[ { "id": "authors:4d0yn-88k35", "collection": "authors", "collection_id": "4d0yn-88k35", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221220-222320267", "type": "monograph", "title": "Efficient Certifiable Randomness from a Single Quantum Device", "author": [ { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" }, { "family_name": "Vazirani", "given_name": "Umesh", "clpid": "Vazirani-Umesh-V" }, { "family_name": "Vidick", "given_name": "Thomas", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "abstract": "Brakerski et. al [BCM+18] introduced the model of cryptographic testing of a single untrusted quantum device and gave a protocol for certifiable randomness generation. We use the leakage resilience properties of the Learning With Errors problem to address a key issue left open in previous work - the rate of generation of randomness. Our new protocol can certify \u03a9(n) fresh bits of randomness in constant rounds, where n is a parameter of the protocol and the total communication is O(n), thus achieving a nearly optimal rate. The proof that the output is statistically random is conceptually simple and technically elementary.", "doi": "10.48550/arXiv.2204.11353", "publisher": "arXiv", "publication_date": "2022-04-24" }, { "id": "authors:r0cch-tzd63", "collection": "authors", "collection_id": "r0cch-tzd63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210921-144712064", "type": "article", "title": "A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device", "author": [ { "family_name": "Brakerski", "given_name": "Zvika", "clpid": "Brakerski-Zvika" }, { "family_name": "Christiano", "given_name": "Paul", "clpid": "Christiano-Paul" }, { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" }, { "family_name": "Vazirani", "given_name": "Umesh", "clpid": "Vazirani-Umesh-V" }, { "family_name": "Vidick", "given_name": "Thomas", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "abstract": "We consider a new model for the testing of untrusted quantum devices, consisting of a single polynomial time bounded quantum device interacting with a classical polynomial time verifier. In this model, we propose solutions to two tasks\u2014a protocol for efficient classical verification that the untrusted device is \"truly quantum\" and a protocol for producing certifiable randomness from a single untrusted quantum device. Our solution relies on the existence of a new cryptographic primitive for constraining the power of an untrusted quantum device: post-quantum secure trapdoor claw-free functions that must satisfy an adaptive hardcore bit property. We show how to construct this primitive based on the hardness of the learning with errors (LWE) problem.", "doi": "10.1145/3441309", "issn": "0004-5411", "publisher": "Association for Computing Machinery", "publication": "Journal of the ACM", "publication_date": "2021-08", "series_number": "5", "volume": "68", "issue": "5", "pages": "Art. No. 31" }, { "id": "authors:53pwq-zng55", "collection": "authors", "collection_id": "53pwq-zng55", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200805-133628530", "type": "book_section", "title": "Classical Homomorphic Encryption for Quantum Circuits", "book_title": "2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)", "author": [ { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" } ], "abstract": "We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties. Finally, we show that a classical homomorphic encryption scheme with the required properties can be constructed from the learning with errors problem.", "doi": "10.1109/focs.2018.00039", "isbn": "9781538642306", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-10", "pages": "332-338" }, { "id": "authors:bcz19-xa962", "collection": "authors", "collection_id": "bcz19-xa962", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200805-144416533", "type": "book_section", "title": "Classical Verification of Quantum Computations", "book_title": "2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)", "author": [ { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" } ], "abstract": "We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum prover as a trusted measurement device. The protocol forces the prover to behave as follows: the prover must construct an n qubit state of his choice, measure each qubit in the Hadamard or standard basis as directed by the verifier, and report the measurement results to the verifier. The soundness of this protocol is enforced based on the assumption that the learning with errors problem is computationally intractable for efficient quantum machines.", "doi": "10.1109/focs.2018.00033", "isbn": "9781538642306", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-10", "pages": "259-267" }, { "id": "authors:54rbf-hkb86", "collection": "authors", "collection_id": "54rbf-hkb86", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190201-143229032", "type": "book_section", "title": "A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device", "book_title": "2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)", "author": [ { "family_name": "Brakerski", "given_name": "Zvika", "clpid": "Brakerski-Zvika" }, { "family_name": "Christiano", "given_name": "Paul", "clpid": "Christiano-Paul" }, { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" }, { "family_name": "Vazirani", "given_name": "Umesh", "clpid": "Vazirani-Umesh-V" }, { "family_name": "Vidick", "given_name": "Thomas", "orcid": "0000-0002-6405-365X", "clpid": "Vidick-T" } ], "abstract": "We give a protocol for producing certifiable randomness from a single untrusted quantum device that is polynomial-time bounded. The randomness is certified to be statistically close to uniform from the point of view of any computationally unbounded quantum adversary, that may share entanglement with the quantum device. The protocol relies on the existence of post-quantum secure trapdoor claw-free functions, and introduces a new primitive for constraining the power of an untrusted quantum device. We then show how to construct this primitive based on the hardness of the learning with errors (LWE) problem. The randomness protocol can also be used as the basis for an efficiently verifiable \"quantum supremacy\" proposal, thus answering an outstanding challenge in the field.", "doi": "10.1109/focs.2018.00038", "isbn": "9781538642306", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-10", "pages": "320-331" }, { "id": "authors:bd8f9-z9x61", "collection": "authors", "collection_id": "bd8f9-z9x61", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200805-141909801", "type": "monograph", "title": "Interactive Proofs for Quantum Computations", "author": [ { "family_name": "Aharonov", "given_name": "Dorit", "clpid": "Aharonov-D" }, { "family_name": "Ben-Or", "given_name": "Michael", "clpid": "Ben-Or-M" }, { "family_name": "Eban", "given_name": "Elad", "clpid": "Eban-E" }, { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" } ], "abstract": "The widely held belief that BQP strictly contains BPP raises fundamental questions: if we cannot efficiently compute predictions for the behavior of quantum systems, how can we test their behavior? In other words, is quantum mechanics falsifiable? In cryptographic settings, how can a customer of a future untrusted quantum computing company be convinced of the correctness of its quantum computations? To provide answers to these questions, we define Quantum Prover Interactive Proofs (QPIP). Whereas in standard interactive proofs the prover is computationally unbounded, here our prover is in BQP, representing a quantum computer. The verifier models our current computational capabilities: it is a BPP machine, with access to only a few qubits. Our main theorem states, roughly: 'Any language in BQP has a QPIP, which also hides the computation from the prover'. We provide two proofs, one based on a quantum authentication scheme (QAS) relying on random Clifford rotations and the other based on a QAS which uses polynomial codes (BOCG+ 06), combined with secure multiparty computation methods.\nThis is the journal version of work reported in 2008 (ABOE08) and presented in ICS 2010; here we have completed the details and made the proofs rigorous. Some of the proofs required major modifications and corrections. Notably, the claim that the polynomial QPIP is fault tolerant was removed. Similar results (with different protocols) were reported independently around the same time of the original version in BFK08. The initial independent works (ABOE08, BFK08) ignited a long line of research of blind verifiable quantum computation, which we survey here, along with connections to various cryptographic problems. Importantly, the problems of making the results fault tolerant as well as removing the need for quantum communication altogether remain open.", "doi": "10.48550/arXiv.1704.04487", "publisher": "arXiv", "publication_date": "2017-04-14" }, { "id": "authors:5xmdk-jwa42", "collection": "authors", "collection_id": "5xmdk-jwa42", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200805-142950586", "type": "article", "title": "Rational approximations and quantum algorithms with postselection", "author": [ { "family_name": "Mahadev", "given_name": "Urmila", "clpid": "Mahadev-Urmila" }, { "family_name": "de Wolf", "given_name": "Ronald", "clpid": "de-Wolf-R" } ], "abstract": "We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using post-selection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We give optimal (up to constant factors)\nquantum algorithms with postselection for the Majority function, slightly improving upon an earlier algorithm of Aaronson. Finally we show how Newman's classic theorem about low-degree rational approximation of the absolute-value function follows from these algorithms.", "doi": "10.48550/arXiv.1401.0912", "issn": "1533-7146", "publisher": "Rinton Press", "publication": "Quantum Information and Computation", "publication_date": "2015-03", "series_number": "3-4", "volume": "15", "issue": "3-4", "pages": "295-307" } ]