Chemically Aware Unitary Coupled Cluster with ab initio Calculations on System Model H1 A Refrigerant Chemicals Application

2025-04-30 1 0 1.33MB 12 页 10玖币
侵权投诉
Chemically Aware Unitary Coupled Cluster with ab initio
Calculations on System Model H1: A Refrigerant Chemicals’
Application
October 27, 2022
I. T. Khan, M. Tudorovskaya, J. J. M. Kirsopp, D. Mu˜
noz Ramo
Quantinuum, Terrington House, 13–15 Hills Road, Cambridge CB2 1NL, United Kingdom
P. Warrier, D. K. Papanastasiou, R. Singh
Honeywell Advanced Materials, 20 Peabody St, Buffalo, NY 14210, United States
Abstract
Circuit depth reduction is of critical importance for quantum chemistry simulations on current and near
term quantum computers. This issue is tackled by introducing a chemically aware strategy for the Unitary
Coupled Cluster ansatz. The objective is to use the chemical description of a system to aid in the synthesis
of a quantum circuit. We combine this approach with two flavours of Symmetry Verification for the
reduction of experimental noise. These method enable the use of System Model H1 for a 6-qubit Quantum
Subspace Expansion calculation. We present (i) calculations to obtain methane’s optical spectra; (ii) an
atmospheric gas reaction simulation involving [CH·
3— H — OH]. Using our chemically aware unitary
coupled cluster state-preparation strategy in tandem with state of the art symmetry verification methods,
we improve device yield for CH4at 6-qubits. This is demonstrated by a 90% improvement in two-qubit
gate count and reduction in relative error to 0.2% for electronic energy calculated on System Model H1.
Keywords: Quantum Computation ·Unitary Coupled Cluster ·UV/ VIS Spectra ·Quantum Subspace Expansion
The simulation of molecules and materials using quantum
chemistry methods is a well established field, with applica-
tions in many scientific and industrial areas of interest [1].
However, there is awareness about the shortcomings of per-
forming these simulations on classical machines [2]. The
main workhorse of classical simulations, Density Functional
Theory, fails to capture the qualitative behaviour of chemi-
cals with strong correlation [3]. One naturally turns to wave
function methods, such as Hartree-Fock (HF), Coupled Clus-
ter (CC) theory and Configuration Interaction (CI) methods.
However, the steep memory requirements of these techniques
have limited their practicality in the study of complex chem-
icals. This issue also plagues classical excited state heuris-
tics that provide CI- or CCSD-like accuracy. For instance,
Equation of Motion Coupled Cluster (EOM-CCSD) scales
as O(N6), where Nis the number of spin orbitals [4].
Quantum computers provide an alternative path to enable
the use of wave function methods on problems of practical
interest. In particular, two state of the art algorithms have
been proposed, the Variational Quantum Eigensolver (VQE)
and Quantum Subspace Expansion (QSE) algorithms, as the
earliest candidates for scalable alternatives to classical wave
function methods [5, 6, 7]. VQE approximates the ground-
state of a Hamiltonian variationally, and QSE estimates ex-
cited states non-variationally. Despite the rapid develop-
ment and deployment of quantum resources, progress has
been limited due to quantum hardware being unable to meet
performance requirements of these algorithms. Neverthe-
less, the exploration of quantum computing applications for
chemistry is necessary for the progression of computational
chemistry, and also serve as important benchmarks for to-
day’s hardware and its relevance to the chemicals industry.
Quantum algorithms for chemistry require a large amount
of quantum resources for the state-preparation component of
these simulations. Broadly, two families of state-preparation
methods have been introduced in literature: Unitary Cou-
pled Cluster (UCC), and hardware-efficient ans¨atze. With
UCC, the number of variational circuit parameters and the
2-qubit gate depth scale as O(N4), leading to circuits beyond
the capability of today’s machines [8]. Hardware-efficient
methods require less coherent resources, but suffer from the
“barren plateau” problem [9]. Initial effort has been focused
on improving the 2-qubit depth scaling for the UCC ansatz.
