Researchers have successfully created a 100-site spin chain on IBM quantum hardware, a scale large enough to minimize limitations common in these experiments. The work demonstrates 97.9-99.0% fidelity in preparing ground states of the spin-1/2 bond-alternating Heisenberg chain, allowing for reliable extraction of data about symmetry-protected topological (SPT) phases.

This programmable approach utilizes a tensor-network-based approximate quantum compiling protocol to achieve circuits with a CNOT depth of 18-39, directly extracting non-local diagnostics of SPT order, including string order for lengths up to 20, and establishing digital quantum devices as flexible platforms for studying complex quantum matter.

Symmetry-Protected Topological Order Beyond Landau Paradigm

This achievement bypasses limitations of traditional material platforms used to study symmetry-protected topological (SPT) phases, which often restrict tuning of Hamiltonian parameters and access to the underlying quantum state. The team’s success hinges on the ability to move beyond the Landau paradigm of quantum matter, which traditionally relies on identifying local order parameters; SPT phases, however, exhibit distinct characteristics lacking such conventional markers.

Diagnosing these phases typically depends on indirect probes like boundary states, but the IBM processor enabled direct extraction of non-local properties of the many-body wavefunction, offering a more complete picture of the system’s quantum state. 97.9-99.0%, ensuring the reliability of extracted data. These observations, coupled with the detection of characteristic features in the entanglement spectrum and symmetry-protected edge modes, provide a robust and scalable method for characterizing these complex quantum phases.

The researchers explain, highlighting the ability to tune system parameters and directly probe the bulk wave function. The researchers specifically focused on the spin-1/2 bond-alternating Heisenberg chain, examining four ground states with varying coupling strengths, and demonstrating the preparation of states with a bond dimension of up to 40. This advancement represents a step forward, exceeding previous efforts that were limited to a bond dimension of only 2, and opening new avenues for investigating the fundamental properties of quantum materials.

Site Spin Chain Prepared via Tensor-Network Compiling

Digital quantum processors are increasingly utilized to investigate complex quantum systems, yet scaling these simulations while maintaining fidelity presents a significant challenge. Recent work at IBM has demonstrated the construction of a 100-site spin chain, a substantial increase over previous efforts limited to a bond dimension of 2, enabling researchers to minimize that often distort experimental results. This achievement relies on a tensor-network-based approximate quantum compiling (AQC) protocol, a method for translating complex quantum states into shallow quantum circuits.

The resulting circuits required only 18-39 CNOT depth, a measure of circuit complexity, to prepare the ground states. This programmability allows for the exploration of non-equilibrium dynamics and the potential for measurement-based quantum computation.

IBM Quantum Hardware Validates SPT Phase Diagnostics

This achievement moves beyond previous limitations in material platforms, which offer inflexibility in tuning Hamiltonian parameters and restricted experimental probes focused on boundary signatures rather than the underlying quantum state. Achieving high fidelity in this preparation was critical; the experiments demonstrated 97.9-99.0% fidelity with density matrix renormalization group (DMRG) ground states, ensuring the reliability of extracted data.

“Crucially, the programmable nature of the platform addresses both limitations of static material systems,” Pennington and colleagues write in npj Quantum Information. Their method establishes a practical foundation for further research, such as simulating non-equilibrium SPT dynamics or utilizing SPT states as a resource for quantum computation, and offers a flexible platform for exploring complex quantum matter.

Shallow Circuits Achieve 97.9-99.0% Fidelity for SPT States

Constructing a quantum simulation of a 100-site spin chain demanded a significant reduction in the complexity of the required quantum circuits; George Pennington and colleagues at IBM achieved circuits with a CNOT depth of only 18 to 39 gates. This level of circuit simplification is critical because the number of operations directly impacts the accumulation of errors during computation, a major obstacle in current quantum processors.

