Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms

García-Pérez, Guillermo; Rossi, Matteo A. C.; Sokolov, Boris; Tacchino, Francesco; Barkoutsos, Panagiotis Kl.; Mazzola, Guglielmo; Tavernelli, Ivano; Maniscalco, Sabrina

doi:10.1103/prxquantum.2.040342

Cited by 70 publications

(56 citation statements)

References 61 publications

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“…We demonstrate that the proposed algorithm is able to correctly reproduce the target GF in such proof-of-principle experiments, although a rather large (compared to the usual VQE requirements) number of measurements is needed to obtain reliable estimates of the excitation energies, due to statistical and hardware noise. Although we expect this measurement overhead to become more prominent for larger systems when the standard form of our algorithm is considered, more effective strategies for observable reconstruction may be applied to meet such demand in an efficient way [41][42][43][44], together with classical post-processing techniques aimed at enhancing the overall numerical stability and, possibly, the parallelization of the qEOM procedure.…”

Section: Discussionmentioning

confidence: 99%

“…The latter, other than being subject to general improvements of current quantum hardware, would require applying a full set of quantum error mitigation techniques [45][46][47][48][49][50] and considering more efficient and application-specific ansätze [51]. As already mentioned above, controlling the number of required measurements with effective observable reconstruction strategies [41][42][43][44] could also significantly extend the range of applicability of the qEOM approach.…”

Section: Discussionmentioning

confidence: 99%

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One-particle Green's functions from the quantum equation of motion algorithm

Rizzo,

Libbi,

Tacchino

et al. 2022

Preprint

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

One-particle Green's functions from the quantum equation of motion algorithm

Rizzo,

Libbi,

Tacchino

et al. 2022

Preprint

Self Cite

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“…We use datasets from Ref. [63] where authors developed an adaptive measurement scheme that improves performance of VQE.…”

Section: Circuits Of a Form Of Generic Hamiltonian-independent Vqe An...mentioning

confidence: 99%

“…5 does not consist of parameters chosen randomly, but of unitaries that were (numerically) found optimal by VQE optimization (in Ref. [63]). Here results are qualitatively similar to previous figure in case of states and channels, but significantly different for quantum measurements.…”

Section: (Channels) Presented In Figs 4ementioning

confidence: 99%

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Exploring Quantum Average-Case Distances: proofs, properties, and examples

Maciejewski¹,

Puchała²,

Oszmaniec³

2021

Preprint

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In this work, we perform an in-depth study of recently introduced average-case quantum distances . The average-case distances approximate, up to relative error, the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in which quantum objects of interest (states, measurements, or channels) are intertwined with random quantum circuits. Contrary to conventional distances, such as trace distance or diamond norm, they quantify average-case statistical distinguishability via random quantum circuits.We prove that once a family of random circuits forms an δ-approximate 4-design, with δ = o(d −8 ), then the average-case distances can be approximated by simple explicit functions that can be expressed via simple degree two polynomials in objects of interest. For systems of moderate dimension, they can be easily explicitly computed -no optimization is needed as opposed to diamond norm distance between channels or operational distance between measurements. We prove that those functions, which we call quantum average-case distances, have a plethora of desirable properties, such as subadditivity w.r.t. tensor products, joint convexity, and (restricted) data-processing inequalities. Notably, all of the distances utilize the Hilbert-Schmidt (HS) norm in some way. This gives the HS norm an operational interpretation that it did not possess before. We also provide upper bounds on the maximal ratio between worst-case and average-case distances, and for each of them we provide an example that saturates the bound. Specifically, we show that for each dimension d this ratio is at most d 1 2 , d, d 3 2 for states, measurements, and channels, respectively. To support the practical usefulness of our findings, we study multiple examples in which average-case quantum distances can be calculated analytically. Furthermore, we perform an extensive numerical study of systems up to 10 qubits where circuits have a form of variational ansätze with randomly chosen parameters. Despite the fact that such circuits are not known to form unitary designs, our results suggest that average-case distances are more suitable than the conventional distances for studying the performance of NISQ devices in such settings.

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Few‐Copy Entanglement Detection in the Presence of Noise

Saggio

Walther

2022

Annalen der Physik

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Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum entanglement, which allows for quantum computations outperforming their classical counterparts. However, the task of entanglement detection is not always straightforward for several reasons. One of the main challenges is that standard methods rapidly become unfeasible when dealing with quantum states containing more than a few qubits. Typically, this is due to the fact that a vast number of measurements are needed on many copies of the state. Generally, it is not unusual to deal with a very limited number of state copies in experimental settings—in fact, this may be the case for many large quantum systems. In this article, an overview is provided of a probabilistic approach that enables high‐confidence genuine multipartite entanglement detection using an exceptionally low number of state copies. Additionally, a study is presented that shows that this protocol remains efficient also in the presence of noise, thus confirming the practicality of the method for near‐term quantum devices and its suitability for complex experimental settings.

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Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms

Cited by 70 publications

References 61 publications

One-particle Green's functions from the quantum equation of motion algorithm

One-particle Green's functions from the quantum equation of motion algorithm

Exploring Quantum Average-Case Distances: proofs, properties, and examples

Few‐Copy Entanglement Detection in the Presence of Noise

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