{"type":"conference","page":"53:1-53:23","publication":"14th Innovations in Theoretical Computer Science (ITCS)","date_created":"2022-06-13T14:40:46Z","status":"public","author":[{"last_name":"Gharibian","full_name":"Gharibian, Sevag","first_name":"Sevag","id":"71541","orcid":"0000-0002-9992-3379"},{"first_name":"Dorian","last_name":"Rudolph","full_name":"Rudolph, Dorian"}],"_id":"31872","intvolume":"       251","year":"2023","doi":"10.4230/LIPIcs.ITCS.2023.53","abstract":[{"text":"Savitch's theorem states that NPSPACE computations can be simulated in\r\nPSPACE. We initiate the study of a quantum analogue of NPSPACE, denoted\r\nStreaming-QCMASPACE (SQCMASPACE), where an exponentially long classical proof\r\nis streamed to a poly-space quantum verifier. Besides two main results, we also\r\nshow that a quantum analogue of Savitch's theorem is unlikely to hold, as\r\nSQCMASPACE=NEXP. For completeness, we introduce Streaming-QMASPACE (SQMASPACE)\r\nwith an exponentially long streamed quantum proof, and show SQMASPACE=QMA_EXP\r\n(quantum analogue of NEXP). Our first main result shows, in contrast to the\r\nclassical setting, the solution space of a quantum constraint satisfaction\r\nproblem (i.e. a local Hamiltonian) is always connected when exponentially long\r\nproofs are permitted. For this, we show how to simulate any Lipschitz\r\ncontinuous path on the unit hypersphere via a sequence of local unitary gates,\r\nat the expense of blowing up the circuit size. This shows quantum\r\nerror-correcting codes can be unable to detect one codeword erroneously\r\nevolving to another if the evolution happens sufficiently slowly, and answers\r\nan open question of [Gharibian, Sikora, ICALP 2015] regarding the Ground State\r\nConnectivity problem. Our second main result is that any SQCMASPACE computation\r\ncan be embedded into \"unentanglement\", i.e. into a quantum constraint\r\nsatisfaction problem with unentangled provers. Formally, we show how to embed\r\nSQCMASPACE into the Sparse Separable Hamiltonian problem of [Chailloux,\r\nSattath, CCC 2012] (QMA(2)-complete for 1/poly promise gap), at the expense of\r\nscaling the promise gap with the streamed proof size. As a corollary, we obtain\r\nthe first systematic construction for obtaining QMA(2)-type upper bounds on\r\narbitrary multi-prover interactive proof systems, where the QMA(2) promise gap\r\nscales exponentially with the number of bits of communication in the\r\ninteractive proof.","lang":"eng"}],"volume":251,"title":"Quantum space, ground space traversal, and how to embed multi-prover  interactive proofs into unentanglement","external_id":{"arxiv":["2206.05243"]},"publication_status":"published","date_updated":"2023-02-28T11:06:55Z","language":[{"iso":"eng"}],"department":[{"_id":"623"},{"_id":"7"}],"citation":{"short":"S. Gharibian, D. Rudolph, in: 14th Innovations in Theoretical Computer Science (ITCS), 2023, p. 53:1-53:23.","ama":"Gharibian S, Rudolph D. Quantum space, ground space traversal, and how to embed multi-prover  interactive proofs into unentanglement. In: <i>14th Innovations in Theoretical Computer Science (ITCS)</i>. Vol 251. ; 2023:53:1-53:23. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2023.53\">10.4230/LIPIcs.ITCS.2023.53</a>","bibtex":"@inproceedings{Gharibian_Rudolph_2023, title={Quantum space, ground space traversal, and how to embed multi-prover  interactive proofs into unentanglement}, volume={251}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2023.53\">10.4230/LIPIcs.ITCS.2023.53</a>}, booktitle={14th Innovations in Theoretical Computer Science (ITCS)}, author={Gharibian, Sevag and Rudolph, Dorian}, year={2023}, pages={53:1-53:23} }","chicago":"Gharibian, Sevag, and Dorian Rudolph. “Quantum Space, Ground Space Traversal, and How to Embed Multi-Prover  Interactive Proofs into Unentanglement.” In <i>14th Innovations in Theoretical Computer Science (ITCS)</i>, 251:53:1-53:23, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2023.53\">https://doi.org/10.4230/LIPIcs.ITCS.2023.53</a>.","mla":"Gharibian, Sevag, and Dorian Rudolph. “Quantum Space, Ground Space Traversal, and How to Embed Multi-Prover  Interactive Proofs into Unentanglement.” <i>14th Innovations in Theoretical Computer Science (ITCS)</i>, vol. 251, 2023, p. 53:1-53:23, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2023.53\">10.4230/LIPIcs.ITCS.2023.53</a>.","ieee":"S. Gharibian and D. Rudolph, “Quantum space, ground space traversal, and how to embed multi-prover  interactive proofs into unentanglement,” in <i>14th Innovations in Theoretical Computer Science (ITCS)</i>, 2023, vol. 251, p. 53:1-53:23, doi: <a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2023.53\">10.4230/LIPIcs.ITCS.2023.53</a>.","apa":"Gharibian, S., &#38; Rudolph, D. (2023). Quantum space, ground space traversal, and how to embed multi-prover  interactive proofs into unentanglement. <i>14th Innovations in Theoretical Computer Science (ITCS)</i>, <i>251</i>, 53:1-53:23. <a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2023.53\">https://doi.org/10.4230/LIPIcs.ITCS.2023.53</a>"},"user_id":"71541"}