Prior attempts to simulate similar systems on quantum hardware often suffered from errors that obscured the underlying physics, limiting the ability to draw meaningful conclusions. The high fidelity demonstrated by Pennington’s team enables the extraction of subtle signatures of SPT order, such as non-local string order extending up to 20 sites, a characteristic that distinguishes these phases from conventional quantum matter.

This extended range of detectable correlation is a direct consequence of the improved circuit fidelity and larger system size. Beyond simply achieving high fidelity, the researchers demonstrated the versatility of their approach by exploring multiple points within the phase diagram of the spin-1/2 bond-alternating Heisenberg chain. They prepared ground states representing both the odd- and even-Haldane phases, verifying their preparation through multiple independent diagnostics.

These included observing symmetry-protected edge modes and identifying characteristic degeneracies in the entanglement spectrum. “The simultaneous observation of these independent diagnostics provides a scalable and programmable approach to preparing and characterising SPT phases on quantum processors,” the researchers write.

String Order Extends to 20 Sites in Bond-Alternating Chain

While conventional materials often limit the extent to which researchers can probe the intricacies of quantum states, a new demonstration utilizing IBM quantum hardware has extended the measurable range of, a key indicator of exotic quantum phases, to 20 sites within a meticulously constructed 100-site spin chain. This achievement surpasses previous limitations imposed by finite-size effects, which typically obscure the true characteristics of quantum systems in smaller simulations.

This is a critical advancement, as shallower circuits are less susceptible to the errors that plague quantum computations. This high accuracy is not merely a technical feat, but a validation of the simulation itself, enabling reliable extraction of data about these complex phases.

The entanglement spectrum, a powerful tool for characterising quantum states, provides further insight into the SPT phases realised on the quantum processor. The authors state that the characteristic features of the entanglement spectrum, specifically the emergence of a zero-mode peak, serve as a robust diagnostic of the topological order. This peak, indicative of the ground-state degeneracy protected by the symmetry of the system, was observed with high clarity, confirming the presence of the SPT phase.

The ability to resolve these subtle features is a testament to the quality of the prepared states, which were achieved with 97. 0% fidelity. This level of precision is crucial for distinguishing between different topological phases and validating the theoretical predictions.

Entanglement Spectrum Reveals SPT Phase Characteristics

Prior investigations of SPT order often relied on indirect probes like boundary state detection, limiting access to the underlying quantum state; this work overcomes that limitation by providing a platform for extracting non-local properties of many-body wavefunctions. Beyond string order, the team also analyzed characteristic features of the entanglement spectrum and identified symmetry-protected edge modes, further confirming the successful preparation of the SPT phases.

This programmability is a key advantage, addressing limitations found in static material systems by allowing for on-demand tuning of system size, Hamiltonian parameters, and boundary conditions. The ability to manipulate these parameters within a single device opens new avenues for exploring non-equilibrium dynamics and potentially utilizing SPT states as resources for measurement-based quantum computation.

SPT Edge Modes Observed on Superconducting Qubits

This achievement minimizes the impact of distortions in observed behavior due to the limited size of the simulated system, a persistent challenge in the field of quantum materials research. The researchers observed symmetry-protected edge modes, confirming the presence of these unique quantum states.

Here, we use a tensor-network-based approximate quantum compiling (AQC) protocol to construct shallow quantum circuits (18-39 CNOT depth) that prepare 100-site ground states of the spin-1/2 bond-alternating Heisenberg chain across distinct SPT phases with 97. 0% fidelity.

Executing these circuits on IBM quantum hardware, we directly extract multiple non-local diagnostics of SPT order, including string order for lengths up to 20, persisting well beyond the decay of conventional two-point correlations, characteristic features of the entanglement spectrum, and symmetry-protected edge modes. The simultaneous observation of these independent diagnostics provides a scalable and programmable approach to preparing and characterising SPT phases on quantum processors.

