We calculate spin correlation functions using IBM quantum processors, accessed online. We demonstrate the rotational invariance of the singlet state, interesting properties of the triplet states, and surprising features of a state of three entangled qubits. This exercise is ideal for remote learning and generates data with real quantum mechanical systems that are impractical to investigate in the local laboratory. Students learn a wide variety of skills, including calculation of multipartite spin correlation functions, design and analysis of quantum circuits, and remote measurement with real quantum processors.

1.
P. W.
Shor
, “
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
,”
SIAM Rev.
41
,
303
332
(
1999
).
2.
A.
Kandala
et al, “
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
,”
Nature
549
,
242
246
(
2017
).
3.
M.
Anderson
, “
Can quantum computers help us respond to the coronavirus?
,” In
Proceedings of IEEE Spectrum
, April 10,
2020
.
4.
The IBM quantum processors are accessed here: <https://quantum-computing.ibm.com/>.
5.
A.
Asfaw
et al, Learn quantum computing using qiskit, found here <https://qiskit.org/textbook/preface.html>.
6.
D.
García-Martín
and
G.
Sierra
, “
Five experimental tests on the 5-Qubit IBM quantum computer
,”
J. Appl. Math. Phys.
6
,
1460
1475
(
2018
).
7.
A. M.
Cetto
,
A.
Valdés-Hernández
, and
L.
de la Peña
, “
On the spin projection operator and the probabilistic meaning of the bipartite correlation function
,”
Found. Phys.
50
,
27
39
(
2020
).
8.
J. S.
Bell
, “
On the Einstein Podolsky Rosen paradox
,”
Phys. Phys. Fiz.
1
,
195
200
(
1964
).
9.
M. A.
Nielsen
and
I.
Chuang
,
Quantum Computation and Quantum Information
(
Cambridge U. P
.,
New York
,
2000
), see p.
74
for the Kronecker product.
10.
B.
Zygelman
,
A First Introduction to Quantum Computing and Information
(
Springer
,
Cham, Switzerland
,
2018
), see pp.
45
46
for the Kronecker product.
11.
F.
de Lima Marquezino
,
R.
Portugal
, and
C.
Lavor
,
A Primer on Quantum Computing
(
Springer
,
Cham, Switzerland
,
2019
), see p.
17
for the Kronecker product.
12.
M.
Walter
,
D.
Gross
, and
J.
Eisert
, “
Multipartite entanglement
,” in
Quantum Information: From Foundations to Quantum Technology Applications
, edited by
D.
Bruß
and
G.
Leuchs
(
Wiley-VCH Verlag GmbH & Co. KGaA
,
Weinheim, Germany
,
2019
), p.
301
.
13.
V.
Scarani
, “
Quantum computing
,”
Am. J. Phys.
66
,
956
960
(
1998
).
14.
D.
Candela
, “
Undergraduate computational physics projects on quantum computing
,”
Am. J. Phys.
83
,
688
702
(
2015
).
16.
The Qiskit notebook generating our results for |11⟩ is available at <http://www.physics.emory.edu/faculty/brody/11.ipynb>, and the notebook for the W state is available at <http://www.physics.emory.edu/faculty/brody/w.ipynb>. These notebooks should be imported at <https://quantum-computing.ibm.com/jupyter> or opened with Jupyter Notebook.
17.
M.
Beck
,
Quantum Mechanics: Theory and Experiment
(
Oxford U.P
.,
New York
,
2012
).
18.
Calibration data are shown when a backend is selected on the right side of <https://quantum-computing.ibm.com/>.
19.
A.
Smith
,
M. S.
Kim
,
F.
Pollman
, and
J.
Knolle
, “
Simulating quantum many-body dynamics on a current digital quantum computer
,”
NPJ Quantum Inf.
5
,
106
(
2019
).
20.
E.
Wilson
,
S.
Singh
, and
F.
Mueller
, “
Just-in-time quantum circuit transpilation reduces noise
,” preprint arXiv:2005.12820 (
2020
).
22.
B. K.
Kamaka
, “
Quantum transpiler optimization: On the development, implementation, and use of a quantum research testbed
,” M.S. thesis, Air Force Institute of Technology,
2020
. This thesis is available at <https://scholar.afit.edu/etd/3590>.
23.
V. V.
Shende
and
I. L.
Markov
, “
On the CNOT-cost of TOFFOLI gates
,”
Quantum Inf. Comput.
9
,
461
486
(
2009
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.