Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer

Abstract

Quantum systems evolve in time in one of two ways: through the Schrödinger equation or wavefunction collapse. So far, deterministic control of quantum many-body systems in the lab has focused on the former, due to the probabilistic nature of measurements. This imposes serious limitations: preparing long-range entangled states, for example, requires extensive circuit depth if restricted to unitary dynamics. In this work, we use mid-circuit measurement and feed-forward to implement deterministic non-unitary dynamics on Quantinuum's H1 programmable ion-trap quantum computer. Enabled by these capabilities, we demonstrate for the first time a constant-depth procedure for creating a toric code ground state in real-time. In addition to reaching high stabilizer fidelities, we create a non-Abelian defect whose presence is confirmed by transmuting anyons via braiding. This work clears the way towards creating complex topological orders in the lab and exploring deterministic non-unitary dynamics via measurement and feed-forward.

arXiv comment5 + 8 pages, 3 + 5 figures, v2: added a reference

References in corpus (38)

• Fault-tolerant quantum computation by anyons
• Variational Quantum Algorithms
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Topological quantum memory
• Quantum Error Correction for Quantum Memories
• Predicting Many Properties of a Quantum System from Very Few Measurements
• An Open-System Quantum Simulator with Trapped Ions
• Efficient quantum state tomography
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Dynamical quantum phase transitions: a review
• Probing entanglement entropy via randomized measurements
• Quantum Simulators: Architectures and Opportunities
• Demonstration of the trapped-ion quantum-CCD computer architecture
• Random Quantum Circuits
• Models for gapped boundaries and domain walls
• Quantum orders in an exact soluble model
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Exponential suppression of bit or phase flip errors with repetitive error correction
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Repeated quantum error correction on a continuously encoded qubit by real-time feedback
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• Long-range quantum entanglement in noisy cluster states
• The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
• Measurement as a shortcut to long-range entangled quantum matter
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Digital simulation of non-Abelian anyons with 68 programmable superconducting qubits
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Algorithms for quantum simulation at finite energies
• A Compact Fermion to Qubit Mapping
• Long-range entanglement from measuring symmetry-protected topological phases
• Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Entanglement dynamics in hybrid quantum circuits
• Synthetic Topological Degeneracy by Anyon Condensation

Cited by in corpus (49)

• A dual-species Rydberg array
• Speed limits and locality in many-body quantum dynamics
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
• Measurement-Based Long-Range Entangling Gates in Constant Depth
• Quantum phase transition between topologically distinct quantum critical points
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Efficient Detection of Strong-To-Weak Spontaneous Symmetry Breaking via the Rényi-1 Correlator
• Qutrit Toric Code and Parafermions in Trapped Ions
• Highly entangled stationary states from strong symmetries
• Quantum dimer models with Rydberg gadgets
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases
• Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
• Generalized toric codes on twisted tori for quantum error correction
• Protocols for Creating Anyons and Defects via Gauging
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Free fermions under adaptive quantum dynamics
• Gauge theory and mixed state criticality
• A Universal Circuit Set Using the $S_3$ Quantum Double
• Measurement-Induced Heating of Trapped Ions
• Statistical Mechanics of Stochastic Quantum Control: $d$-adic Rényi Circuits
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Non-invertible symmetries in finite-group gauge theory
• Preparing matrix product states via fusion: constraints and extensions
• Variational LOCC-assisted quantum circuits for long-range entangled states
• Mixed-State Topological Order under Coherent Noise
• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Randomized Benchmarking Protocol for Dynamic Circuits
• Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
• Measurement-invisible quantum correlations in scrambling dynamics
• Post-measurement Quantum Monte Carlo
• Robust preparation of ground state phases under noisy imaginary time evolution
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Local fermion-to-qudit mappings: a practical recipe for four-level systems
• Probing anyonic statistics via Mach-Zehnder interferometry in quantum computers
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Robustness of a state with Ising topological order against local projective measurements
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems
• Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Partons from stabilizer codes
• Exact large deviations and emergent long-range correlations in sequential quantum East circuits
• Adaptive time Compressed QITE (ACQ) and its geometrical interpretation