Fault-tolerant quantum error detection

Linke, Norbert; Gutiérrez, Mauricio; Landsman, K. A.; Figgatt, Caroline; Debnath, Shantanu; Brown, Kenneth R.; Monroe, Christopher

doi:10.1126/sciadv.1701074

Cited by 166 publications

(147 citation statements)

References 38 publications

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“…Recently, the question of what constitutes a minimal experimental demonstration of fault-tolerance was considered [13]. Fault-tolerant state preparation was demonstrated soon thereafter using a quantum error detecting code with trapped atomic ions [14]. Here we go beyond that result, implementing fault-tolerant state preparation on a superconducting qubit system with supporting evidence including quantum state tomography of prepared codewords, acceptance and logical error probabilities with and without error insertion, and analysis of the measured logical observables under free evolution.…”

mentioning

confidence: 99%

Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits

Takita¹,

Cross²,

Córcoles³

et al. 2017

Phys. Rev. Lett.

207

163

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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 faulttolerant 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 codewords 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.The possibility of robust quantum computation rests on the fact that quantum information can be encoded in degrees of freedom that are difficult for local noise processes to change. Quantum codes with this potential have been demonstrated in many physical systems [1][2][3][4][5][6][7][8][9][10]. To make practical use of these codes, however, it is necessary not only to encode, decode, and observe errors, but to compute with faulty and inaccurate operations in a way that does not spread errors. The well-developed theory of fault-tolerant quantum computing reveals a steep experimental path toward this goal [11,12]. Recently, the question of what constitutes a minimal experimental demonstration of fault-tolerance was considered [13]. Fault-tolerant state preparation was demonstrated soon thereafter using a quantum error detecting code with trapped atomic ions [14]. Here we go beyond that result, implementing fault-tolerant state preparation on a superconducting qubit system with supporting evidence including quantum state tomography of prepared codewords, acceptance and logical error probabilities with and without error insertion, and analysis of the measured logical observables under free evolution.We implement one of the smallest quantum codes, a four qubit code encoding two qubits [15], and characterize output states produced by fault-tolerant state preparation circuits. The circuits are fault-tolerant for only one of the two encoded qubits, which allows direct comparison of their error rates. The circuits are applied in a five-qubit transmon device with nearest-neighbor connectivity. This device is a nontrivial subset of a surface code lattice in the sense that it provides resources for detection of any single-qubit error. Although the connectivity and size places limits on the set of fault-tolerant circuits we can implement on the four-qubit code, we can use stabilizer measurements to prepare codewords in a way that is analogous to surface code state preparation.Four qubit code -The four-qubit code [15] encodes two logical qubits into four physical qubits and can detect any error that acts on one of those physical qubits. It...

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mentioning

confidence: 99%

Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits

Takita¹,

Cross²,

Córcoles³

et al. 2017

Phys. Rev. Lett.

207

163

View full text Add to dashboard Cite

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“…Note that the use of magnetic clock transitions [119,130], decoherence free subspaces [131], or sympathetic cooling ions [129] during computation has been observed to increase the T 2 coherence times of the qubits to the order of seconds. A 5-qubit system that has implemented small quantum algorithms [17] and the 4, 2, 2  error detection code [62] with hyperfine qubits exhibits a T 2 * of ≈0.5 s [47], but further magnetic field stabilization could improve this as shown in [129] which exhibits over a 10 minute coherence time for trapped 171 Yb + ions.…”

Section: Single Error Source Dominant Effectsmentioning

confidence: 99%

“…This current error rate is well above the reported pseudothreshold for the surface-17 code, but gates with a 99.9% fidelity shown in two-ion experiments [51] are, in principle, achievable in larger chains with appropriate control to handle the more complex mode structure [57,58]. The two-ion gates simulated in this paper to determine the gate times have, in principle, fidelities of 99.99%.Atomic ion experiments have already demonstrated classical error correction [59, 60], encoding logical states for quantum error correction [61], and fault-tolerant quantum error detection [62]. In addition, multiple theoretical studies have examined implementation of quantum error correcting codes with trapped ions.…”

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confidence: 97%

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Simulating the performance of a distance-3 surface code in a linear ion trap

Trout

Gutiérrez

et al. 2018

New J. Phys.

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We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171 Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. Measurement of the ion state by fluorescence requires that the ancilla qubits be physically separated from the data qubits to avoid errors on the data due to scattered photons. We minimize the time required to measure one round of stabilizers by optimizing the mapping of the two-dimensional surface code to the linear chain of ions. We develop a physically motivated Pauli error model that allows for fast simulation and captures the key sources of noise in an ion trap quantum computer including gate imperfections and ion heating. Our simulations showed a consistent requirement of a two-qubit gate fidelity of 99.9% for the logical memory to have a better fidelity than physical two-qubit operations. Finally, we perform an analysis of the error subsets from the importance sampling method used to bound the logical error rates to gain insight into which error sources are particularly detrimental to error correction.

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“…While further improvements can come from more carefully engineering the qubit systems to remove undesired noise sources and reduce the number of decoherence channels, achieving fault tolerance will still require some form of quantum error correction (QEC). Recent developments include both theoretical proposals for more powerful QEC protocols [6] and experimental attempts at correcting or detecting quantum errors [7][8][9][10]. Despite these advances, we have rarely seen experiments yielding better error rate of the error-corrected qubit than the best single qubit in the same system [11].…”

Section: Introductionmentioning

confidence: 99%

Protecting solid-state spins from a strongly coupled environment

et al. 2018

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Quantum memories are critical for solid-state quantum computing devices and a good quantum memory requires both long storage time and fast read/write operations. A promising system is the nitrogen-vacancy (NV) center in diamond, where the NV electronic spin serves as the computing qubit and a nearby nuclear spin as the memory qubit. Previous works used remote, weakly coupled 13 C nuclear spins, trading read/write speed for long storage time. Here we focus instead on the intrinsic strongly coupled 14 N nuclear spin. We first quantitatively understand its decoherence mechanism, identifying as its source the electronic spin that acts as a quantum fluctuator. We then propose a scheme to protect the quantum memory from the fluctuating noise by applying dynamical decoupling on the environment itself. We demonstrate a factor of 3 enhancement of the storage time in a proofof-principle experiment, showing the potential for a quantum memory that combines fast operation with long coherence time.

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Fault-tolerant quantum error detection

Abstract: We show the fault-tolerant encoding, measurement, and operation of a logical qubit via quantum error detection.

Cited by 166 publications

References 38 publications

Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits

Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits

Simulating the performance of a distance-3 surface code in a linear ion trap

Protecting solid-state spins from a strongly coupled environment

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