Output ONLY the corrected section text, nothing else. 0% Fidelity for SPT States

Shallow Circuits Achieve 97.9-99.0% Fidelity for SPT States …including string order for lengths up to 20, persisting well beyond the decay of conventional two-point correlations…

Output ONLY the corrected section text, nothing else. …characteristic features of the entanglement spectrum…

Output ONLY the corrected section text, nothing else. …SPT phases extend the Landau paradigm of quantum matter by admitting distinct phases that lack local order parameters…

Output ONLY the corrected section text, nothing else. Recent work has begun to demonstrate the promise of digital quantum platforms toward probing nontrivial SPT physics.

Recent work has begun to demonstrate the promise of digital quantum platforms toward probing nontrivial SPT physics.

SECTION “SPT physics has been explored experimentally in a number of platforms including cold atoms 8, 9, Rydberg analogue simulators 10, 11, trapped-ion systems 12, and two material realisations of the Haldane phase using nanographene, namely: the spin-1/2 bond-alternating Heisenberg chain (BAHC) 13 and the spin-1 bilinear-biquadratic (BLQP) model 14.” TO CORRECT:
SPT physics has been explored experimentally in a number of platforms including cold atoms 8, 9, Rydberg analogue simulators 10, 11, trapped-ion systems 12, and two material realisations of the Haldane phase using nanographene, namely: the spin-1/2 bond-alternating Heisenberg chain (BAHC) 13 and the spin-1 bilinear-biquadratic (BLQP) model 14.

SPT physics has been explored experimentally in a number of platforms including cold atoms 8, 9, Rydberg analogue simulators 10, 11, trapped-ion systems 12, and two material realisations of the Haldane phase using nanographene, namely: the spin-1/2 bond-alternating Heisenberg chain (BAHC) 13 and the spin-1 bilinear-biquadratic (BLQP) model 14.

SECTION “The latter material realisations of SPT order provide elegant physical instances of these phases. While such solid-state platforms realise the target physics, they face two important limitations. First, they exhibit structural inflexibility: the bond alternation and boundary conditions are fixed during synthesis by the chemical linkages of the molecular precursors, limiting the ability to tune Hamiltonian parameters in situ. Second, the nature of available experimental probes restricts the characterisation of the resulting SPT phase.

Diagnosing SPT order in these systems typically relies on indirect, boundary-restricted signatures, such as the spectroscopic detection of fractionalised edge excitations or the mapping of bulk excitations using scanning tunnelling microscopy (STM), leaving direct access to the underlying bulk wave function severely limited.” TO CORRECT:
The latter material realisations of SPT order provide elegant physical instances of these phases. While such solid-state platforms realise the target physics, they face two important limitations.

First, they exhibit structural inflexibility: the bond alternation and boundary conditions are fixed during synthesis by the chemical linkages of the molecular precursors, limiting the ability to tune Hamiltonian parameters in situ. Diagnosing SPT order in these systems typically relies on indirect, boundary-restricted signatures, such as the spectroscopic detection of fractionalised edge excitations or the mapping of bulk excitations using scanning tunnelling microscopy (STM), leaving direct access to the underlying bulk wave function severely limited.

Output ONLY the corrected section text, nothing else. First, they exhibit structural inflexibility: the bond alternation and boundary conditions are fixed during synthesis by the chemical linkages of the molecular precursors, limiting the ability to tune Hamiltonian parameters in situ.

Second, the nature of available experimental probes restricts the characterisation of the resulting SPT phase. Diagnosing SPT order in these systems typically relies on indirect, boundary-restricted signatures, such as the spectroscopic detection of fractionalised edge excitations or the mapping of bulk excitations using scanning tunnelling microscopy (STM), leaving direct access to the underlying bulk wave function severely limited.

SECTION “Programmable digital quantum processors offer a powerful complementary approach, bridging the gap between physical realisation and microscopic observability. In this setting, the SPT state is physically realised on the quantum hardware through circuit-based state preparation. Crucially, the programmable nature of the platform addresses both limitations of static material systems: site-resolved control enables the tuning of system size, Hamiltonian parameters, and boundary conditions within a single device, while measurement-basis rotations offer a route to direct probes of the bulk wave function.

