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arXiv:cond-mat/0701469

Fault-tolerant superconducting qubit

Mateusz Cholascinski, Yuriy Makhlin, Gerd Schön

Published Jan 19, 2007• 0 citations
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Abstract

We describe a qubit encoded in continuous quantum variables of an rf superconducting quantum interference device. Since the number of accessible states in the system is infinite, we may protect its two-dimensional subspace from small errors introduced by the interaction with the environment and during manipulations. We show how to prepare the fault-tolerant state and manipulate the system. The discussed operations suffice to perform quantum computation on the encoded state, syndrome extraction, and quantum error correction. We also comment on the physical sources of errors and possible imperfections while manipulating the system.

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We describe a qubit encoded in continuous quantum variables of an rf superconducting quantum interference device. Since the number of accessible states in the system is infinite, we may protect its two-dimensional subspace from small errors introduced by the interaction with the environment and during manipulations. We show how to prepare the fault-tolerant state and manipulate the system. The discussed operations suffice to perform quantum computation on the encoded state, syndrome extraction, and quantum error correction. We also comment on the physical sources of errors and possible imperfections while manipulating the system.
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit superconducting transmon device and demonstrate fault-tolerant state preparation. We characterize the resulting code words through quantum process tomography and study the free evolution of the logical observables. Our results are consistent with fault-tolerant state preparation in a protected qubit subspace.
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.
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. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant 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.
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimentally demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6% and a Clifford gate error of 0.3% after error correction. Additionally, we prepare magic states with fidelities exceeding the distillation threshold, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant operation. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.
The implementation of large-scale fault-tolerant quantum computers calls for the integration of millions of physical qubits with very low error rates. This outstanding engineering challenge may benefit from emerging qubits that are protected from dominating noise sources in the qubits' environment. In addition to different noise reduction techniques, protective approaches typically encode qubits in global or local decoherence-free subspaces, or in dynamical sweet spots of driven systems. We exemplify such protected qubits by reviewing the state-of-art in protected solid-state qubits based on semiconductors, superconductors, and hybrid devices.