Protecting Expressive Circuits with a Quantum Error Detection Code

Abstract

A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing quantum computers. In this context we develop a quantum error detection code for implementations on existing trapped-ion computers. By encoding $k$ logical qubits into $k+2$ physical qubits, this code presents fault-tolerant state initialisation and syndrome measurement circuits that can detect any single-qubit error. It provides a universal set of local and global logical rotations that have physical support on only two qubits. A high-fidelity -- though non fault-tolerant -- compilation of this universal gate set is possible thanks to the two-qubit physical rotations present in trapped-ion computers with all-to-all connectivity. Given the particular structure of the logical operators, we nickname it the Iceberg code. We demonstrate the protection of circuits of 8 logical qubits with up to 256 layers, saturate the logical quantum volume of $2^8$, and show the positive effect of increasing the frequency of syndrome measurements within the circuit. These results illustrate the practical usefulness of the Iceberg code to protect expressive circuits on existing trapped-ion quantum computers.

arXiv comment16 pages, 9 figures. Published version

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• Many-hypercube codes: High-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing
• A model of randomly-coupled Pauli spins
• Continuous Hamiltonian dynamics on digital quantum computers without discretization error
• Performance of Quantum Approximate Optimization with Quantum Error Detection
• Practicality of quantum adiabatic algorithm for chemistry applications
• Adaptive Syndrome Extraction
• Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits
• Programming higher-order interactions of Rydberg atoms
• Minimizing readout-induced noise for early fault-tolerant quantum computers
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Provable and Verifiable Quantum Advantage in Sample Complexity
• Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation
• End-to-End Quantum Algorithms for the Jones Polynomial
• Error detection without post-selection in adaptive quantum circuits
• Zero-Noise Extrapolation via Cyclic Permutations of Quantum Circuit Layouts