
frigerants has proven challenging due to trade-offs in key
molecular properties such as global warming potential and
ozone depletion potential, whilst also considering other prop-
erties such as toxicity, flammability, and stability. As such,
molecular simulations have become increasingly used for in-
vestigating the structure-activity relationship of candidate
refrigerants [19]. As a test case, we consider methane (CH4)
and its reaction with the hydroxyl radical (OH·),
CH4+ OH·→[CH·
3—H—OH]‡→CH·
3+ H2O.(1)
CH4’s atmospheric properties have been thoroughly studied
[20] and can provide guidelines in the application of quantum
computers for search of new environment-friendly refriger-
ants. In order to characterise this process, one also needs to
calculate a series of energies corresponding to the products,
methyl radical (CH·
3) and water (H2O). To estimate the re-
action barrier that governs the kinetics of the reaction, we
also simulate the transition state, [CH·
3—H—OH]‡.
In Section II, we give a detailed overview combining exci-
tation filtering based on Z2symmetries, hard-core Boson
representation, and favourable two-qubit gate cancellation
(via Pauli-gadget synthesis scheme of Ref. [21]). Section III
is devoted to the results obtained with our state-preparation
strategy on System Model H1, powered by Honeywell. We
focus on the resource reduction, and consider noisy calcu-
lations for CH4’s optical spectra. Finally, we complete our
investigation with a simulation of [CH·
3—H—OH]‡and other
reaction participants. We also apply symmetry verification
to our calculations [22]. The two symmetry verification tech-
niques we use are Partition Measurement Symmetry Veri-
fication (PMSV) and Mid-circuit Measurement Symmetry
Verification (MMSV) [23].
1 Methods
1.1 Chemically Aware Unitary Coupled
Cluster
For our state-preparation strategy, we use Jordan-Wigner
Encoding (JWE) to map Trotterised Fermionic exponents
to Pauli operators acting on qubits [24, 25]. We refer to the
by-product sequence of Pauli-Zoperations as JWE-strings,
which consequently increase the effective k-locality of UCC
exponents. Our spin orbitals and therefore the qubit reg-
ister have alpha-beta ordering (each even-odd indexed spin
orbital corresponds to a spatial orbital). Appendix A has
more information on the UCC state-preparation method and
conventional circuit decompositions (Individual and Com-
muting Sets synthesis). The steps of the chemically aware
strategy are as follows:
I. Symmetry Filtering: Filter the set of excitations com-
posing the ansatz via use of molecular symmetry to identify
forbidden terms. We used two techniques:
(a) Defining Z2symmetries to check commutation
against the UCC excitation operators [26, 27, 17];
(b) A point group symmetry filtering method for CCSD
adapted to be used for UCCSD [28].
II. Spatial Orbital to Spatial Orbital: There are three
steps to compactly describe a pair of electrons excited be-
tween spatial orbitals. For this method, we necessarily
change the ordering of the excitations to benefit from the
two-qubit gate savings associated with spatial to spatial
UCC excitation.
(a) Specify Double Occupied Spatial Orbitals:
Only doubly occupied (|1i) and virtual spatial
orbitals (|0i) are considered. For example, the
Hartree-Fock state |111000idefining molecular spin
orbital occupation, would be processed to return
|100iin the molecular spatial orbital occupation.
These occupations are mapped to the even-indexed
qubits on the circuit, |100000i. Single occupied spa-
tial orbitals are ignored.
(b) Hard-core Boson Representation: Operations
that excite a pair electrons from and to the same
spatial orbital can be synthesised more efficiently.
These excitations are of the type:
ˆa†
2pˆa2qˆa†
2p+1ˆa2q+1 −h.c., (2)
where q < p, and both variables track the spatial
orbital index. Applying JWE results in 8 unique
Pauli exponents over 4-qubits.
These excitations lack JWE-strings, signifying zero
parity exchange as these adjacent electrons hop be-
tween different spatial orbitals. It can be seen that
these excitations act on spin-orbitals, but excite and
de-excite electrons between spatial orbitals. These
adjacent electrons travel together, yet cannot oc-
cupy the same spatial orbital with another pair of
electrons. Equation 2 can also be expressed as,
ˆ
b†
pˆ
bq−h.c., (3)
where ˆ
bdenotes a Hard-core Bosonic operation.
Eq. 3 can be re-expressed by using the equiva-
lence between Hard-core Bosons and Pauli opera-
tions [29, 30],
1j
2nˆ
Yqˆ
Xp−ˆ
Xqˆ
Ypo.(4)
We relabel the indices of equation 4 from p→2p
and q→2q. Each of these spatial orbital to spatial
orbital excitations act on 2 qubits and require 2 two-
qubit gates.
(c) Introduce Spin Orbitals: We apply two-qubit
gates on relevant even-odd qubits. Each even-
indexed qubit corresponds to the alpha spin-orbital
of a spatial orbital, and similarly each beta spin-
orbital is represented by an odd-indexed qubit 3.
single occupation of a spatial orbital is included by
initializing the relevant alpha-index qubit to the |1i
state.
III. Commuting sets of Pauli strings: The remaining
double and single excitations are synthesised. Each double
excitation contains 8 Pauli-sub terms and these terms natu-
rally form a commuting set. We synthesise these excitations
in commuting sets with tket, resulting in 14 two-qubit gates
2