Surface codes: Towards practical large-scale quantum computation

Fowler, Austin G.; Mariantoni, M.; Martinis, John M.; Cleland, A. N.

doi:10.1103/physreva.86.032324

Cited by 2,215 publications

(2,559 citation statements)

References 197 publications

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“…Nominally, the threshold fidelity of the surface code is 0.99 [7], provided one assumes there is no leakage, the two-qubit interaction is the dominant source of error, and gates can be performed perfectly in parallel. The physical device described in this work has complex behavior outside these assumptions, necessitating a device-specific calculation of the surface code threshold fidelity.…”

Section: Verifying Experimental Fidelities Are At the Surface Code Thmentioning

confidence: 99%

“…Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code 7 is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-cycled entangling gates. The gate fidelity requirements are modest: The per-step fidelity threshold is only about 99%.…”

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confidence: 99%

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Superconducting quantum circuits at the surface code threshold for fault tolerance

Barends

Kelly

Megrant

et al. 2014

Nature

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1,577

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A quantum computer can solve hard problems -such as prime factoring 1,2 , database searching 3,4 , and quantum simulation 5 -at the cost of needing to protect fragile quantum states from error. Quantum error correction 6 provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code 7 is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-cycled entangling gates. The gate fidelity requirements are modest: The per-step fidelity threshold is only about 99%. Here, we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity up to 99.4%. This places Josephson quantum computing at the fault-tolerant threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit GreenbergerHorne-Zeilinger (GHZ) state 8,9 using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.The high fidelity performance we demonstrate here is achieved through a combination of highly coherent qubits, a straightforward interconnection architecture, and a novel implementation of the two-qubit controlled-phase (CZ) entangling gate. The CZ gate uses a fast but adiabatic frequency tuning of the qubits 10 , which is easily adjusted yet minimises decoherence and leakage from the computational basis [Martinis, J., et al., in preparation]. We note that previous demonstrations of two-qubit gates achieving better than 99% fidelity used fixed-frequency qubits: Systems based on nuclear magnetic resonance and ion traps have shown two-qubit gates with fidelities of 99.5% 11 and 99.3% 12 . Here, the tuneable nature of the qubits and their entangling gates provides, remarkably, both high fidelity and fast control.Superconducting integrated circuits give flexibility in building quantum systems due to the macroscopic nature of the electron condensate. As shown in Fig. 1, we have designed a processor consisting of five Xmon qubits with nearestneighbour coupling, arranged in a linear array. The crossshaped qubit 14 offers a nodal approach to connectivity while maintaining a high level of coherence (see Supplementary Information for decoherence times). Here, the four legs of the cross allow for a natural segmentation of the design into coupling, control and readout. We chose a modest inter-qubit capacitive coupling strength of g/2π = 30 MHz and use alternating qubit idle frequencies of 5.5 and 4.7 GHz, enabling a CZ gate in 40 ns when two qubits are brough...

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Section: Verifying Experimental Fidelities Are At the Surface Code Thmentioning

confidence: 99%

mentioning

confidence: 99%

Superconducting quantum circuits at the surface code threshold for fault tolerance

Barends

Kelly

Megrant

et al. 2014

Nature

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1,577

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“…The surface code architecture [24,25,28] is a measurement-based scheme for quantum computation. It uses projective measurements of commuting operators-called "stabilizers"-acting on a 2D array of physical qubits to produce a highly entangled "code state" jψi.…”

Section: Majorana Surface Codementioning

confidence: 99%

“…The random measurement of an operator in the surface code corresponds to nucleating pairs of anyons, a process that can be reliably measured by tracking the eigenvalues of the commuting stabilizers. Reliable error detection hinges on having (i) a large number of physical qubits for a given encoded logical qubit and (ii) a sufficiently low error rate for stabilizer measurements [28]. For the previously studied surface code with bosonic physical qubits, it has been estimated [59,60] that below a threshold as high as 1% error rate per physical qubit operation, scaling the size of the surface code permits an exponential suppression of errors propagated.…”

Section: Majorana Surface Codementioning

confidence: 99%

“…In the surface code, measurements of nontrivial commuting operators (stabilizers) are used to project onto a "code state," and logical qubits are effectively encoded in the anyon charge of a region by ceasing certain stabilizer measurements [26][27][28][29]. The logical gates necessary for universal quantum computation are realized through sequences of measurements used to move and braid the logical qubits.…”

Section: Introductionmentioning

confidence: 99%

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Majorana Fermion Surface Code for Universal Quantum Computation

2015

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We introduce an exactly solvable model of interacting Majorana fermions realizing Z 2 topological order with a Z 2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.

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Quantum Memory

Bashkansky¹,

Black²,

Kwolek³

et al. 2021

Wiley Encyclopedia of Electrical and Electronics Engineering

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Quantum Memory (QM) commonly refers to a system that reversibly transfers quantum states between a material storage system and a propagating electromagnetic field. It represents a key component in quantum information science and technology. Over the past 25 years, a wide range of theoretical protocols and experimental approaches to QM has been studied. These include optical delays, mechanical resonators, topological approaches, solid state spins, trapped single atoms and ions, and atomic ensembles. New applications of QM are being investigated and discovered all the time, including quantum computation, long‐distance entanglement distribution, quantum teleportation, and long‐distance quantum key distribution. Challenges to the implementation of QM include inefficiencies in storing and recovering the quantum state, and decoherence, which usually manifests by environment‐induced dephasing. In this monograph we describe, in general terms, methods and protocols that are used in many forms of QM. We also discuss the various experimental systems in which QM has been demonstrated or proposed. Additionally, we discuss the applications of QM that have been identified and progress made in implementing those applications.

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Surface codes: Towards practical large-scale quantum computation

Cited by 2,215 publications

References 197 publications

Superconducting quantum circuits at the surface code threshold for fault tolerance

Superconducting quantum circuits at the surface code threshold for fault tolerance

Majorana Fermion Surface Code for Universal Quantum Computation

Quantum Memory

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