1Τμήμα Πληροφορικής, Πανεπιστήμιο του Sussex, Ηνωμένο Βασίλειο
2Quantinuum (Cambridge Quantum), Terrington House, 13-15 Hills Rd, Cambridge, CB2 1NL, UK
3Τμήμα Επιστήμης και Τεχνολογίας Υπολογιστών, Πανεπιστήμιο του Κέιμπριτζ, Ηνωμένο Βασίλειο
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Περίληψη
Αυτή η εργασία βασίζεται στην ιδέα της προσομοίωσης κυκλωμάτων σταθεροποιητή μέσω μετασχηματισμών {τετραγωνικών επεκτάσεων μορφής}. Αυτή είναι μια αναπαράσταση μιας κβαντικής κατάστασης που καθορίζει έναν τύπο για την επέκταση στην τυπική βάση, που περιγράφει πραγματικές και φανταστικές σχετικές φάσεις χρησιμοποιώντας ένα πολυώνυμο βαθμού 2 πάνω στους ακέραιους αριθμούς. Δείχνουμε πώς, με επιδέξια διαχείριση της αναπαράστασης επέκτασης τετραγωνικής φόρμας, μπορούμε να προσομοιώσουμε μεμονωμένες λειτουργίες σταθεροποιητή σε χρόνο $mathcal{O}(n^2)$ που ταιριάζουν με τη συνολική πολυπλοκότητα άλλων τεχνικών προσομοίωσης [1,2,3]. Our techniques provide economies of scale in the time to simulate simultaneous measurements of all (or nearly all) qubits in the standard basis. Our techniques also allow single-qubit measurements with deterministic outcomes to be simulated in constant time. We also describe throughout how these bounds may be tightened when the expansion of the state in the standard basis has relatively few terms (has low `rank'), or can be specified by sparse matrices. Specifically, this allows us to simulate a `local' stabiliser syndrome measurement in time $mathcal{O}(n)$, for a stabiliser code subject to Pauli noise --- matching what is possible using techniques developed by Gidney [4] χωρίς την ανάγκη αποθήκευσης των λειτουργιών που έχουν μέχρι τώρα προσομοιωθεί.
► Δεδομένα BibTeX
► Αναφορές
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Αναφέρεται από
[1] Matthew Amy, Owen Bennett-Gibbs, and Neil J. Ross, "Symbolic synthesis of Clifford circuits and beyond", arXiv: 2204.14205.
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