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arXiv:2009.06242 · Proceedings of the National Academy of Sciences

Quantum teleportation of physical qubits into logical code spaces

Yi-Han Luo, Ming-Cheng Chen, Manuel Erhard, Han-Sen Zhong, Dian Wu, Haoyang Tang, Qi Zhao, Xi‐Lin Wang, Keisuke Fujii, Li Li, Nai-Le Liu, Kae Nemoto, William J. Munro, Chao‐Yang Lu, Anton Zeilinger, Jian-Wei Pan

Published Sep 3, 2021• 45 citations
arXivHTMLPDF

Abstract

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.

DOI
10.1073/pnas.2026250118

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Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.
Quantum state teleportation is commonly used in designs for large-scale quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we demonstrate fault-tolerant state teleportation circuits for a quantum error correction code-specifically the Steane code. The circuits use up to 30 qubits at the physical level and employ real-time quantum error correction. We conducted experiments on several variations of logical teleportation circuits using both transversal gates and lattice surgery. We measured the logical process fidelity to be 0.975 ± 0.002 for the transversal teleportation implementation and 0.851 ± 0.009 for the lattice surgery teleportation implementation as well as 0.989 ± 0.002 for an implementation of Knill-style quantum error correction.
Quantum computing relies on quantum error correction for high-fidelity logical operations, but scaling to achieve near-term quantum utility is highly resource-intensive. High-rate quantum LDPC codes can reduce error correction overhead, yet realizing high-rate fault-tolerant computation with these codes remains a central challenge. Apart of the lattice surgery approach, standard schemes for realizing logical gates have so far been restricted to performing global operations on all logical qubits at the same time. Another approach relies on low-rate code switching methods. In this work, we introduce a gate-based protocol for addressable single- and multi-qubit Clifford operations on individual logical qubits encoded within one or more quantum LDPC codes. Our scheme leverages logical transversal operations via an auxiliary Bacon-Shor code to perform logical operations with constant time overhead enabled by teleportation. We demonstrate the implementation of an overcomplete logical Clifford gate set and perform numerical simulations to evaluate the error-correction performance of our protocol. Finally, we observe that our scheme can be integrated with magic state cultivation protocols to achieve universal, gate-based, and fully addressable quantum computation.
Quantum state teleportation is commonly used in designs for large-scale fault-tolerant quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we implement the first demonstration of a fault-tolerant state teleportation circuit for a quantum error correction code - in particular, the planar topological [[7,1,3]] color code, or Steane code. The circuits use up to 30 trapped ions at the physical layer qubits and employ real-time quantum error correction - decoding mid-circuit measurement of syndromes and implementing corrections during the protocol. We conduct experiments on several variations of logical teleportation circuits using both transversal gates and lattice surgery protocols. Among the many measurements we report on, we measure the logical process fidelity of the transversal teleportation circuit to be 0.975(2) and the logical process fidelity of the lattice surgery teleportation circuit to be 0.851(9). Additionally, we run a teleportation circuit that is equivalent to Knill-style quantum error correction and measure the process fidelity to be 0.989(2).
Quantum error correction is a crucial tool for mitigating hardware errors in quantum computers by encoding logical information into multiple physical qubits. However, no single error-correcting code allows for an intrinsically fault-tolerant implementation of all the gates needed for universal quantum computing [1-3]. One way to tackle this problem is to switch between two suitable error-correcting codes, while preserving the encoded logical information, which in combination give access to a fault-tolerant universal gate set [4-6]. In this work, we present the first experimental implementation of fault-tolerant code switching between two codes. One is the seven-qubit color code [7], which features fault-tolerant CNOT and HHH quantum gates, while the other one, the 10-qubit code [8], allows for a fault-tolerant TTT-gate implementation. Together they form a complementary universal gate set. Building on essential code switching building blocks, we construct logical circuits and prepare 12 different logical states which are not accessible natively in a fault-tolerant way within a single code. Finally, we use code switching to entangle two logical qubits employing the full universal gate set in a single logical quantum circuit. Our results experimentally open up a new route towards deterministic control over logical qubits with low auxiliary qubit overhead, not relying on the probabilistic preparation of resource states.
A major goal for fault-tolerant quantum computation (FTQC) is to reduce the overhead needed for error correction. One approach is to use block codes that encode multiple qubits, which can achieve significantly higher rates for the same code distance than single-qubit code blocks or topological codes. We present a scheme for universal quantum computation using multi-qubit Calderbank-Shor-Steane (CSS) block codes, where codes admitting different transversal gates are used to achieve universality, and logical teleportation is used to move qubits between code blocks. All circuits for both computation and error correction are transversal. We also argue that single shot fault-tolerant error correction can be done in Steane syndrome extraction. Then, we present estimates of information lifetime for a few possible codes, which suggests that highly nontrivial quantum computations can be achieved at reasonable error rates, using codes that require significantly less than 100 physical qubits per logical qubit.
Abstract The development of quantum computing architectures from early designs and current noisy devices to fully fledged quantum computers hinges on achieving fault tolerance using quantum error correction1–4. However, these correction capabilities come with an overhead for performing the necessary fault-tolerant logical operations on logical qubits (qubits that are encoded in ensembles of physical qubits and protected by error-correction codes)5–8. One of the most resource-efficient ways to implement logical operations is lattice surgery9–11, where groups of physical qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here we report the experimental realization of lattice surgery between two qubits protected via a topological error-correction code in a ten-qubit ion-trap quantum information processor. In this system, we can carry out the necessary quantum non-demolition measurements through a series of local and entangling gates, as well as measurements on auxiliary qubits. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation between them. The demonstration of these operations—fundamental building blocks for quantum computation—through lattice surgery represents a step towards the efficient realization of fault-tolerant quantum computation.