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IEEE International Conference on Quantum Computing and Engineering (QCE)

Detection-Based Measurements for Quantum Emulation Devices

S. Andrew Lanham, Brian R. La Cour

Published Oct 1, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1109/qce49297.2020.00015

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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.
This paper describes a simple, causally deterministic model of quantum measurement based on an amplitude threshold detection scheme. Surprisingly, it is found to reproduce many phenomena normally thought to be uniquely quantum in nature. To model an NNN -dimensional pure state, the model uses NNN complex random variables given by a scaled version of the wave vector with additive complex noise. Measurements are defined by threshold crossings of the individual components, conditioned on single-component threshold crossings. The resulting detection probabilities match or approximate those predicted by quantum mechanics according to the Born rule. Nevertheless, quantum phenomena such as entanglement, contextuality, and violations of Bell’s inequality under local measurements are all shown to be exhibited by the model, thereby demonstrating that such phenomena are not without classical analogs.
Abstract In quantum information, device-independent (DI) protocols offer a new approach to information processing tasks, making minimal assumptions about the devices used. Typically, since these protocols draw conclusions directly from the data collected in a meaningful Bell test, the no-signaling conditions, and often even Born’s rule for local measurements, are taken as premises of the protocol. Here, we demonstrate how to test such premises in an (almost) DI setting, i.e. directly from the raw data and with minimal assumptions. In particular, for IBM’s quantum computing cloud services, we implement the prediction-based ratio protocol to characterize how well the qubits can be accessed locally and independently. More precisely, by performing a variety of Clauser–Horne–Shimony–Holt-type experiments on these systems and carrying out rigorous hypothesis tests on the collected data, we provide compelling evidence showing that some of these qubits suffer from measurement cross-talks, i.e. their measurement statistics are affected by the choice of measurement bases on another qubit. Unlike standard randomized benchmarking, our approach does not rely on assumptions such as gate-independent Markovian noise. Moreover, despite the relatively small number of experimental trials, the direction of ‘signaling’ may also be identified in some cases. Our approach thus serves as a complementary tool for benchmarking the local addressability of quantum computing devices.
The engineering problem of building scalable quantum computers has prompted the development of a rich theory modeling the evolution of quantum systems as well as techniques to preserve quantum information in the presence of noise. Such techniques offer systems-level approaches to the problem of robustly encoding and preserving information and, as a result, see applicability in a wide variety of architectures for computing systems. In this thesis, we visit the mathematical underpinnings of quantum information and apply strategies inspired by quantum information processing to two non-quantum systems to demonstrate advantage. We first describe the construction of a quantum emulation device, an analog electronic system with the same mathematical structure as a gate-based quantum computer, and introduce novel time-domain information encoding methods to increase the computational capacity of the device. We confirm the sustained performance of the improved system by successfully transforming emulated states by randomly selected quantum gates. We then visit similarities between quantum information processing and signal processing in the noncoherent wireless communication setting, the latter being an environment characterized by a lack of instantaneous channel knowledge. We describe the theoretical underpinnings of the noncoherent communication environment from both an information theoretic and signal processing perspective. This leads us to propose a multi-antenna space-time code construction based on a family of quantum error correcting codes known as stabilizer codes. For this code, we derive the optimal decoder in Rayleigh and Ricean fading and benchmark the its performance against coherent and differential coding at comparable rates.
Recent development in quantum information sciences and technologies, especially building programmable quantum computers, provide us new opportunities to study fundamental aspects of quantum mechanics. We propose qubit models to emulate the quantum measurement process, in which the quantum information of a qubit is mapped to a collection of qubits acting as the measurement device. One model is motivated by single-photon detection and the other by spin measurement. Both models are scalable to generate Schrödinger cat-like state, and their corresponding quantum circuits are shown explicitly. Large-scale simulations could be realised in near-term quantum computers, while classical computers cannot perform the same task efficiently. Due to the scalability of the models, such simulations can help explore the quantum-to-classical boundary, if exists, in the quantum measurement problem. Besides, our protocol to generate cat states may have important applications in quantum computing and metrology.
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