Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2112.03061

Efficiently preparing Schrödinger's cat, fractons and non-Abelian topological order in quantum devices

Ruben Verresen, Nathanan Tantivasadakarn, Ashvin Vishwanath

Published Dec 2, 2021• 10 citations
arXivHTMLPDF

Abstract

Long-range entangled quantum states -- like cat states and topological order -- are key for quantum metrology and information purposes, but they cannot be prepared by any scalable unitary process. Intriguingly, using measurements as an additional ingredient could circumvent such no-go theorems. However, efficient schemes are known for only a limited class of long-range entangled states, and their implementation on existing quantum devices via a sequence of gates and measurements is hampered by high overheads. Here we resolve these problems, proposing how to scalably prepare a broad range of long-range entangled states with the use of existing experimental platforms. Our two-step process finds an ideal implementation in Rydberg atom arrays, only requiring time-evolution under the intrinsic atomic interactions, followed by measuring a single sublattice (by using, e.g., two atom species). Remarkably, this protocol can prepare the 1D Greenberger-Horne-Zeilinger (GHZ) 'cat' state and 2D toric code with fidelity per site exceeding $0.9999$, and a 3D fracton state with fidelity $\gtrapprox 0.998$. In light of recent experiments showcasing 3D Rydberg atom arrays, this paves the way to the first experimental realization of fracton order. While the above examples are based on efficiently preparing and measuring cluster states, we also propose a multi-step procedure to create $S_3$ and $D_4$ non-Abelian topological order in Rydberg atom arrays and other quantum devices -- offering a route towards universal topological quantum computation.

DOI
10.48550/arxiv.2112.03061

Related papers

Shortest Route to Non-Abelian Topological Order on a Quantum Processor

Nathanan Tantivasadakarn, Ruben Verresen, Ashvin Vishwanath

A highly coveted goal is to realize emergent non-Abelian gauge theories and their anyonic excitations, which encode decoherence-free quantum information. While measurements in quantum devices provide new hope for scalably preparing such long-range entangled states, existing protocols using the experimentally established ingredients of a finite-depth circuit and a single round of measurement produce only Abelian states. Surprisingly, we show there exists a broad family of non-Abelian states-namely those with a Lagrangian subgroup-which can be created using these same minimal ingredients, bypassing the need for new resources such as feed forward. To illustrate that this provides realistic protocols, we show how D_{4} non-Abelian topological order can be realized, e.g., on Google's quantum processors using a depth-11 circuit and a single layer of measurements. Our work opens the way toward the realization and manipulation of non-Abelian topological orders, and highlights counterintuitive features of the complexity of non-Abelian phases.

arXiv:2209.03964•Physical Review Letters•Aug 11, 2023•76 citations

Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases

Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath +1 more

A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the nonlocal nature of Schrödinger cat states, topological order, and quantum criticality. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. However, a systematic understanding of when and how measurements of SRE give rise to LRE is still lacking. Here, we establish that LRE appears upon performing measurements on symmetry-protected topological (SPT) phases—of which the cluster state is one example. For instance, we show how to implement the Kramers-Wannier transformation by adding a cluster SPT to an input state followed by measurement. This transformation naturally relates states with SRE and LRE. An application is the realization of double-semion order when the input state is the Z 2 Levin-Gu SPT. Similarly, the addition of fermionic SPTs and measurement leads to an implementation of the Jordan-Wigner transformation of a general state. More generally, we argue that a large class of SPT phases protected by G × H symmetry gives rise to anomalous LRE upon measuring G -charges, and we prove that this persists for generic points in the SPT phase under certain conditions. Our work introduces a new practical tool for using SPT phases as resources for creating LRE, and we uncover the classification result that all states related by sequentially gauging Abelian groups or by Jordan-Wigner transformation are in the same equivalence class, once we augment finite-depth circuits with single-site measurements. In particular, any topological or fracton order with a solvable finite gauge group can be obtained from a product state in this way. Published by the American Physical Society 2024

arXiv:2112.01519•Physical Review X•Jun 7, 2024•126 citations

Realizing fracton order from long-range quantum entanglement in programmable Rydberg atom arrays

Andriy H. Nevidomskyy, Hannes Bernien, Alexander Canright

Storing quantum information, unlike information in a classical computer, requires battling quantum decoherence, which results in a loss of information over time. To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another, thus preventing quantum decoherence. One promising concept is that of fracton order -- a phase of matter with a large ground state degeneracy that grows subextensively with the system size. Unfortunately, the models realizing fractons are not friendly to experimental implementations as they require unnatural interactions between a substantial number (of the order of ten) of qubits. We demonstrate how this limitation can be circumvented by leveraging the long-range quantum entanglement created using only pairwise interactions between the code and ancilla qubits, realizable in programmable tweezer arrays of Rydberg atoms. We show that this platform also allows to detect and correct certain types of errors en route to the goal of true error-resistant quantum memory.

