This yields a simplied proof that PSPACE has 3-message quantum interactive proof systems. We prove that any polynomial-round quantum interactive proof system with two-sided bounded error can be parallelized to a quantum interactive proof system with exponentially small one-sided error in which the prover and verier exchange only 3 messages. In this paper we consider quantum interactive proof systems, which are interactive proof systems in which the prover and verier may perform quantum computations and exchange quantum information. Finally, we show that quantum proofs for non-membership and classical proofs for various other group properties can be combined to yield succinct quantum proofs for other group properties not having succinct proofs in the classical setting, such as verifying that a number divides the order of a group and verifying that a group is not a simple group. By considering a certain subproblem of the Group Non-Membership problem we obtain a simple proof that there exists an oracle relative to which BQP is not contained in MA. Classically this is impossible-it is proved that there exists a group oracle relative to which this problem does not have succinct proofs that can be checked classically with bounded error in polynomial time (i.e., the problem is not in MA relative to the group oracle constructed). We prove that for an arbitrary group oracle there exist succinct (polynomial-length) quantum proofs for the Group Non-Membership problem that can be checked with small error in polynomial time on a quantum computer.
Specifically, we consider quantum proofs for properties of black-box groups, which are finite groups whose elements are encoded as strings of a given length and whose group operations are performed by a group oracle. Materials Sciences & Engineering Division USDOE Office of Science (SC), Basic Energy Sciences (BES) OSTI Identifier: 1611438 Alternate Identifier(s): OSTI ID: 1511884 Grant/Contract Number: SC0010526 SC0019275 Resource Type: Accepted Manuscript Journal Name: Physical Review B Additional Journal Information: Journal Volume: 99 Journal Issue: 20 Journal ID: ISSN 2469-9950 Publisher: American Physical Society (APS) Country of Publication: United States Language: English Subject: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY Materials Science Physics Majorana fermions Quantum memories Topological quantum computing Topological superconductors Topological = in ordinary unprotected quantum computation.In this paper we consider a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NP-type proof. of Technology (MIT), Cambridge, MA (United States) Northeastern Univ., Boston, MA (United States) Sponsoring Org.: USDOE Office of Science (SC), Basic Energy Sciences (BES). Publication Date: Fri May 10 00:00: Research Org.: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States) of Technology (MIT), Cambridge, MA (United States) Harvard Univ., Cambridge, MA (United States)
These results, together with the inherent error suppression provided by the superconducting gap in physical realizations of the MSCs, makes this a strong candidate for a robust topological quantum memory. In addition, we derive lattice gauge theories to account for measurement errors.
Alexei kitaev quantum error correction code#
When QP is highly suppressed and fermionic bilinear (“bosonic”) errors become dominant, we find an error threshold of ~16%, which is much higher than the threshold for spin-based topological memories like the surface code or the color code. In physical realizations where QP dominates, we show that errors can be corrected provided that the poisoning rate is below a threshold of ~11%. Furthermore, these quantum memories suffer from purely “fermionic” errors, such as quasiparticle poisoning (QP), that have no analog in conventional platforms with bosonic qubits.
We study the error correcting properties of Majorana surface codes (MSCs), topological quantum codes constructed out of interacting Majorana fermions, which can be used to store quantum information and perform quantum computation.