Measurement-free fault-tolerant quantum error correction in near-term devices

Abstract

Logical qubits can be protected from decoherence by performing QEC cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory that operates for in principle arbitrary long times. All circuit components must be assumed as noisy unless specific assumptions about the form of the noise are made. Modern QEC schemes are challenging to implement experimentally in physical architectures where in-sequence measurements and feed-forward of classical information cannot be reliably executed fast enough or even at all. Here we provide a novel scheme to perform QEC cycles without the need of measuring qubits that is fully fault-tolerant with respect to all components used in the circuit. Our scheme can be used for any low-distance CSS code since its only requirement towards the underlying code is a transversal CNOT gate. Similarly to Steane-type EC, we coherently copy errors to a logical auxiliary qubit but then apply a coherent feedback operation from the auxiliary system to the logical data qubit. The logical auxiliary qubit is prepared fault-tolerantly without measurements, too. We benchmark logical failure rates of the scheme in comparison to a flag-qubit based EC cycle. We map out a parameter region where our scheme is feasible and estimate physical error rates necessary to achieve the break-even point of beneficial QEC with our scheme. We outline how our scheme could be implemented in ion traps and with neutral atoms in a tweezer array. For recently demonstrated capabilities of atom shuttling and native multi-atom Rydberg gates, we achieve moderate circuit depths and beneficial performance of our scheme while not breaking fault tolerance. These results thereby enable practical fault-tolerant QEC in hardware architectures that do not support mid-circuit measurements.

24 pages, 19 figures

References in corpus (27)

• An Open-System Quantum Simulator with Trapped Ions
• Suppressing quantum errors by scaling a surface code logical qubit
• An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
• Topological Quantum Distillation
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• High-fidelity parallel entangling gates on a neutral atom quantum computer
• Quantum computing with neutral atoms
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Realization of the quantum Toffoli gate with trapped ions
• A Race Track Trapped-Ion Quantum Processor
• Low-distance Surface Codes under Realistic Quantum Noise
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit
• Topological Computation without Braiding
• Erasure conversion in a high-fidelity Rydberg quantum simulator
• Mid-circuit correction of correlated phase errors using an array of spectator qubits
• Lossless State Detection of Single Neutral Atoms
• Mid-circuit qubit measurement and rearrangement in a ${}^{171}$Yb atomic array
• Mid-circuit measurements on a single species neutral alkali atom quantum processor
• Single-step implementation of high fidelity $n$-bit Toffoli gate
• Repetitive readout and real-time control of nuclear spin qubits in ${}^{171}$Yb atoms
• On fault-tolerance with noisy and slow measurements
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• Measurement-free implementations of small-scale surface codes for quantum dot qubits
• Measurement-free fault-tolerant logical zero-state encoding of the distance-three nine-qubit surface code in a one-dimensional qubit array
• Minimal instances for toric code ground states
• The role of quantum measurements in physical processes and protocols

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• Measurement-free quantum error correction optimized for biased noise
• Realization and Calibration of Continuously Parameterized Two-Qubit Gates on a Trapped-Ion Quantum Processor
• Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
• Towards self-correcting quantum codes for neutral atom arrays
• Multiqubit Rydberg Gates for Quantum Error Correction
• Expedited Noise Spectroscopy of Transmon Qubits
• Measurement-free code-switching for low overhead quantum computation using permutation invariant codes
• Universal quantum computation via scalable measurement-free error correction
• Impure codes exceeding the pure bounds for quantum local recovery