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
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
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 global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms. Published by the American Physical Society 2024
Accurately estimating expectation values of quantum observables with as few measurements as possible is crucial to many quantum computing applications. We introduce a framework that covers many of existing measurement strategies and introduce heuristics that can be used to enhance randomized schemes, including those based on Pauli grouping with inverse probability weighting and variants of the classical shadow algorithm. We show how to maximize information gain from such schemes, while carefully optimizing the distribution of possible measurements, and show that simple grouping algorithms can get close to, and in some cases exceed, state-of-the-art accuracy for unbiased estimation of expectation values on a standard quantum chemistry benchmark. We show how these randomized methods may be compared to more recent measurement schemes, such as shadow grouping, derandomized shadow, and overlapped grouping measurement, we show how the same strategies can be used to augment these schemes, and we demonstrate that we can reduce measurement costs by up to a factor of two by allowing Clifford measurement circuits for otherwise Clifford-less methods.
We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust regarding drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement. Then we prepare the ground state of the transverse-field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by our increasing the circuit depth. Published by the American Physical Society 2024
Quantum computers have great potential to uncover new and unexpected physical phenomena.They can simulate classically intractable many-particle quantum systems and probe them in a programmable, computational manner.They can also process experimental quantum data directly, enabling us to probe unseen aspects of physical systems that cannot be reached by any classical means.In both roles, refining quantum algorithms toward their fundamental limits expands and sharpens the reach of quantum computers.Among quantum algorithms, quantum estimation is of central importance because it elicits the physical properties of interest from quantum systems.Even in an ideal, noiseless setting, however, obtaining precise estimates of such properties is significantly resource-intensive, unless one leverages coherent quantum operations.While many quantum-enhanced (i.e., higher performance than any classical means enabled by quantum effects) estimation algorithms have been proposed under reasonable access assumptions, it is still an ongoing quest to design quantum algorithms achieving ultimate estimation efficiency allowed by quantum mechanics.In addition, rapid experimental progress makes us envision an early fault-tolerant regime with large-scale yet not fully error-corrected quantum computers.Toward this regime, it is also crucial to develop quantum estimation algorithms that elicit as much information of interest as possible from a quantum system subject to noise.In these contexts, this thesis advances quantum-enhanced algorithms for estimating physical properties in two respects: Heisenberg-limited multi-observable estimation and single-observable estimation for the early faulttolerant quantum computing (FTQC) regime.First, we provide an adaptive quantum algorithm for estimating expectation values of multiple observables simultaneously in an ideal (noiseless) setting.Given common access to block-encoded observables, a state-preparation unitary, and its inverse, this algorithm achieves a double quantum enhancement in query complexity to the state preparation and its inverse: the mean-squared-error (MSE) scaling at the Heisenberg limit and sublinear scaling in the number of observables.It also essentially matches the query lower bound in the small-additive-error regime (not in MSE), previously derived in quantum complexity theory.In addition, the proposed algorithm significantly reduces the number of ancilla qubits and the classical computation for circuit synthesis, compared to prior art for this task.The double enhancement and the circuit simplification come from a novel algorithm design that integrates key ideas from adaptive phase estimation, quantum amplification, and quantum gradient estimation.Next, we focus on expectation value estimation for a single observable in the early FTQC regime.In this regime, available coherent resources are mostly consumed for a state preparation unitary, and the dominant noise stems from that costly unitary and its inverse.Under a specific model reflecting these aspects, we derive the quantum-enhanced precision limit, that is, the minimal quantum Cramér-Rao bound over all possible estimation strategies in the model.Then, by designing an adaptive optimization based on Fisher information, we propose a quantum-enhanced estimation algorithm, with rigorous estimation guarantees, that asymptotically achieves the quantum Cramér-Rao bound, when the target system size is sufficiently large.Finally, we numerically demonstrate that the asymptotic behavior holds with only a few hundred measurements per step and a few tens of qubits.
Estimating properties of a quantum state is an indispensable task in various applications of quantum information processing. To predict properties in the postprocessing stage, it is inherent to first perceive the quantum state with a measurement protocol and store the information acquired. In this paper, we propose a general framework for constructing classical approximations of arbitrary quantum states with quantum reservoirs. A key advantage of our method is that only a single local measurement setting is required for estimating arbitrary properties, while most of the previous methods need an exponentially increasing number of measurement settings. To estimate M properties simultaneously, the size of the classical approximation scales as lnM . Moreover, this estimation scheme is extendable to higher-dimensional systems and hybrid systems with nonidentical local dimensions, which makes it exceptionally generic. We support our theoretical findings with extensive numerical simulations. Published by the American Physical Society 2024