Estimating properties of quantum states via randomized measurements has become a significant part of quantum information science. In this paper, we design an innovative approach leveraging metasurfaces to perform randomized measurements on photonic qubits, together with error mitigation techniques that suppress realistic metasurface measurement noise. Through fidelity and purity estimation, we confirm the capability of metasurfaces to implement randomized measurements and the unbiased nature of our error-mitigated estimator. Our findings show the potential of metasurface-based randomized measurement schemes in achieving robust and resource-efficient estimation of quantum state properties. Published by the American Physical Society 2024
Estimating properties of quantum states via randomized measurements has become a significant part of quantum information science. In this paper, we design an innovative approach leveraging metasurfaces to perform randomized measurements on photonic qubits, together with error mitigation techniques that suppress realistic metasurface measurement noise. Through fidelity and purity estimation, we confirm the capability of metasurfaces to implement randomized measurements and the unbiased nature of our error-mitigated estimator. Our findings show the potential of metasurface-based randomized measurement schemes in achieving robust and resource-efficient estimation of quantum state properties. Published by the American Physical Society 2024
Measurement overhead and hardware noise present fundamental obstacles to the practical realization of quantum algorithms on near-term quantum devices. In many quantum applications, the dominant computational cost arises from repeated measurements needed to extract accurate information and from handling noise effects. This dissertation develops a unified framework for efficient measurement and error mitigation in quantum algorithms.In this work, measurement is treated as a controllable and designable component across hardware, algorithmic, and statistical levels, rather than as a fixed final step. By tailoring measurement schemes and estimators, we show that substantial reductions in measurement cost can be achieved without sacrificing accuracy. This approach is developed and validated across multiple settings, from hardware-level randomized measurement implementations to algorithm-level molecular energy estimation.At the hardware level, we investigate randomized measurement schemes based on photonic metasurfaces. We find that the device itself naturally realizes the required family of measurement bases without repeated active optical reconfiguration, providing an efficient platform for randomized measurements. We analyze the effect of realistic measurement noise and develop calibration-based error mitigation techniques that suppress noise-induced bias. Numerical studies show that this approach enables accurate estimation of state properties under realistic measurement noise.At the algorithmic level, we investigate measurement-efficient quantum eigen solvers through the Non-Orthogonal Quantum Eigensolver (NOQE). We develop a detailed implementation framework for NOQE, including circuit construction and simplification, analysis of measurement complexity, and resource estimation. Building on this understanding, we incorporate randomized measurements as an alternative to standard Hadamard-test-based schemes and develop shadow-tomography-enhanced variants of NOQE that significantly reduce circuit complexity and qubit requirements while maintaining favorable sample complexity. Shadow-based error mitigation methods, including shadow distillation, further improve robustness against noise.Finally, we investigate a more fundamental redesign of the NOQE measurement task by reformulating matrix-element estimation as a quantum amplitude estimation problem. By integrating iterative quantum amplitude estimation into the NOQE framework, we replace the original incoherent sampling-based estimation with coherent information accumulation through amplitude amplification and achieve near-Heisenberg scaling in measurement complexity, improving on the standard sampling-based methods. Numerical results for molecular energy estimation demonstrate that this approach reaches chemical accuracy with fewer queries than the original NOQE.Overall, this dissertation shows that measurement overhead is not a fixed limitation, but a resource bottleneck that can be identified and reduced at multiple levels in quantum applications. Across the settings studied here, improvements are achieved at different layers, including hardware-aware randomized measurements, algorithm-level redesign of measurement protocols, estimator-level error mitigation, and statistical improvements based on coherent information accumulation. Taken together, these results provide a unified framework for understanding and reducing measurement cost under realistic noise, and offer practical guidance for the design of quantum algorithms on near-term quantum devices.
We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state. This consists in performing randomized measurements on a quantum processor and comparing the results with those obtained from a classical computer that stores an approximation of the quantum state. We provide unbiased estimators for expectation values of multicopy observables and present performance guarantees in terms of variance bounds that depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through experimental and numerical examples detecting mixed-state entanglement, and estimating polynomial approximations of the von Neumann entropy and state fidelities. Published by the American Physical Society 2024
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible measurements, serving as the building block of prominent schemes like shadow estimation. In the real world, however, the implementation of the random gates at the core of these schemes is susceptible to various sources of noise and imperfections, strongly limiting the applicability of protocols. To attenuate the impact of this shortcoming, in this work we introduce an error-mitigated method of randomized measurements, giving rise to a robust shadow estimation procedure. On the practical side, we show that error mitigation and shadow estimation can be carried out using the same session of quantum experiments, hence ensuring that we can address and mitigate the noise affecting the randomization measurements. Mathematically, we develop a picture derived from Fourier-transforms to connect randomized benchmarking and shadow estimation. We prove rigorous performance guarantees and show the functioning using comprehensive numerics. More conceptually, we demonstrate that, if properly used, easily accessible data from randomized benchmarking schemes already provide such valuable diagnostic information to inform about the noise dynamics and to assist in quantum learning procedures.
Randomized measurement protocols such as classical shadows represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation. Recently, the notion of measurement dual frames, in which classical shadows are generalized to dual operators of positive operator-valued measure (POVM) effects, resurfaced in the literature. This brought attention to additional degrees of freedom in the postprocessing stage of randomized measurements that are often neglected by established techniques. In this work, we leverage dual frames to construct improved observable estimators from informationally complete measurement samples. We introduce novel classes of parametrized frame superoperators and optimization-free dual frames based on empirical frequencies, which offer advantages over their canonical counterparts while retaining computational efficiency. Remarkably, this comes at almost no quantum or classical cost, thus rendering dual frame optimization a valuable addition to the randomized measurement toolbox. Published by the American Physical Society 2024
Real photonic devices are subject to photon losses that can decohere quantum information encoded in the system. In the absence of full fault tolerance, quantum error mitigation techniques have been introduced to help manage errors in noisy quantum devices. In this paper, we introduce an error mitigation protocol inspired by probabilistic error cancellation (a popular error mitigation technique in discrete variable systems) for continuous variable systems. We show that our quantum error cancellation protocol can undo photon losses in expectation value estimation tasks. To do this, we analytically derive the (nonphysical) inverse photon loss channel and decompose it into a sum over physically realizable channels with potentially negative coefficients. The bias of our ideal expectation value estimator can be made arbitrarily small at the cost of increasing the sampling overhead. The protocol requires a noiseless amplification followed by a series of photon subtractions. While these operations can be implemented probabilistically, for certain classes of initial state one can avoid the burden of carrying out the amplification and photon subtractions by leveraging Monte Carlo methods to give an unbiased estimate of the ideal expectation value. We validate our proposed mitigation protocol by simulating the scheme on squeezed vacuum states, cat states, and entangled coherent states. Published by the American Physical Society 2024
Optical quantum information processing relies critically on Bell-state measurement, a ubiquitous operation for quantum communication and computing. Its practical realization involves the interference of optical modes and the detection of a single photon in an indistinguishable manner. Yet, in the absence of efficient photon-number-resolution capabilities, errors arise from multiphoton components, decreasing the overall process fidelity. Here, we introduce a hybrid detection scheme for Bell-state measurement, leveraging both on-off single-photon detection and quadrature conditioning via homodyne detection. We derive explicit fidelities for quantum teleportation and entanglement-swapping processes employing this strategy, demonstrating its efficacy. We also compare with photon-number-resolving detectors and find a strong advantage of the hybrid scheme in a wide range of parameters. This work provides a new tool for linear-optics schemes, with applications to quantum state engineering and quantum interconnects. Published by the American Physical Society 2024