14-Qubit Entanglement: Creation and Coherence

Monz, Thomas; Schindler, Philipp; Barreiro, Julio T.; Chwalla, M.; Nigg, Daniel; Coish, W. A.; Harlander, Maximilian; Hänsel, Wolfgang; Hennrich, Markus; Blatt, R.

doi:10.1103/physrevlett.106.130506

Cited by 1,102 publications

(1,212 citation statements)

References 22 publications

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“…It is interesting to note that the ratio of the off-diagonal to diagonal amplitudes |ρ |0 ⊗N ,|1 ⊗N | 2 /ρ |0 ⊗N ,|0 ⊗N ρ |1 ⊗N ,|1 ⊗N have the values 0.99, 0.98, 0.99 and 0.99, suggesting that dephasing is small and/or uncorrelated. The five-qubit GHZ state is the largest multi-qubit entanglement demonstrated to date in the solid state 8,9 , with state fidelity similar to results obtained in ion traps 27 . This demonstrates that complex quantum states can be constructed with high fidelity in a modular fashion, highlighting the potential for more intricate algorithms on this multi-purpose quantum processor.…”

supporting

confidence: 64%

Superconducting quantum circuits at the surface code threshold for fault tolerance

Barends

Kelly

Megrant

et al. 2014

Nature

1,634

1,785

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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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supporting

confidence: 64%

Superconducting quantum circuits at the surface code threshold for fault tolerance

Barends

Kelly

Megrant

et al. 2014

Nature

1,634

1,785

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“…Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1][2][3][4][5][6][7][8][9][10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11,12], and very recently in large atomic ensembles [13][14][15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state.…”

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confidence: 99%

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

McConnell

Zhang

et al. 2015

Nature

215

218

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Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1][2][3][4][5][6][7][8][9][10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11,12], and very recently in large atomic ensembles [13][14][15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. This is the first time a negative Wigner function or the mutual entanglement of virtually all atoms have been attained in an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.Entanglement is now recognized as a resource for secure communication, quantum information processing, and precision measurements. An important goal is the creation of entangled states of many-particle systems while retaining the ability to characterize the quantum state and validate entanglement. Entanglement can be verified in a variety of ways, with one of the strictest criteria being a negative-valued Wigner function [16,17], that necessarily implies that the entangled state has a non-Gaussian wavefunction. To date, the metrologically useful spin-squeezed states[1-10] have been produced in large ensembles. These states have Gaussian spin distributions and therefore can largely be modeled as systems with a classical source of spin noise, where quantum mechanics enters only to set the amount of Gaussian noise. Non-Gaussian states with a negative Wigner function, however, are manifestly non-classical, since the Wigner function as a quasiprobability function must remain nonnegative in the classical realm. While prior to this work a negative Wigner function had not been attained for atomic ensembles, in the optical domain, a negativevalued Wigner function has very recently been measured for states with up to 110 microwave photons [18]. Another entanglement measure is the entanglement depth [19], i.e. the minimum number of atoms that are demonstrably, but possibly weakly, entangled with one another. This paramete...

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“…The limits of two common noise channels are instructive: the symmetric depolarizing channel converges to a completely mixed state, and the amplitude damping channel causes decay toward the ground state. We note that, though we do not do so in this study, it is also possible include the effects of correlated noise 33,34 , which can lead to a faster total decay known as superdecoherence.…”

Section: Background and Methods 21 Environmental Noise In Quantum CImentioning

confidence: 99%

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

Sawaya

Smelyanskiy

McClean

et al. 2016

J. Chem. Theory Comput.

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Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHi PSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated eighteen 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure- * To whom correspondence should be addressed † Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA ‡ Parallel Computing Lab, Intel Corporation, Santa Clara, CA 95054, USA ¶ Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.

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14-Qubit Entanglement: Creation and Coherence

Cited by 1,102 publications

References 22 publications

Superconducting quantum circuits at the surface code threshold for fault tolerance

Superconducting quantum circuits at the surface code threshold for fault tolerance

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

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