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Performing Quantum Computing Experiments in the Cloud

Simon J. Devitt

arXiv:1605.05709v4quant-ph

TL;DR

Four protocols had not previously been demonstrated on an active quantum processor. The authors implemented them using IBM’s five-qubit cloud-accessible chip, and obtained intended, theory-consistent results despite noise and low fidelity.

  • Problem

    The paper addresses the lack of demonstrations of these four protocols on an active quantum processor.

    Source: §IV · p. 11

  • Method

    The authors designed, simulated, and implemented four quantum-information protocols on IBM’s five-qubit cloud chip, treating the interface as a black box.

    Source: §I · p. 1

  • Results

    All four protocols produced results consistent with theory and intended outputs, though fidelity was low and noise affected experiments to differing degrees.

    Source: §I · p. 1, §III · p. 11

  • Takeaways & Limitations

    The Quantum Experience makes investigation of small quantum protocols straightforward, and the authors hope their work encourages wider access to online hardware.

    Source: §IV · p. 11

    The authors did not perform rigorous error analysis, and experiments varied in their susceptibility to noise.

    Source: §III · p. 11

Abstract

from arXiv · show

Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated by many, the first realisation of quantum computing technology would occur over the cloud, with users logging onto dedicated hardware over the classical internet. Recently IBM has released the {\em Quantum Experience} which allows users to access a five qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments that have never been demonstrated before. We utilise the IBM chip to realise protocols in Quantum Error Correction, Quantum Arithmetic, Quantum graph theory and Fault-tolerant quantum computation, by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage development in quantum information technology.

I. INTRODUCTION

After earlier cloud access to a two-qubit optical chip supported few quantum-computing experiments, IBM’s five-qubit Quantum Experience offered reprogrammable circuit design, simulation, testing, and execution. The paper used the platform as a black box to implement four quantum-information protocols, which returned theory-consistent intended outputs at low fidelity.

I. INTRODUCTION

  • IBM’s five-qubit reprogrammable platform expanded on Bristol’s two-qubit cloud chip, which supported few quantum-computing experiments.The Quantum Experience enabled circuit design, simulation, testing, and execution on a physical device.Source: §I · p. 1
  • The authors independently designed and ran four protocols on IBM’s Quantum Experience, treating its website, interface, and chip as a black box.The protocols address error correction, quantum arithmetic, quantum graph theory, and fault-tolerant circuit design.Source: §I · p. 1
  • Each protocol returned results consistent with theory and its intended output, but at low fidelity.The experiments used the chip’s simple output, with simulations and experimental data compared for each protocol.Source: §I · p. 1

II. RESULTS

The results section reports four cloud-based quantum experiments spanning encoded Rabi oscillations, Fourier addition, five-qubit graph complementarity, and T-gate correction. It describes their observed outputs and the QE interface limitation that leaves T-gate verification correct only 75% of the time under ideal conditions.

Error Corrected Rabi Oscillations

  • Post-selection restored nonzero visibility in encoded Rabi oscillations, but the error-corrected experiment did not outperform a bare-qubit run.The simulator showed improvement over the uncorrected circuit but overestimated chip performance; circuit complexity and limited control prevented fault-tolerant operation.Source: Figure 3 · p. 3, §II · p. 3

Fourier Addition

  • For most tested inputs, Fourier addition returned the correct output as a plurality, but the target-register Bell-state input did not yield an inferable correct answer.Each register had two qubits, so addition was modulo 2; simulations and experiments were averaged over 8192 runs.Source: §II · pp. 3–4, Figure 5 · p. 5

Deterministic T-Gates

  • Selective source and destination teleportation make T-gate corrections deterministic by routing measurement-dependent corrections into X- or Z-basis choices.The hardware test emulated T or T†, tracked Pauli corrections, and reversed the input circuit; without circuit errors, the final X-basis measurement should return |0⟩.Source: §II · pp. 8–9

Local Complementarity in Quantum Graph States

  • Five-qubit local complementarity transformed a star graph to a fully connected graph and then to a star with a different center, with measured stabilizer parities matching expectations.Some parities flipped during the operations, but appropriate Pauli operations could reverse them; the small circuit produced nearly 100% probability of correct parity.Source: §II · p. 7, Figure 9 · p. 8, Figure 10 · p. 9

II. RESULTS

  • After Pauli correction, the ideal circuit yields the correct result only 75% of the time because the QE interface cannot dynamically feed forward teleportation measurement outcomes.An X-correction can interfere with the final T† gate; in an operating computer, those measurement results must be known before applying the next gate, and corrections may also arise from error correction [4] or topological information tracking [37].Source: §II · pp. 9–10
  • Using T instead of T† to invert the original gate reverses the probability distribution, while dynamically adapting the circuit would restore a 100% probability of measuring |0⟩.The approximately 3%-probability outputs have X-corrections that interfere with the final HT† gate; Figure 18 marks outputs that yield |0⟩ after Pauli correction and tracking.Source: §II · p. 10
  • The experiment demonstrates why T-depth matters [35]: without dynamic circuit changes, measurement-dependent corrections prevent a fully deterministic T-gate, even when a circuit appears to have T-depth one [7].With dynamic changes available in the QE interface, the authors could demonstrate a fully deterministic T-gate.Source: §II · p. 10

III. DISCUSSION

The discussion reports expected outcomes across all four experiments despite differing noise sensitivity, but does not analyze chip noise in detail. The deterministic T-gate result highlights the need for an up-to-date Pauli frame.

