Matrix product state representations

Pérez-Garcı́a, David; Verstraete, Frank; Wolf, Michael M.; Cirac, J. Ignacio

doi:10.26421/qic7.5-6-1

Cited by 866 publications

(1,322 citation statements)

References 38 publications

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“…The cluster model realizes an SPT phase with fourfold ground state degeneracy, protected by the global 2 × 2 symmetry identified above. The cluster state can be written in the matrix-product form with the bond dimension D = 2 [122]. The Schmidt values of a bipartition λ 1 = λ 2 = 1/ 2 result in the entanglement entropy S = log 2, which is in agreement with our numerical findings deep in the SPT region IV.…”

Section: B Gauging the Transverse-field Ising Chainsupporting

confidence: 85%

Gauging the Kitaev chain

et al. 2021

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We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.

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Section: B Gauging the Transverse-field Ising Chainsupporting

confidence: 85%

Gauging the Kitaev chain

et al. 2021

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“…We study a quench protocol [58,59] where the system is initialized in a low-entangled state, which we take to be a matrix product state (MPS) [60,61]…”

mentioning

confidence: 99%

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

2021

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We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54." For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical nonequilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.

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“…These states can be mapped to quantum circuits by taking the MPS tensors in isometric form and identifying them with the circuit unitaries as described in the "Methods" section. A variety of techniques have been developed for the classical manipulation of these states for quantum simulation 3,17,18 . Here we confine ourselves to discussing the quantum circuit realisation.…”

Section: Parallel Simulation With Quantum Tensor Networkmentioning

confidence: 99%

“…Algorithms for manipulating iMPS (iDMRG, TDVP, etc.) 3,17,18 are classically efficient-they have the complexity of OðD 3 Þ. Where then is the room for improvement by implementation on a quantum circuit?…”

Section: Parallel Simulation With Quantum Tensor Networkmentioning

confidence: 99%

Parallel quantum simulation of large systems on small NISQ computers

Barratt

Dborin

Bal³

et al. 2021

npj Quantum Inf

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Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.

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Matrix product state representations

Cited by 866 publications

References 38 publications

Gauging the Kitaev chain

Gauging the Kitaev chain

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

Parallel quantum simulation of large systems on small NISQ computers

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