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History-state Hamiltonians are critical
[article]
2018
arXiv
pre-print
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Pr U ∼νs |f h,W (U )| ≥ δ 2 ≤ 8 6144s d n δ 2 s/2 . ...
) that Pr U ∼νs |Re(f h,W (U ))| ≥ δ √ 2 2 ≤ 1 (δ/2 √ 2) s 2 768s d n s/2 + 2ǫ(2d 2n ) s = 4 6144s d n δ 2 s/2 . ...
arXiv:1810.06528v1
fatcat:kxfdeg7myjgh7brkd6pc2iwmvm
Uncomputably Complex Renormalisation Group Flows
[article]
2021
arXiv
pre-print
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We give a mathematically rigorous construction of the block-renormalisation-group map for the original undecidable many-body system that appeared in the literature (Cubitt, P\'erez-Garcia, Wolf, Nature ...
That is, the head(s) of the arrow(s) in one tile and the tail(s) of the 4 cross tiles arrow(s) in the other tile must match exactly on the edges put into contact. × × × × × × × × × 6 up tiles × × × × × ...
λ 0 (H| S 1 ) 01 ≥ Evolve-to-Illegal Subspace, S 2 : All standard basis states |x ∈ S 2 ⊂ B ⊗L will evolve either forwards or backwards in time to an illegal state in O(L 2 ) steps under the transition ...
arXiv:2102.05145v1
fatcat:pemuiuogxzgv3oatda3oel4dku
Uncomputability of Phase Diagrams
[article]
2019
arXiv
pre-print
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This work builds off recent results from Cubitt et al. and Bausch et al., proving undecidability of the spectral gap problem. ...
Hence for Cubitt, Perez-Garcia, and Wolf, = 0 if the UTM halted on its input. ...
For the second claim, by the same process we thus get λ min (H s | A ) = E edge (s) + E pen,non-halt (s) ≥ 0. Then for the third claim, λ min (H s | A ) = E edge (s) + E pen,halt (s) < 0. ...
arXiv:1910.01631v1
fatcat:azmuyephnbhy3gy7sxttcurn4q
Entanglement in the stabilizer formalism
[article]
2004
arXiv
pre-print
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We further define the local subgroup S loc of S as S loc ≡ j S j . (12) In the bipartite case, S loc = S A · S B . ...
Assuming the list is completed with e AB ≡ n − |S A | − |S B | operators generating the subgroup S AB , then, S can be decomposed as S = S A · S B · S AB . Note that |P A (S)| = n − |S B |. ...
arXiv:quant-ph/0406168v1
fatcat:pjxw4yea2zaajdz6lpsnvqizr4
Universal Refocusing of Systematic Quantum Noise
[article]
2016
arXiv
pre-print
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holds for all s, and the lower bound holds for s ≤ π/4. ...
Thus Lemma 4 in [20] provides the result
4
10
s ≤ exp(s) − 1 ≤ s
• if ν ≤ π/4, then vol(exp(B ν )) ≥ 4
10 vol(B ν ) = 4
10 cν d 2 −1 ; and
A, B = Tr(A † B) [19] 2 [a, b] = a T Ωb, where ...
arXiv:1602.07963v1
fatcat:bhk6wy4m2jhefd57ndj6ivifhm
Computational Complexity of the Ground State Energy Density Problem
[article]
2021
arXiv
pre-print
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Lockhart, S. Gharibian, and J. Sullivan. J.D.W. is supported by the EPSRC Centre for Doctoral Training in Delivering Quantum Technologies (grant EP/L015242/1). ...
the total number of complete n-squares of T within S, and the number of complete n-squares of R within S. ...
( Lemma 44 Let D be a defect set in a region S, G = (D, E) its defect graph, and R a Robinson tiling of S. ...
arXiv:2107.05060v1
fatcat:5nvhdl6f2ndsvorirbss75t2vy
Are problems in Quantum Information Theory (un)decidable?
[article]
2011
arXiv
pre-print
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Given a Boolean combi- nation φ(X, A) of the F i 's and Ψ(A) := Q 1 (X 1 ∈ S 1 ) . . . ...
Q n (X n ∈ S n ) : φ(X, A) , (5) where Q j ∈ {∃, ∀} and the S i 's are semialgebraic sets (e.g. those specified in Lemma 1). Then there exists an effective algorithm which decides Ψ(A). ...
arXiv:1111.5425v1
fatcat:tivo3fmt3new3neekoe43fs76y
Comment on "On the uncomputability of the spectral gap"
[article]
2016
arXiv
pre-print
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Cubitt, D. Perez-Garcia, M.M. Wolf, Undecidability of the spectral gap, Nature 528, 207-211 (2015), arXiv:1502.04573] and his 1994 paper [S. ...
