurement operations are frequently not at the center of the quantum algorithm design. However, the most novel and error-prone quantum algorithms will likely require sophisticated measurement schemes. Thus, the central message of this article is to broaden the view of measurement operations and highlight their importance at every level of quantum algorithm design.
Quantum emulation devices use analog electronic signals to mimic precisely the behavior of a gate-based quantum computer. These devices also introduce the flexibility to choose different detection rules to generate measurement outcomes. Such rules may depend on deterministic decisions rather than the randomized decisions occurring in Born rule-based measurements of true quantum systems. In this paper, we leverage this flexibility in an emulation device to consider implementations of measurement detection rules with better performance than the Born rule. We visit physically-inspired detection strategies such as maximum-energy and threshold detectors, as well the optimal maximum-likelihood detector. We gauge the detectors by how often they successfully produce the correct outcome of a quantum algorithm in the presence of noise, deriving computationally efficient implementations and comparing their probability of error performance to the Born rule detectors. We find that efficient detectors may be defined with significantly better performance than the Born rule detector at comparable signal-to-noise ratios. We also introduce a theoretical performance comparison to a true quantum computing system operating in a generalized depolarizing channel.
Abstract In this work, we investigate the question of which objects can be discriminated by totally “interaction-free” measurements. To this end, we interpret the Elitzur–Vaidman bomb-tester experiment as a quantum channel discrimination problem and generalize the notion of “interaction-free” measurement to arbitrary quantum channels. Our main result is a necessary and sufficient criterion for when it is possible or impossible to discriminate quantum channels in an “interaction-free” manner (i.e., such that the discrimination error probability and the “interaction” probability can be made arbitrarily small). For the case where our condition holds, we devise an explicit protocol with the property that both probabilities approach zero with an increasing number of channel uses, N. More specifically, the “interaction” probability in our protocol decays as 1N\frac{1}{N}N1​ 1 N and we show that this rate is the optimal achievable one. Furthermore, our protocol only needs at most one ancillary qubit and might thus be implementable in near-term experiments. For the case where our condition does not hold, we prove an inequality that quantifies the trade-off between the error probability and the “interaction” probability.
In this paper, we study the following question: given a black box performing some unknown quantum measurement on a multi-qudit system, how do we test whether this measurement has certain property or is far away from having this property. We call this task \textit{property testing} of quantum measurement. We first introduce a metric for quantum measurements, and show that it possesses many nice features. Then we show that, with respect to this metric, the following classes of measurements can be efficiently tested: 1. the stabilizer measurements, which play a crucial role for quantum error correction; 2. the kkk-local measurements, i.e. measurements whose outcomes depend on a subsystem of at most kkk qudits; 3. the permutation-invariant measurements, which include those measurements used in quantum data compression, state estimation and entanglement concentration. In fact, all of them can be tested with query complexity independent of the system's dimension. Furthermore, we also present an algorithm that can test any finite set of measurements. Finally, we consider the following natural question: given two black-box measurement devices, how do we estimate their distance? We give an efficient algorithm for this task, and its query complexity is also independent of the system's dimension. As a consequence, we can easily test whether two unknown measurements are identical or very different.