IBM quantum hardware has successfully simulated a 100-site spin chain, achieving 97.9-99.0% fidelity in preparing ground states of the chain, a scale previously limited by the entanglement needed for accurate results. Researchers used a tensor-network-based approximate quantum compiling protocol to construct shallow circuits, with a depth of only 18-39 CNOT gates, to explore symmetry-protected topological (SPT) order.
The work directly measured string order for lengths up to 20, persisting beyond the decay of conventional correlations, alongside other non-local diagnostics, offering a new way to characterise these complex quantum states. This establishes digital quantum devices as flexible platforms for studying complex quantum matter.
Symmetry-Protected Topological Phases Extend Quantum Matter Understanding
These circuits, ranging from 18 to 39 CNOT gates in depth, enabled the preparation of the 100-site ground states, a scale that pushes the boundaries of current digital quantum hardware. This reduction in circuit complexity is crucial for minimizing errors and maintaining the coherence of quantum information. The ability to prepare these states with high fidelity is a major step forward in the field of quantum simulation, allowing for more accurate and reliable studies of complex quantum phenomena.
Beyond simply preparing the quantum state, the researchers directly measured multiple non-local diagnostics of SPT order. This observation provides strong evidence for the presence of SPT order, a characteristic difficult to observe with traditional experimental techniques. The team observed entanglement spectrum degeneracies and detected 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, as detailed in their published work.
This establishes digital quantum devices as versatile platforms for investigating complex quantum matter, with access to microscopic observables that are difficult to obtain in conventional experimental systems. This also establishes digital quantum devices as flexible platforms for studying complex quantum matter and provides a practical foundation for exploring non-equilibrium dynamics in regimes that challenge classical computational methods.
Site Spin Chain Prepared via Tensor-Network Compiling
Recent advances in programmable quantum processors are expanding the scale at which complex quantum systems can be simulated, with a new demonstration achieving a 100-site spin chain prepared on IBM quantum hardware. This accomplishment addresses a key limitation in the field: the difficulty of creating states with sufficient entanglement to avoid the effects of finite system size, a challenge traditionally posed by the circuit depth required for accurate simulation.
The results achieved fidelities of 97.9 and 99.0 percent when compared to results from the density matrix renormalisation group (DMRG) algorithm. This high fidelity is crucial for ensuring that observed quantum behaviour accurately reflects the intended system, rather than errors introduced during the simulation process.
Shallow Circuits Achieve 97.9-99.0% Fidelity on IBM Hardware
George Pennington and colleagues have demonstrated a significant advance in quantum simulation by achieving high-fidelity preparation of a complex quantum state on superconducting hardware. The team successfully prepared ground states of a 100-site spin-1/2 bond-alternating Heisenberg chain with fidelities ranging from 97.9 to 99.0 percent, a scale previously constrained by the limitations of circuit depth needed to capture entanglement. Executing these circuits on IBM quantum hardware allowed direct extraction of multiple non-local diagnostics of symmetry-protected topological (SPT) order.
String Order Extracted Up To 20 Sites Demonstrates SPT Order
The ability to directly observe quantum states with complex entanglement is expanding thanks to a recent demonstration on IBM quantum hardware. Researchers have successfully prepared and analysed a 100-site spin-1/2 bond-alternating Heisenberg chain, a model system for exploring symmetry-protected topological (SPT) order, with high fidelity. Executing these circuits on IBM quantum hardware, they directly extracted string order for lengths extending up to 20 sites, a non-local property that signals the presence of topological order and persists even as conventional, shorter-range correlations decay.
This measurement provides a more complete picture of the system’s quantum state than traditional methods, which often rely on indirect probes like boundary state detection. This level of control and measurement capability opens new avenues for studying complex quantum matter. Unlike material platforms where Hamiltonian parameters are fixed, the digital quantum processor allows for tuning of system size, parameters, and boundary conditions. This programmability, combined with the ability to directly probe the bulk wave function, addresses limitations inherent in solid-state systems used to investigate SPT order.
The team observed entanglement spectrum degeneracies and symmetry-protected edge modes.
BAHC Model Bridges Material Realizations & Quantum Control
Digital quantum processors are increasingly used to model complex physical systems, and recent work has demonstrated the preparation of a 100-site spin chain using IBM quantum hardware. This achievement expands the scale of simulations beyond previous limitations imposed by the difficulty of maintaining entanglement in deeper quantum circuits. This level of accuracy is crucial for extracting meaningful physical insights from the simulation. The ability to create these shallow circuits is vital, as the accumulation of errors in deeper circuits quickly degrades the simulation’s reliability. The resulting circuits allowed for the direct measurement of several non-local properties, providing a more complete characterisation of the quantum state than traditional methods allow. The string order persisted beyond the decay of conventional two-point correlations, confirming the robustness of the observed topological order.
Characteristic features of the entanglement spectrum were also observed, alongside symmetry-protected edge modes, providing a scalable and programmable approach to preparing and characterising SPT phases on quantum processors. More broadly, this establishes digital quantum devices as flexible platforms for studying complex quantum matter and provides a practical foundation for exploring non-equilibrium dynamics in regimes that challenge classical computational methods.
This achievement surpasses previous limitations imposed by the rapid accumulation of errors in quantum circuits, enabling the study of symmetry-protected topological (SPT) phases with unprecedented scale and fidelity. Programmable digital quantum processors offer a powerful complementary approach, bridging the gap between physical realisation and microscopic observability.
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