arXiv:2407.05885•Jul 8, 2024•0 citations

Measurement-Free Toric-Code Memory in Array Globally Controlled Rydberg Array

Han Wang, Yusheng Zhao, Xiuhao Deng +1 more

The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires: mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a $4 \times 4$ rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold $p^\star \approx 0.034$. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.

quant-pharXiv:2606.12030•Jun 11, 2026•0 citations

Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward

Nathanan Tantivasadakarn, Ashvin Vishwanath, Ruben Verresen

Long-range entanglement-the backbone of topologically ordered states-cannot be created in finite time using local unitary circuits, or, equivalently, adiabatic state preparation.Recently, it has come to light that single-site measurements provide a loophole, allowing for finite-time state preparation in certain cases.Here we show how this observation imposes a complexity hierarchy on long-range entangled states based on the minimal number of measurement layers required to create the state, which we call "shots."First, similar to Abelian stabilizer states, we construct single-shot protocols for creating any non-Abelian quantum double of a group with nilpotency class 2 (such as D 4 or Q 8 ).We show that after the measurement, the wave function always collapses into the desired non-Abelian topological order, conditional on recording the measurement outcome.Moreover, the clean quantum double ground state can be deterministically prepared via feedforward-gates that depend on the measurement outcomes.Second, we provide the first constructive proof that a finite number of shots can implement the Kramers-Wannier duality transformation (i.e., the gauging map) for any solvable symmetry group.As a special case, this gives an explicit protocol to prepare twisted quantum doubles for all solvable groups.Third, we argue that certain topological orders, such as nonsolvable quantum doubles or Fibonacci anyons, define nontrivial phases of matter under the equivalence class of finite-depth unitaries and measurement, which cannot be prepared by any finite number of shots.Moreover, we explore the consequences of allowing gates to have exponentially small tails, which enables, for example, the preparation of any Abelian anyon theory, including chiral ones.This hierarchy paints a new picture of the landscape of long-range entangled states, with practical implications for quantum simulators.

arXiv:2209.06202•PRX Quantum•Jun 9, 2023•123 citations

Preparing topological states with finite depth simultaneous commuting gates

Yarden Sheffer, Erez Berg, Ady Stern

We present protocols for preparing two-dimensional Abelian and non-Abelian topologically ordered states by employing finite depth unitary circuits composed of long-ranged, simultaneous, and mutually commuting two-qubit gates. Our protocols are motivated by recent proposals for circuits in trapped ion systems, which allow each qubit to participate in multiple gates simultaneously. Our circuits are shown to be optimal, in the sense that the number of two-qubit gates and ancilla qubits scales as $O({L}^{2})$, where $L$ is the linear size of the system. Examples include the ground states of the toric code, certain Kitaev quantum-double models, and string-net models. Going beyond two dimensions, we extend our scheme to more general Calderbank-Shor-Steane codes. As an application, we present protocols for realizing the three-dimensional Haah's code and X-cube fracton models.

