Duality as a feasible physical transformation for quantum simulation

Ashkenazi, Shachar; Zohar, Erez

doi:10.1103/physreva.105.022431

Cited by 16 publications

(6 citation statements)

References 37 publications

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“…It will be interesting to see how the gauging approach can be seen from the quantum operations perspective (see, for e.g., Ref. [5]) and how it is related to our approach here which does not involve gauge fields. This may also pave the way to thinking about 't Hooft anomalies from the point of view of quantum information theory.…”

Section: Discussionmentioning

confidence: 99%

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Assessment of stress factors among post-graduate students / a case of Aligarh Muslim University, Aligarh (India)

Khan

Parveen

2020

IJKL

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We study the Kramers-Wannier duality for the transverse-field Ising lattice on a ring. A careful consideration of the ring boundary conditions shows that the duality has to be implemented with a proper treatment of different charge sectors of both the twisted and untwisted Ising and the dual-Ising Hilbert spaces. We construct a superoperator that explicitly maps the Ising operators to the dual-Ising operators. The superoperator naturally acts on the tensor product of the Ising and the dual-Ising Hilbert space. We then show that the relation between our superoperator and the Kramers-Wannier duality operator that maps the Ising Hilbert space to the dual-Ising Hilbert space is naturally provided by quantum operations and the duality can be understood as a quantum operation that we construct. We provide the operator-sum representation for the Kramers-Wannier quantum operations and reproduce the well-known fusion rules. In addition to providing the quantum information perspective on the Kramers-Wannier duality, our explicit protocol will also be useful in implementing the Kramers-Wannier duality on a quantum computer.

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Section: Discussionmentioning

confidence: 99%

“…We will show how the * maazkhan5507@gmail.com † anausha80@gmail.com ‡ arif7de@gmail.com duality action on states can be understood as quantum operations and how the well known fusion rules can be derived through this perspective. Some articles in which similar ideas are discussed, implicitly or explicitly, are [4][5][6][7][8][9][10].…”

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confidence: 99%

Assessment of stress factors among post-graduate students / a case of Aligarh Muslim University, Aligarh (India)

Khan

Parveen

2020

IJKL

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“…[7,8] (see also Ref. [20]), our novel perspec-tive in terms of disentangling wave functions provides an intuitive comprehension of the connection between SPT order and topological order via measurements. In addition, our idea immediately shows how to prepare certain symmetry-enriched topological (SET) order by measuring SRE states.…”

Section: Adaptive Circuits Via Disentangling Fluctuating Domain Wallsmentioning

confidence: 99%

“…This perspective provides the following three advances: (i) It provides a simple physical picture demonstrating that measuring an SPT with Z 2 × Z 2 symmetry leads to a Z 2 long-range order, thus complementing the perspectives in Ref. [7,8,20]. (ii) Considering domain walls that result from certain classical models without spatial locality, one can construct a finite-depth adaptive circuit that prepares any CSS code [21,22].…”

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confidence: 94%

Measurement as a shortcut to long-range entangled quantum matter

Lu¹,

Lessa²,

Kim³

et al. 2022

Preprint

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The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback ("adaptive circuits") can evade such restrictions. We introduce four classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The four classes are inspired by distinct physical insights, including tensornetwork constructions, short-range entangled states with non-trivial braiding structures, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral and symmetry-enriched topological orders, can be prepared in constant depth or time, and one-dimensional CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size. Our work illustrates the practical and conceptual versatility of measurement for state preparation.

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“…Recently there has been renewed interest in the physical realization of duality transformations and their applications in quantum technologies. In the context of quantum simulation, the fact that dualities typically change the phase of the states on which they act can be exploited to efficiently prepare states in a given phase [78][79][80][81]. The same duality transformations can also be used to generate quantum circuits that permute the anyons of a topologically ordered state [82], which has applications in the construction of topological quantum memories [83].…”

Section: Sec I | Introductionmentioning

confidence: 99%

Dualities in one-dimensional quantum lattice models: topological sectors

Lootens¹,

Delcamp²,

Verstraete³

2022

Preprint

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It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Building on ref. [arXiv:2112.09091], whereby dualities are defined between (categorically) symmetric models that only differ in a choice of module category, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. Using matrix product operators, we construct from the data of module functors explicit symmetry operators preserving boundary conditions as well as intertwiners mapping topological sectors of dual models onto one another. We illustrate our construction with a family of examples that are in the duality class of the spin-1 2 Heisenberg XXZ model. One model has symmetry operators forming the fusion category Rep(S3) of representations of the group S3. We find that the mapping between its topological sectors and those of the XXZ model is associated with the non-trivial braided auto-equivalence of the Drinfel'd center of Rep(S3).

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Duality as a feasible physical transformation for quantum simulation

Cited by 16 publications

References 37 publications

Assessment of stress factors among post-graduate students / a case of Aligarh Muslim University, Aligarh (India)

Assessment of stress factors among post-graduate students / a case of Aligarh Muslim University, Aligarh (India)

Measurement as a shortcut to long-range entangled quantum matter

Dualities in one-dimensional quantum lattice models: topological sectors

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