Practical and efficient experimental characterization of multiqubit stabilizer states

Greganti, Chiara; Roehsner, Marie-Christine; Barz, Stefanie; Waegell, Mordecai; Walther, Philip

doi:10.1103/physreva.91.022325

Cited by 10 publications

(13 citation statements)

References 35 publications

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“…1 provides a corresponding hierarchy of benchmarks. Lower Bounding the Fidelity:-The correlator also serves to bound the fidelity from below [34],…”

Section: Resultsmentioning

confidence: 99%

Benchmarks of nonclassicality for qubit arrays

Waegell

Dressel

2019

npj Quantum Inf

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We present a set of practical benchmarks for N -qubit arrays that economically test the fidelity of achieving multiqubit nonclassicality. The benchmarks are measurable correlators similar to 2-qubit Bell correlators, and are derived from a particular set of geometric structures from the N -qubit Pauli group. These structures prove the Greenberger-Horne-Zeilinger (GHZ) theorem, while the derived correlators witness genuine N -partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only M ≤ N +1 distinct measurement settings, as opposed to the 2 2N − 1 settings that would normally be required to tomographically verify their associated stabilizer states. We optimize the measurements of these correlators for a physical array of qubits that can be nearest-neighbor-coupled using a circuit of controlled-Z gates with constant gate depth to form N -qubit linear cluster states. We numerically simulate the provided circuits for a realistic scenario with N = 3, ..., 9 qubits, using ranges of T 1 energy relaxation times, T 2 dephasing times, and controlled-Z gate-fidelities consistent with Google's 9-qubit superconducting chip. The simulations verify the tightness of the fidelity bounds and witness nonclassicality for all nine qubits, while also showing ample room for improvement in chip performance.

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“…1 provides a corresponding hierarchy of benchmarks. Lower Bounding the Fidelity:-The correlator also serves to bound the fidelity from below [34],…”

Section: Resultsmentioning

confidence: 99%

Benchmarks of nonclassicality for qubit arrays

Waegell

Dressel

2019

npj Quantum Inf

Self Cite

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“…With regards to receive-and-measure protocols, and in particular the measurement-only protocol of Subsection 3.1, Greganti et al implemented [98] some of the elements of these protocols with a fourphoton experiment, similar to the experiment of Barz et al mentioned above [96]. This demonstration builds on previous work in the experimental characterisation of stabiliser states [99]. In this case, two four-qubit cluster states were generated: the linear cluster state and the star graph state, where in the latter case the only entanglement is between one central qubit and pairwise with every other qubit.…”

Section: Experiments and Implementationsmentioning

confidence: 91%

Verification of Quantum Computation: An Overview of Existing Approaches

2018

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Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can check whether quantum computers are indeed producing correct results. This task, known as quantum verification, has been highlighted as a significant challenge on the road to scalable quantum computing technology. We review the most significant approaches to quantum verification and compare them in terms of structure, complexity and required resources. We also comment on the use of cryptographic techniques which, for many of the presented protocols, has proven extremely useful in performing verification. Finally, we discuss issues related to fault tolerance, experimental implementations and the outlook for future protocols. arXiv:1709.06984v2 [quant-ph] 9 Jul 2018Problem 1 (Verifiability of BQP computations). Does every problem in BQP admit an interactive-proof system in which the prover is restricted to BQP computations?As mentioned, this complexity theoretic formulation of the problem was considered by Gottesman, Aaronson and Vazirani [10,11] and, in fact, Aaronson has offered a 25$ prize for its resolution [10]. While, as of yet, the question remains open, one does arrive at a positive answer through slight alterations of the 4 BPP and MA are simply the probabilistic versions of the more familiar classes P and NP. Under plausible derandomization assumptions, BPP = P and MA = NP [13]. 5 Even if this were the case, i.e. BQP ⊆ MA, for this to be useful in practice one would require that computing the witness can also be done in BQP. In fact, there are candidate problems known to be in both BQP and MA, for which computing the witness is believed to not be in BQP (a conjectured example is [17]). 6 MA can be viewed as an interactive-proof system where only one message is sent from the prover (Merlin) to the verifier (Arthur).consideration for any realistic implementation of a verification protocol. Finally, in Subsection 5.3 we outline some of the existing experimental implementations of these protocols. Throughout the review, we are assuming familiarity with the basics of quantum information theory and some elements of complexity theory. However, we provide a brief overview of these topics as well as other notions that are used in this review (such as measurement-based quantum computing) in the appendix, Section 7. Note also, that we will be referencing complexity classes such as BQP, QMA, QPIP and MIP * . Definitions for all of these are provided in Subsection 7.3 of the appendix. We begin with a short overview of blind quantum computing. Blind quantum computingThe concept of blind computing is highly relevant to quantum verification. Here, we simply give a succinct outline of the subject. For more details, see this review of blind quantum computing protocols by Fitzsimons [34] as well as [35][36][37][38][39]. Note that, while the review of Fitzsimons covers all of the material ...

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“…With regards to receive-and-measure protocols, and in particular the measurementonly protocol of Section 3.1, Greganti et al implemented [98] some of the elements of these protocols with a four-photon experiment, similar to the experiment of Barz et al mentioned above [96]. This demonstration builds on previous work in the experimental characterisation of stabiliser states [99]. In this case, two four-qubit cluster states were generated: the linear cluster state and the star graph state, where in the latter case the only entanglement is between one central qubit and pairwise with every other qubit.…”

Section: Experiments and Implementationsmentioning

confidence: 92%