Entanglement from Tensor Networks on a Trapped-Ion Quantum Computer

Foss‐Feig, Michael; Ragole, Stephen; Potter, Andrew C.; Dreiling, Joan; Figgatt, Caroline; Gaebler, John; Hall, Alex; Moses, Steven; Pino, Juan; Spaun, Ben; Neyenhuis, Brian; Hayes, David

doi:10.1103/physrevlett.128.150504

Cited by 20 publications

(15 citation statements)

References 38 publications

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“…6. Notably, the bipartite entanglement content between the physical and bond subsystems is physically equivalent to that of a semi-infinite chain with an entanglement cut adjacent to the last prepared physical site [44,45]. This feature will be exploited later in this work to experimentally characterize and validate preparation of the AKLT state via measurements of its entanglement spectrum.…”

Section: A Sequential Preparation Of a Generic Mpsmentioning

confidence: 99%

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Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements

Smith¹,

Crane²,

Wiebe³

et al. 2022

Preprint

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The ground state of the spin-1 Affleck, Kennedy, Lieb and Tasaki (AKLT) model is a paradigmatic example of both a matrix product state and a symmetry-protected topological phase, and additionally holds promise as a resource state for measurement-based quantum computation. Having a nonzero correlation length, the AKLT state cannot be exactly prepared by a constant-depth unitary circuit composed of local gates. In this work, we demonstrate that this no-go limit can be evaded by augmenting a constant-depth circuit with fusion measurements, such that the total preparation time is independent of system size and entirely deterministic. We elucidate our preparation scheme using the language of tensor networks, and furthermore show that the Z2 × Z2 symmetry of the AKLT state directly affords this speed-up over previously known preparation methods. To demonstrate the practical advantage of measurement-assisted preparation on noisy intermediate-scale quantum (NISQ) devices, we carry out our protocol on an IBM Quantum processor. We measure both the string order and entanglement spectrum of prepared AKLT chains and, employing these as metrics, find improved results over the known (purely unitary) sequential preparation approach. We conclude with a demonstration of quantum teleportation using the AKLT state prepared by our measurement-assisted scheme. This work thus serves to provide an efficient strategy to prepare a specific resource in the form of the AKLT state and, more broadly, experimentally demonstrates the possibility for realizable improvement in state preparation afforded by measurement-based circuit depth reduction strategies on NISQ-era devices.

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Section: A Sequential Preparation Of a Generic Mpsmentioning

confidence: 99%

“…Inspired by arguments presented in Ref. [45], we achieve this through state tomography of the residual boundary memory qubits following preparation of the spin-1 chain.…”

Section: Measurement Of the Entanglement Spectrummentioning

confidence: 99%

Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements

Smith¹,

Crane²,

Wiebe³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, we would like to find an ordering that will yield a qubit-efficient mapping from PEPs networks to quantum circuits. Ideally, we want to make use of mid-circuit measurement and reset so that our circuit contains fewer qubits than are present in the corresponding PEPs state, along the lines of the "holographic" simulation of MPS tensor networks employed in recent works [6][7][8] . To this end, we order the PEPs tensor network in a zig-zag pattern, as depicted in Fig.…”

Section: Mapping Tensor Network To Quantum Channelsmentioning

confidence: 99%

“…Such capability has recently become available on some quantum processors 5 , allowing one to simulate quantum systems consisting of more qubits than are present on the physical device. Several recent works have taken this approach, simulating both static and dynamical one-dimensional (1D) matrix product states (MPS) of quasi-infinite length using a constant number of qubits [6][7][8] . Since most physical quantum states of interest are not maximally entangled, it should not be necessary to use N qubits to simulate most relevant N-qubit states.…”

Section: Introductionmentioning

confidence: 99%

“…Here we take an approach similar to the one used for MPS [6][7][8] , but with two-dimensional (2D) tensor networks. Specifically, we map a subset of projected entangled pair states (PEPs) tensor networks -which represent 2D quantum states on a square lattice -to a quantum circuit, and run the resulting circuit on a trapped-ion quantum device.…”

Section: Introductionmentioning

confidence: 99%

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Simulating Large PEPs Tensor Networks on Small Quantum Devices

MacCormack

Galda²,

Lyon

2022

Preprint

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We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an N x M square-lattice PEPs network, for arbitrary M, of bond dimension 2 can be performed using N + 2 qubits. We employ this approach to calculate the values of a long-range loop observable in the topological Wen plaquette model by mapping a 3 x 3 PEPs tensor network to a 5-qubit quantum circuit and executing it on the Honeywell System Model H1-1 trapped-ion device. We find that, for this system size, the noisy observable values are sufficient for observing the phase transition from topological to trivial order, as the Wen model is perturbed by a magnetic field term in the Hamiltonian. Our results serve as a proof-of-concept of the utility of the measure-and-reuse approach for simulating large two-dimensional quantum systems on small quantum devices.

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Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms

Dwivedi,

Lopez-Ruiz,

Iyengar

2024

J. Phys. Chem. A

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The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2′-bipyridine, and compared to exact diagonalization numerical results.

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Entanglement from Tensor Networks on a Trapped-Ion Quantum Computer

Cited by 20 publications

References 38 publications

Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements

Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements

Simulating Large PEPs Tensor Networks on Small Quantum Devices

Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms

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