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arXiv:quant-ph/0510021 · Physical Review A

Quantum error correction of a qubit loss in an addressable atomic system

Jiří Vala, K. Birgitta Whaley, David S. Weiss

Published Nov 18, 2005• 41 citations
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Abstract

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum nondemolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum nondemolition and projective measurements are implemented using a cavity quantum electrodynamics system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons.

DOI
10.1103/physreva.72.052318

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We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum nondemolition measurement and then transformed into a standard qubit error by inserting a new atom in the vacated lattice site. The logical qubit, encoded here into four physical qubits with the Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective measurement, two single-qubit gates, and three controlled-NOT operations. No ancillary qubits are required. Both quantum nondemolition and projective measurements are implemented using a cavity quantum electrodynamics system which can also detect a general leakage error and thus allow qubit loss to be corrected within the same framework. The scheme can also be applied in quantum computation with trapped ions or with photons.
Long-distance quantum communication with high fidelity is the main obstacle to creating a quantum network. A scheme to recover the loss of one photon with a three-to-eight qubit encoding is presented. The qubit loss is first detected using a quantum nondemolition measurement and is then transformed into a standard qubit error by inserting a new photon. The state of qubits is reconstructed via a sequence of one projective measurement, two single-qubit gates, and seven controlled-NOT operations. No ancillary qubits are required. Finally, the cost of resources is analyzed.
Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical error rates required for valuable algorithms. However, it requires flexible control of high-fidelity operations performed on large numbers of qubits. We demonstrate fault-tolerant quantum computation on a quantum processor with 256 qubits, each an individual neutral Ytterbium atom. The operations are designed so that key error sources convert to atom loss, which can be detected by imaging. Full connectivity is enabled by atom movement. We demonstrate the entanglement of 24 logical qubits encoded into 48 atoms, at once catching errors and correcting for, on average 1.8, lost atoms. We also implement the Bernstein-Vazirani algorithm with up to 28 logical qubits encoded into 112 atoms, showing better-than-physical error rates. In both cases, "erasure conversion," changing errors into a form that can be detected independently from qubit state, improves circuit performance. These results begin to clear a path for achieving scientific quantum advantage with a programmable neutral atom quantum processor.
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single-qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single-qubit errors, and measure the fidelity of the encoded logical gate operations.
Qubit loss occurs when the physical carrier of a qubit leaves the computational system without directly revealing the event's location. Such errors are a major obstacle to fault-tolerant quantum computation on platforms including photonic, neutral-atom, and trapped-ion systems. Loss locations are commonly identified using additional hardware operations such as leakage-detection units (LDUs), which introduce space-time overhead and may themselves become a source of error. We investigate whether qubit loss on stabilizer codes can instead be inferred from syndrome data obtained through standard repeated stabilizer measurements. Under a non-entangling model for gates involving a lost qubit, we derive a sufficient condition for loss detectability in general stabilizer codes. The condition is based on the emergence of anticommutation between stabilizer checks after their support on the lost qubits is removed. By using that condition, we formulate the exact loss-inference problem using the observed set of non-deterministic checks together with its maximum-likelihood formulation. We then relax the problem to the minimum set cover problem with a greedy heuristic algorithm. We evaluate the resulting inference and loss-correction protocols on the rotated surface code via circuit-level noise simulations for trapped-ion and neutral-atom platforms. On both platforms, inference-based and adaptive protocols reduce the logical error rate relative to a noisy-LDU baseline in the low-to-moderate loss-rate regime relevant to near-term hardware, while requiring fewer space-time overheads.
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent detection or correction of errors without destroying the logical state itself through direct measurement. We show the encoding and syndrome measurement of a fault-tolerantly prepared logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates the robustness of a logical qubit to imperfections in the very operations used to encode it. The advantage persists in the face of large added error rates and experimental calibration errors.
We propose a new scheme of measurement-based quantum computation (MBQC) using an error-correcting code against photon-loss in circuit quantum electrodynamics. We describe a specific protocol of logical single-qubit gates given by sequential cavity measurements for logical MBQC and a generalised Schrödinger cat state is used for a continuous-variable (CV) logical qubit captured in a microwave cavity. To apply an error-correcting scheme on the logical qubit, we utilise a d-dimensional quantum system called a qudit. It is assumed that a three CV-qudit entangled state is initially prepared in three jointed cavities and the microwave qudit states are individually controlled, operated, and measured through a readout resonator coupled with an ancillary superconducting qubit. We then examine a practical approach of how to create the CV-qudit cluster state via a cross-Kerr interaction induced by intermediary superconducting qubits between neighbouring cavities under the Jaynes-Cummings Hamiltonian. This approach could be scalable for building 2D logical cluster states and therefore will pave a new pathway of logical MBQC in superconducting circuits toward fault-tolerant quantum computing.