The aim of this short note is to clarify some of the claims made in the comparison made in [S. Lloyd, On the uncomputability of the spectral gap, arXiv:1602.05924] between our recent result [T.S. ...
Our result, proven in [Cubitt et al. 2015a,b] , is: Result 3 (Our result). Problem 2 is undecidable. (This also immediately implies that Problem 1 is undecidable.) ...
arXiv:1603.00825v1
fatcat:cib6crzgljcbdpq22lnqnrogfq
An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma
[article]
2013
arXiv
pre-print
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S. Cubitt. Preparing topological
projected entangled pair states on a quantum computer. Physical Review A, 88(032321), 2013.
[VWC09] F. Verstraete, M. M. Wolf, and J. I. Cirac. ...
s].nbr ← S[s].nbr + 1 mod k 42: if S[s].nbr = 0 then 43:F [l] ← F [l] + 1 if F [l] then 47: s ← s − 1 S[s + 1].proj ← S[s + 1].proj − Γ + (S[s].proj, S[s].nbr) term[l + 1] ← term[l + 1] + 1 log(N ) log ...
arXiv:1311.6474v1
fatcat:dafl3h2mrvffrn27few3pz3gae
A constructive commutative quantum Lovasz Local Lemma, and beyond
[article]
2013
arXiv
pre-print
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. , Π at ) = G] = s:G(s)=G Pr(s) ≤ s∈S p G (s) · t i=1 Tr[Π a i ρ] = v∈G Tr[Π v ρ] · s∈S p G (s) = v∈G Tr[Π v ρ]. (52)
Partial Resample DAGs Later on, we will need to consider a variant of the resample ...
Cubitt et al. [2009] ). Either way, this means that the problem instance itself sets a lower-bound on the spectral gap. ...
arXiv:1112.1413v2
fatcat:i5a5hb7eivho7cublvucquvvam
Undecidability of the Spectral Gap in One Dimension
2020
Physical Review X
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(Phase-estimation QTM, Cubitt et al. ...
This phase estimation QTM is the only ingredient we require from Cubitt et al. ...
doi:10.1103/physrevx.10.031038
fatcat:7jfxyubuhfasbb5p7fduzat5py
The Complexity of Relating Quantum Channels to Master Equations
[article]
2011
arXiv
pre-print
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Mathematically, such a Markovian master equation generates a one-parameter (time t) semi-group (evolving for time t and then time s is equivalent to evolving for time t + s) of CPT maps (the evolution ...
If we choose the first n C diagonal elements of S to be 1/2, and choose the next n v diagonal elements of S to be 5/6, then it is straightforward to verify that the equations in the ccp condition of Eq ...
arXiv:0908.2128v2
fatcat:7g7boizeirag3j6fcd2k5obilq
Complexity Classification of Local Hamiltonian Problems
2014
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
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One way of making the problem more physically meaningful is to restrict the Hamiltonian in question by picking its terms from a fixed set S. ...
whose terms are picked from a fixed set S correspond to problems either in P; polynomial-time equivalent to the Ising model with transverse magnetic fields; or QMAcomplete. ...
and 1's. ...
doi:10.1109/focs.2014.21
dblp:conf/focs/CubittM14
fatcat:j6iwgcvi3zchpai3kukmcohpny
An Extreme form of Superactivation for Quantum Zero-Error Capacities
[article]
2011
arXiv
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S. Cubitt was supported by a Leverhulme early-career fellowship, and through the integrated EC project "QAP" (contract no. IST-2005-15848). G. ...
S. Cubitt is with the Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, Ciudad Universitaria, 28040 Madrid, Spain (email: tcubitt@mat.ucm.es). G. ...
arXiv:0912.2737v2
fatcat:mxmnpowuhbbi7enrgmxkzfubsu
Entanglement can Completely Defeat Quantum Noise
2011
Physical Review Letters
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S. is supported by the DARPA QuEST contract HR0011-09-C-0047. Tr½E 1 E 2 ðc ÞE 1 E 2 ð'Þ ¼ 0 [Eq. ...
i, where X is the unitary consisting of 1's down the anti-main diagonal (i.e., one possible generalization of the Pauli matrix x ). ...
doi:10.1103/physrevlett.107.250504
pmid:22243059
fatcat:5zvit5wdqjbpxbmrzsxvu4duw4
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