III. DISCUSSION

  • Detailed comparison of experiment outputs with characterized chip errors is left as future work to refine simulation models.The QE interface makes error data for each run available.Source: §III · p. 11
  • All four experiments produced expected results, but only the error-correction Rabi experiment showed significant deviation between simulation and experiment.The authors did not conduct significant analysis of individual qubit or gate error behavior.Source: §III · p. 11
  • The deterministic T-gate results illustrate the importance of maintaining a real-time, up-to-date Pauli frame when programming a quantum device.Source: §III · p. 11

IV. CONCLUSIONS

The authors ran four cloud-based experiments on the IBM QE chip across quantum error correction, arithmetic, graph theory, and fault-tolerant circuit design. The chip returned noisy but expected results, and its accessible interface supports investigation of small quantum protocols.

IV. CONCLUSIONS

  • Four experiments on the IBM QE chip demonstrated protocols in error correction, quantum arithmetic, quantum graph theory, and fault-tolerant circuit design.The authors describe these protocols as not previously achievable with an active quantum processor.Source: §IV · p. 11
  • The cloud interface supported specifying and testing protocols in ideal and simulated-error cases before running them on hardware for noisy but expected results.Source: §IV · p. 11
  • The five-qubit processor showed flexibility across a large class of quantum information protocols, while higher fidelities and more qubits may support further small-scale protocols.Source: §IV · p. 12

VI. SUPPLEMENTARY MATERIAL

The supplementary material provides raw experiment data and additional experiments for each protocol.

VI. SUPPLEMENTARY MATERIAL

  • The supplementary material contains raw data for the main-text experiments and additional experiments for each protocol.Source: §VI · p. 18

VII. ERROR CORRECTED RABI OSCILLATIONS.

The supplementary discussion explains how the distance-two surface-code Rabi experiment relates to phase errors and the |+, −⟩ basis. Its proposed logical-Hadamard circuit differs by swapping qubits 2 and 4, and the resulting experiment is expected to match the results already shown.

VII. ERROR CORRECTED RABI OSCILLATIONS.

  • To examine phase errors, the supplementary discussion proposes a Rabi oscillation in the |+, −⟩ basis using a logical Hadamard and logical measurement in that basis.Source: §VII · p. 18
  • For the symmetric planar distance-two code, a logical Hadamard uses transversal Hadamards on all five qubits and swaps qubits 2 and 4.Source: §VII · p. 18
  • The |+, −⟩-basis Rabi circuit matches the previously described circuit apart from swapping qubits 2 and 4, because the logical X operator is X2X4.Source: §VII · p. 18
  • A direct |+, −⟩-basis Rabi experiment is expected to produce results identical to those already shown.Source: §VII · p. 18
  • Rabi experiments in rotated bases would require future interface support for arbitrary rotations, either through added gates or more circuit space and fidelity.Source: §VII · p. 18

VIII. FOURIER ADDITION

Most Fourier addition circuits returned correct results as the most frequent outcome, though some produced substantial competing incorrect outcomes. The supplementary figures cover additional binary and superposition inputs.

VIII. FOURIER ADDITION

  • Additional figures show other binary inputs and more complex superposition inputs, with correct results marked in red.Not all experiments returned the correct results.Source: §VIII · p. 18
  • Most Fourier addition circuits returned the correct result as the most frequent outcome, but some had non-answers as the second most probable output.In a few cases, only half of the wavefunction was concentrated in the dominant result.Source: §VIII · p. 18
  • QE simulations were omitted because their overlap was much better than in the error-corrected Rabi experiments and showed effectively the same behavior as the main-text results.Source: §VIII · p. 18

IX. QUANTUM GRAPH COMPLEMENTARITY

This experiment examines two permutations of a five-qubit loop graph, selected from a larger class of non-locally-equivalent graphs. Increased circuit complexity brought more noise, and the K4 stabiliser for the first permutation did not produce the correct output.

IX. QUANTUM GRAPH COMPLEMENTARITY

  • The study focuses on two permutations of a five-qubit loop graph rather than simulating the larger class of non-locally-equivalent graphs.Source: §IX · p. 18
  • The permutations apply G = √X5√Z4 and G = √X3√Z4, with the initial loop graph built using the QE circuit.The three graphs and their stabilisers are illustrated in Figure 29; the circuit is shown in Figure 28.Source: §IX · p. 18
  • The first graph permutation's K4 stabiliser did not produce the correct output, amid noisier measurements attributed to the more complex circuits.Measurements for each stabiliser and graph are shown in Figures 30–32.Source: §IX · p. 18
  • Calibration data are provided for this second graph-complementarity experiment and for the star-graph experiment in the main text.Source: §IX · p. 18

X. DETERMINISTIC T-GATE

This section does not elaborate on the deterministic T-gate experiment; it provides IBM calibration data associated with the main-text results.

X. DETERMINISTIC T-GATE

  • The section limits its coverage to IBM calibration data for the deterministic T-gate experiment reported in the main text.Source: §X · p. 18, Figure 35 · p. 29
  • No further elaboration of the experiment is provided in this section.Source: §X · p. 18
  • Figure 35 is identified as calibration data from the IBM machine for the deterministic T-gate experiment.Source: §X · p. 18, Figure 35 · p. 29
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