Testing quantum foundations with quantum computers

Letter
Open Access

Testing quantum foundations with quantum computers

Simanraj Sadana, Lorenzo Maccone, and Urbasi Sinha

Phys. Rev. Research 4, L022001 – Published 1 April 2022

Abstract

We present two complementary viewpoints for combining quantum computers and the foundations of quantum mechanics. On the one hand, ideal devices can be used as test beds for experimental tests of the foundations of quantum mechanics: We provide algorithms for the Peres test for complex numbers in quantum superpositions and the Sorkin test of Born's rule. On the other hand, noisy intermediate-scale quantum devices can be benchmarked using these same tests. These are deep quantum benchmarks based on the foundations of quantum theory itself. We present test data from Rigetti hardware.

Received 28 November 2021
Accepted 23 February 2022

DOI:https://doi.org/10.1103/PhysRevResearch.4.L022001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum benchmarking Quantum computation Quantum foundations Quantum simulation

Superconducting qubits

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Simanraj Sadana¹, Lorenzo Maccone², and Urbasi Sinha ^1,*

¹Light and Matter Physics, Raman Research Institute, Bengaluru-560080, India
²Dipartimento di Fisica and INFN Sezione di Pavia, University of Pavia, via Bassi 6, I-27100 Pavia, Italy

^*usinha@rri.res.in

Article Text

Click to Expand

References

Click to Expand

Issue

Vol. 4, Iss. 2 — April - June 2022

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Graphical depiction of the algorithm to calculate the $γ$ factor of (7) by creating and projecting superpositions of arbitrary states. The states are created from unitary rotations $R_{ℓ} (λ)$ of an angle $λ$ around the $ℓ$ axis, with $a_{k} = cos θ_{k} / 2$ , $b_{k} = sin θ_{k} / 2$ , followed by a cnot gate and a rotation by angle $- θ_{m}$ for desired projection. For example, to project on $α | 01 〉 + β | 10 〉$ , choose $θ_{m} = 2 {cos}^{- 1} α$ and record the counts of $| 01 〉$ . The unentangled projections ${| 〈 01 | ψ_{1} ψ_{2} 〉 |}^{2}$ , etc., that are necessary for the $γ$ 's can be measured by a similar circuit where the cnot gate and the single-qubit rotation at the end are removed.
Reuse & Permissions
Figure 2
Plots of the $γ_{12}$ and of $F$ for different sets of (uniformly distributed) random states. The green circles are the measured outputs on a Rigetti Aspen-9 device, the blue stars are the (ideal) quantum prediction from Rigetti's quantum virtual machine (QVM), and the red diamonds are the quantum prediction that takes into account the systematic noise sources (the noise parameters are obtained from Rigetti's own calibration data). Most $γ$ values are different from $\pm 1$ , which implies that a real Hilbert space is insufficient. The values of $F$ are all smaller than 1, but they are all statistically compatible with the value corrected by taking into account the readout and dephasing errors in the hardware (as explained in the main text). None of the values of $F$ are outside the interval $[- 1, 1]$ , so the superposition principle is not violated.
Reuse & Permissions
Figure 3
Sorkin-test circuits. (a) Circuit to prepare arbitrary three-level states (14): $R_{ℓ} (λ)$ represents a rotation around the $ℓ$ axis by an angle $λ$ . (b) Complete circuit that includes also the measurements. The parameters $t_{1}$ and $t_{2}$ are used to select the different measurements. For example, the projection onto $| 00 〉 + | 10 〉 + | 11 〉$ discussed in the text is obtained by choosing $t_{1} = 2 {cos}^{- 1} (1 / \sqrt{3})$ , $t_{2} = 2 {cos}^{- 1} (1 / \sqrt{2})$ .
Reuse & Permissions
Figure 4
Plot of $κ_{3}$ of Eq. (11) of the Sorkin test for randomly chosen states performed using the circuit of Fig. 3. All obtained values are compatible with the theoretical value $κ_{3} = 0$ expected from standard quantum mechanics. The error bars are produced using the same method as in the case of the Peres test in Fig. 2.
Reuse & Permissions
Figure 5
Results of the joint Peres and Sorkin test using the same set of states and circuits for both. The data acquired to perform the Sorkin test in this case were sufficient to perform the Peres test, and therefore the same data set is used to plot both $κ_{3}$ and $F$ . The results of the joint Peres-Sorkin test are consistent with theoretical expectations, taking into account the readout and dephasing errors present in the system. These results are also consistent with the results of the standalone versions of the Peres test and the Sorkin test shown in Figs. 2 and 4 (the values are, however, different because the set of random states used in each case is different).
Reuse & Permissions

Physical Review Research