[
    {
        "id": "authors:9fwfb-sxf89",
        "collection": "authors",
        "collection_id": "9fwfb-sxf89",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220406-136312115",
        "type": "book_section",
        "title": "Exponential Separations Between Learning With and Without Quantum Memory",
        "book_title": "2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)",
        "author": [
            {
                "family_name": "Chen",
                "given_name": "Sitan",
                "clpid": "Chen-Sitan"
            },
            {
                "family_name": "Cotler",
                "given_name": "Jordan",
                "orcid": "0000-0003-3161-9677",
                "clpid": "Cotler-Jordan-S"
            },
            {
                "family_name": "Huang",
                "given_name": "Hsin-Yuan",
                "orcid": "0000-0001-5317-2613",
                "clpid": "Huang-Hsin-Yuan"
            },
            {
                "family_name": "Li",
                "given_name": "Jerry",
                "clpid": "Li-Jerry"
            }
        ],
        "abstract": "We study the power of quantum memory for learning properties of quantum systems and dynamics, which is of great importance in physics and chemistry. Many state-of-the-art learning algorithms require access to an additional external quantum memory. While such a quantum memory is not required a priori, in many cases, algorithms that do not utilize quantum memory require much more data than those which do. We show that this trade-off is inherent in a wide range of learning problems. Our results include the following: We show that to perform shadow tomography on an n-qubit state \u03c1 with M observables, any algorithm without quantum memory requires \u03a9\u0305(min(M,2\u207f)) samples of \u03c1 in the worst case. Up to log factors, this matches the upper bound of [1], and completely resolves an open question in [2], [3]. We establish exponential separations between algorithms with and without quantum memory for purity testing, distinguishing scrambling and depolarizing evolutions, and uncovering symmetry in physical dynamics. Our separations improve and generalize prior work of [4] by allowing for a broader class of algorithms without quantum memory. We give the first tradeoff between quantum memory and sample complexity. More precisely, we prove that to estimate absolute values of all n -qubit Pauli observables, algorithms with k",
        "doi": "10.1109/focs52979.2021.00063",
        "isbn": "9781665420556",
        "publisher": "IEEE",
        "place_of_publication": "Piscataway, NJ",
        "publication_date": "2022-02",
        "pages": "574-585"
    }
]