We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of adaptive positive operator valued measures (POVMs) that can be simulated with simple projective measurements without ancillary qubits, we decrease the amount of required qubits and two-qubit gates. Second, by introducing a method based on Quantum Detector Tomography to mitigate the effect of noise, we are able to optimise the POVMs as well as to infer expectation values reliably in the currently available noisy quantum devices. Our numerical simulations clearly indicate that the presented strategies can significantly reduce the number of needed shots to achieve chemical accuracy in variational quantum eigensolvers, thus helping to solve one of the bottlenecks of near-term quantum computing.
We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of adaptive positive operator valued measures (POVMs) that can be simulated with simple projective measurements without ancillary qubits, we decrease the amount of required qubits and two-qubit gates. Second, by introducing a method based on Quantum Detector Tomography to mitigate the effect of noise, we are able to optimise the POVMs as well as to infer expectation values reliably in the currently available noisy quantum devices. Our numerical simulations clearly indicate that the presented strategies can significantly reduce the number of needed shots to achieve chemical accuracy in variational quantum eigensolvers, thus helping to solve one of the bottlenecks of near-term quantum computing.
We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.
We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.
Variational quantum algorithms stand as the most promising approaches towards practical applications of near-term quantum computers. However, these methodologies usually require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a novel approach to tackle this problem: a variational measurement scheme. We present an algorithm that optimises informationally complete POVMs on the fly in order to minimise the statistical fluctuations in the estimation of relevant cost functions. We use it in combination with the Variational Quantum Eigensolver to calculate ground-state energies of molecular Hamiltonians in numerical simulations and show that it is competitive with state-of-the-art measurement reduction approaches. We also highlight the potential of the informational completeness of the measurement outcomes by reusing the ground-state energy estimation data to perform high-fidelity reduced state tomography.
High-precision measurements on near-term quantum devices are important for advancing quantum computing applications. The high readout errors of the current quantum computers complicate any effort to perform quantum simulations with high accuracy. This thesis implements practical techniques to reduce overhead and error, achieving accuracies suitable for quantum chemistry applications. To reduce circuit overhead, we use repeated settings and parallel Quantum Detector Tomography (QDT), and for shot overhead, we use a locally biased randomized measurement scheme. QDT is also used to mitigate readout errors and blending is used to mitigate the effects of drift. These techniques were validated by estimating the expectation values of the energy of the BODIPY molecule on a Hartree-Fock state. All experiments were performed on an IBM Eagle r3 quantum computer, where we were able to reduce the measurement errors by an order of magnitude, from 1-5% to 0.16%. These methods enable reliable quantum computations, essential for precise molecular energy calculations.
Assumption-free reconstruction of quantum states from measurements is essential for benchmarking and certifying quantum devices, but it remains difficult due to the extensive measurement statistics and experimental resources it demands. An approach to alleviating these demands is provided by adaptive measurement strategies, which can yield up to a quadratic improvement in reconstruction accuracy for pure states by dynamically optimizing measurement settings during data acquisition. A key open question is whether these asymptotic advantages remain in realistic experiments, where readout is inevitably noisy. In this work, we analyze the impact of readout noise on adaptive quantum state tomography with readout-error mitigation, focusing on the challenging regime of reconstructing pure states using mixed-state estimators. Using analytical arguments based on Fisher information optimization and extensive numerical simulations using Bayesian inference, we show that any nonzero readout noise eliminates the asymptotic quadratic scaling advantage of adaptive strategies. We numerically investigate the behavior for finite measurement statistics for single- and two-qubit systems with exact readout-error mitigation and find a gradual transition from ideal to sub-optimal scaling. We furthermore investigate realistic scenarios where detector tomography is performed with a limited number of state copies for calibration, showing that insufficient detector characterization leads to estimator bias and limited reconstruction accuracy. Although our result imposes an upper bound on the reconstruction accuracy that can be achieved with adaptive strategies, we nevertheless observe numerically a constant-factor gain in reconstruction accuracy, which becomes larger as the readout noise decreases. This indicates potential practical benefits in using adaptive measurement strategies in well-calibrated experiments.
Quantum chemistry is among the most promising applications of quantum computing, offering the potential to solve complex electronic structure problems more efficiently than classical approaches. A critical component of any quantum algorithm is the measurement step, where the desired properties are extracted from a quantum computer. This review focuses on recent advancements in quantum measurement techniques tailored for quantum chemistry, particularly within the second quantized framework suitable for current and near-term quantum hardware. We provide a comprehensive overview of measurement strategies developed primarily for the Variational Quantum Eigensolver (VQE) and its derivatives. These strategies address the inherent challenges posed by the complexity of the electronic Hamiltonian operator. Additionally, we examine methods for estimating excited states and one- and two-electron properties, extending the applicability of quantum algorithms to broader chemical phenomena. Key aspects of the review include approaches for constructing measurement operators with reduced classical preprocessing and quantum implementation costs, techniques to minimize the number of measurements required for a given accuracy, and error mitigation strategies that leverage symmetries and other properties of the measurement operators. Furthermore, we explore measurement schemes rooted in Quantum Phase Estimation (QPE), which are expected to become viable with the advent of fault-tolerant quantum computing. This review emphasizes foundational concepts and methodologies rather than numerical benchmarks, serving as a resource for researchers aiming to enhance the efficiency and accuracy of quantum measurements in quantum chemistry.