arXiv:2410.11602•Physical review. B./Physical review. B•Mar 28, 2025•2 citations
Long-range entangled quantum states -- like cat states and topological order -- are key for quantum metrology and information purposes, but they cannot be prepared by any scalable unitary process. Intriguingly, using measurements as an additional ingredient could circumvent such no-go theorems. However, efficient schemes are known for only a limited class of long-range entangled states, and their implementation on existing quantum devices via a sequence of gates and measurements is hampered by high overheads. Here we resolve these problems, proposing how to scalably prepare a broad range of long-range entangled states with the use of existing experimental platforms. Our two-step process finds an ideal implementation in Rydberg atom arrays, only requiring time-evolution under the intrinsic atomic interactions, followed by measuring a single sublattice (by using, e.g., two atom species). Remarkably, this protocol can prepare the 1D Greenberger-Horne-Zeilinger (GHZ) 'cat' state and 2D toric code with fidelity per site exceeding 0.99990.99990.9999, and a 3D fracton state with fidelity ⪆0.998\gtrapprox 0.998⪆0.998. In light of recent experiments showcasing 3D Rydberg atom arrays, this paves the way to the first experimental realization of fracton order. While the above examples are based on efficiently preparing and measuring cluster states, we also propose a multi-step procedure to create S3S_3S3​ and D4D_4D4​ non-Abelian topological order in Rydberg atom arrays and other quantum devices -- offering a route towards universal topological quantum computation.
A highly coveted goal is to realize emergent non-Abelian gauge theories and their anyonic excitations, which encode decoherence-free quantum information. While measurements in quantum devices provide new hope for scalably preparing such long-range entangled states, existing protocols using the experimentally established ingredients of a finite-depth circuit and a single round of measurement produce only Abelian states. Surprisingly, we show there exists a broad family of non-Abelian states-namely those with a Lagrangian subgroup-which can be created using these same minimal ingredients, bypassing the need for new resources such as feed forward. To illustrate that this provides realistic protocols, we show how D_{4} non-Abelian topological order can be realized, e.g., on Google's quantum processors using a depth-11 circuit and a single layer of measurements. Our work opens the way toward the realization and manipulation of non-Abelian topological orders, and highlights counterintuitive features of the complexity of non-Abelian phases.
A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the nonlocal nature of Schrödinger cat states, topological order, and quantum criticality. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. However, a systematic understanding of when and how measurements of SRE give rise to LRE is still lacking. Here, we establish that LRE appears upon performing measurements on symmetry-protected topological (SPT) phases—of which the cluster state is one example. For instance, we show how to implement the Kramers-Wannier transformation by adding a cluster SPT to an input state followed by measurement. This transformation naturally relates states with SRE and LRE. An application is the realization of double-semion order when the input state is the Z 2 Levin-Gu SPT. Similarly, the addition of fermionic SPTs and measurement leads to an implementation of the Jordan-Wigner transformation of a general state. More generally, we argue that a large class of SPT phases protected by G × H symmetry gives rise to anomalous LRE upon measuring G -charges, and we prove that this persists for generic points in the SPT phase under certain conditions. Our work introduces a new practical tool for using SPT phases as resources for creating LRE, and we uncover the classification result that all states related by sequentially gauging Abelian groups or by Jordan-Wigner transformation are in the same equivalence class, once we augment finite-depth circuits with single-site measurements. In particular, any topological or fracton order with a solvable finite gauge group can be obtained from a product state in this way. Published by the American Physical Society 2024
Storing quantum information, unlike information in a classical computer, requires battling quantum decoherence, which results in a loss of information over time. To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another, thus preventing quantum decoherence. One promising concept is that of fracton order -- a phase of matter with a large ground state degeneracy that grows subextensively with the system size. Unfortunately, the models realizing fractons are not friendly to experimental implementations as they require unnatural interactions between a substantial number (of the order of ten) of qubits. We demonstrate how this limitation can be circumvented by leveraging the long-range quantum entanglement created using only pairwise interactions between the code and ancilla qubits, realizable in programmable tweezer arrays of Rydberg atoms. We show that this platform also allows to detect and correct certain types of errors en route to the goal of true error-resistant quantum memory.
The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires: mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a 4×44 \times 44×4 rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold p⋆≈0.034p^\star \approx 0.034p⋆≈0.034. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.
Long-range entanglement-the backbone of topologically ordered states-cannot be created in finite time using local unitary circuits, or, equivalently, adiabatic state preparation.Recently, it has come to light that single-site measurements provide a loophole, allowing for finite-time state preparation in certain cases.Here we show how this observation imposes a complexity hierarchy on long-range entangled states based on the minimal number of measurement layers required to create the state, which we call "shots."First, similar to Abelian stabilizer states, we construct single-shot protocols for creating any non-Abelian quantum double of a group with nilpotency class 2 (such as D 4 or Q 8 ).We show that after the measurement, the wave function always collapses into the desired non-Abelian topological order, conditional on recording the measurement outcome.Moreover, the clean quantum double ground state can be deterministically prepared via feedforward-gates that depend on the measurement outcomes.Second, we provide the first constructive proof that a finite number of shots can implement the Kramers-Wannier duality transformation (i.e., the gauging map) for any solvable symmetry group.As a special case, this gives an explicit protocol to prepare twisted quantum doubles for all solvable groups.Third, we argue that certain topological orders, such as nonsolvable quantum doubles or Fibonacci anyons, define nontrivial phases of matter under the equivalence class of finite-depth unitaries and measurement, which cannot be prepared by any finite number of shots.Moreover, we explore the consequences of allowing gates to have exponentially small tails, which enables, for example, the preparation of any Abelian anyon theory, including chiral ones.This hierarchy paints a new picture of the landscape of long-range entangled states, with practical implications for quantum simulators.
We present protocols for preparing two-dimensional Abelian and non-Abelian topologically ordered states by employing finite depth unitary circuits composed of long-ranged, simultaneous, and mutually commuting two-qubit gates. Our protocols are motivated by recent proposals for circuits in trapped ion systems, which allow each qubit to participate in multiple gates simultaneously. Our circuits are shown to be optimal, in the sense that the number of two-qubit gates and ancilla qubits scales as O(L2)O({L}^{2})O(L2), where LLL is the linear size of the system. Examples include the ground states of the toric code, certain Kitaev quantum-double models, and string-net models. Going beyond two dimensions, we extend our scheme to more general Calderbank-Shor-Steane codes. As an application, we present protocols for realizing the three-dimensional Haah's code and X-cube fracton models.