Scalable and Robust Randomized Benchmarking of Quantum Processes

Magesan, Easwar; Gambetta, Jay; Emerson, Joseph

doi:10.1103/physrevlett.106.180504

Cited by 682 publications

(810 citation statements)

References 30 publications

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“…First, there is a key point to emphasize regarding the zeroth and first order fitting models. As depicted in [25] there exist physically relevant noise models for which when the true value of the depolarization fidelity parameter p is used, the first order model fits the experimental data much better than the zeroth order model. However, it may be the case that a least squares fitting procedure using the functional form of the zeroth order model produces a very good fit to the experimental data, albeit producing an incorrect value for p. Therefore in order to obtain a more accurate value for p one should always use the first order fitting model unless prior knowledge of the noise indicates that it is effectively gate-independent.…”

Section: Discussionmentioning

confidence: 99%

“…The fitting formula shows that gatedependent errors can lead to a deviation from the exponential decay (defining a partial test for such effects in the noise), which was illustrated via numerical examples in [25]. State-preparation and measurement errors appear as independent fit parameters in the fitting models and we discuss when the protocol is robust against these errors.…”

Section: Introductionmentioning

confidence: 93%

“…In this section we present both the protocol and a full derivation of the fitting models for randomized benchmarking that were given in [25]. First, we set some notation and make various definitions that will be used throughout the presentation.…”

Section: Randomized Benchmarkingmentioning

confidence: 99%

“…In this paper we give a full analysis of the scalable multi-qubit randomized benchmarking protocol for Clifford gates we proposed in [25] which overcomes the shortcomings described above. We note that since one "gate" in the single-qubit protocol of [26] consists of a random Clifford generator as well as a random Pauli operator, the cost of implementing a gate in this scheme is 2.…”

Section: Introductionmentioning

confidence: 99%

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Characterizing quantum gates via randomized benchmarking

Gambetta²,

2012

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We describe and expand upon the scalable randomized benchmarking protocol proposed in Phys. Rev. Lett. 106, 180504 (2011) which provides a method for benchmarking quantum gates and estimating the gate-dependence of the noise. The protocol allows the noise to have weak time and gate-dependence, and we provide a sufficient condition for the applicability of the protocol in terms of the average variation of the noise. We discuss how state preparation and measurement errors are taken into account and provide a complete proof of the scalability of the protocol. We establish a connection in special cases between the error rate provided by this protocol and the error strength measured using the diamond norm distance.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

Section: Randomized Benchmarkingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Characterizing quantum gates via randomized benchmarking

Gambetta²,

2012

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“…In randomised benchmarking, a logic gate is characterised by measuring its performance when interleaved with many random sequences of gates, making the measured fidelity resilient to state preparation and measurement (SPAM) errors. We perform a control experiment on a ground-state qubit by: I) generating a random sequence of m Cliffords, II) appending the unique recovery Clifford (C r ) that makes the ideal sequence the identity, and III) averaging the experimental sequence fidelity, the final ground state population, over k different sequences 18,19 …”

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confidence: 99%

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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Randomized Benchmarking of Quantum Gates on a GPU

Zawad

Yan

et al. 2019

16th International Conference on Information Technology-New Generations (ITNG 2019)

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Scalable and Robust Randomized Benchmarking of Quantum Processes

Cited by 682 publications

References 30 publications

Characterizing quantum gates via randomized benchmarking

Characterizing quantum gates via randomized benchmarking

Superconducting quantum circuits at the surface code threshold for fault tolerance

Randomized Benchmarking of Quantum Gates on a GPU

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