This enables the extraction of a wide range of non-local observables, including string order across extended distances and characteristic entanglement degeneracies across multiple spatial cuts. Digital quantum architectures therefore provide a highly flexible and programmable platform for studying complex quantum matter, with access to microscopic observables that are difficult to obtain in conventional experimental systems.

Furthermore, going beyond static properties, digital quantum processors offer the prospect of studying dynamical properties of SPT systems, under arbitrary quench Hamiltonians.” TO CORRECT:
Programmable digital quantum processors offer a powerful complementary approach, bridging the gap between physical realisation and microscopic observability. In this setting, the SPT state is physically realised on the quantum hardware through circuit-based state preparation.

Crucially, the programmable nature of the platform addresses both limitations of static material systems: site-resolved control enables the tuning of system size, Hamiltonian parameters, and boundary conditions within a single device, while measurement-basis rotations offer a route to direct probes of the bulk wave function. This enables the extraction of a wide range of non-local observables, including string order across extended distances and characteristic entanglement degeneracies across multiple spatial cuts.

Digital quantum architectures therefore provide a highly flexible and programmable platform for studying complex quantum matter, with access to microscopic observables that are difficult to obtain in conventional experimental systems. going beyond static properties, digital quantum processors offer the prospect of studying dynamical properties of SPT systems, under arbitrary quench Hamiltonians.

Output ONLY the corrected section text, nothing else. In this setting, the SPT state is physically realised on the quantum hardware through circuit-based state preparation.

SECTION “The discovery of symmetry-protected topological (SPT) phases has transformed our understanding of quantum matter by revealing classifications of order that transcend the Landau paradigm 1. Unlike conventional phases characterised by local order parameters, SPT phases preserve the protecting symmetries and are diagnosed by non-local or entanglement-based invariants together with symmetry-protected edge states that are robust to symmetry-preserving perturbations 2, 3. As a result, SPT phases have become a central topic in modern condensed matter physics 1.

These features not only enrich the taxonomy of quantum phases, but also underpin emerging applications in quantum information science 4, including topologically protected spin transport 5, low-dissipation interconnects 6 and robust memory elements 7.” TO CORRECT:
The discovery of symmetry-protected topological (SPT) phases has transformed our understanding of quantum matter by revealing classifications of order that transcend the Landau paradigm 1.

Unlike conventional phases characterised by local order parameters, SPT phases preserve the protecting symmetries and are diagnosed by non-local or entanglement-based invariants together with symmetry-protected edge states that are robust to symmetry-preserving perturbations 2, 3. These features not only enrich the taxonomy of quantum phases, but also underpin emerging applications in quantum information science 4, including topologically protected spin transport 5, low-dissipation interconnects 6 and robust memory elements 7.

Output ONLY the corrected section text, nothing else. Unlike conventional phases characterised by local order parameters, SPT phases preserve the protecting symmetries and are diagnosed by non-local or entanglement-based invariants together with symmetry-protected edge states that are robust to symmetry-preserving perturbations 2, 3.

As a result, SPT phases have become a central topic in modern condensed matter physics 1. These features not only enrich the taxonomy of quantum phases, but also underpin emerging applications in quantum information science 4, including topologically protected spin transport 5, low-dissipation interconnects 6 and robust memory elements 7.

Digital Quantum Processors Enable Complex Quantum Matter Studies

This achievement allows for the study of complex quantum matter phenomena, specifically symmetry-protected topological (SPT) order, with unprecedented detail. The team’s work focuses on the spin-1/2 bond-alternating Heisenberg chain, a model system exhibiting SPT phases that lack conventional order parameters, making their characterization challenging with traditional methods.

Prior efforts faced limitations in both system size and fidelity; for example, previous work demonstrated 80-site MPSs but was limited to a bond dimension of 2, whereas this new method achieves bond dimensions up to 40. The ability to manipulate these parameters allows for the investigation of SPT systems under arbitrary quench Hamiltonians, expanding the scope of potential research.

Source: https://www.nature.com/articles/s41534-026-01334-8

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