Notably, adaptive methods [10], circuit recompilation [11],
and unique UCC circuit synthesis approaches [12]. Adaptive
methods are unattractive. For example, ADAPT-VQE re-
quires additional measurements on top of regular VQE [13].
This encourages us to explore a unique UCC circuit synthesis
approach that improved the 2-qubit gate count by describing
Fermionic UCC spatial orbital to spatial orbital excitations
as hard-core Bosonic operators [14, 15, 16]. In tandem, there
has been additional work on discarding UCC excitations by
using symmetry filtering as a priori [17, 18], also resulting in
lower two-qubit gate count.
One particular example where quantum computing can help
is the simulation of refrigerants. The design of novel re-
arXiv:2210.14834v1 [quant-ph] 26 Oct 2022
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
bqh.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
Xpˆ
Xqˆ
Ypo.(4)
We relabel the indices of equation 4 from p2p
and q2q. 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
Fig. 1. Schematic showing three major steps of the chemically aware ucc state-preparation strategy. Step (i) uses symmetry as a
priori to discard excitations. Step (ii) is a compact synthesis scheme for spatial to spatial excitations. Step (iii) uses tket to
synthesise generic double and single excitations by commuting sets to maximize pauli-string cancellation. Each single or double
UCC excitation is naturally a commuting set of Pauli-strings.
at best. Increasing the length of JWE-strings increases the
number of two-qubit gates for the corresponding decompo-
sition. Circuits for single fermionic excitations contain at
minimum four two-qubit gates and act over 3 qubits. Both
two-qubit gate count and number of qubits grow as the num-
ber of Pauli-Zstrings increase.
2 Results
All the circuits in this paper are prepared using Quantin-
uum’s quantum chemistry package InQuanto [31, 32]. The
integrals to obtain the relevant chemistry Hamiltonians were
obtained using an InQuanto extension to the open-source
chemistry software package, PySCF, known as InQuanto-
PySCF [33]. InQuanto provides the tools provide the pre- &
post-processing logic to perform quantum computation, and
more importantly to map the results from quantum com-
putation back to the Chemistry problem. The UCC state-
preparation techniques used in this paper are available in
InQuanto. NGLView is used to visualize chemical struc-
tures and molecular orbitals via an InQuanto interface. We
use the open-source ADCC library to compute benchmark
optical spectra data at ADC-2 level of theory, [34].
For this investigation, we used system model H1 devices and
emulators [35, 36]. The IBMQ qasm simulator was used to
perform noiseless state-vector calculations, simulations with
finite sampling noise and zero quantum noise. We use tket to
synthesise, optimize and retarget quantum circuits to enable
execution on a H1 hardware [37, 38].
All our benchmark calculation are non-variational operator
averaging calculations (Hamiltonian Averaging or QSE). The
ground-state parameters for our state-preparation circuits
are obtained via a noiseless VQE qasm simulation.
2.1 Improvements due to the Chemically
Aware Strategy
We investigate the two-qubit gate count across three differ-
ent methods, chemically aware, commuting sets, and indi-
vidual UCCSD synthesis. We use CH4at equilibrium geom-
etry as a benchmark system, alongside the D2point group
to describe the molecular orbital symmetry [39]. Fig. 2a
reports an improvement by approximately 81% (commuting
sets) and 95% (individual) in two-qubit gate count for var-
ious active-spaces ranging from 4 qubits to 18 qubits. By
neglecting symmetry (C1point group), we reduce the effi-
cacy of chemically aware to reduce two-qubit gate count,
rendering only a small improvement due to the compact
spatial-orbital-only excitation synthesis. Fig. 2b does not
report any improvement in overall scaling with chemically
aware compared to commuting sets synthesis for CH4with
C1symmetry.
ADAPT-VQE improves upon individual synthesis by iter-
atively constructing a compact ansatz. At the cost of in-
creasing the total number of measurements, ADAPT dis-
cards both symmetry-forbidden and minimally contributing
symmetry-allowed excitations. As a consequence, ADAPT
circuits have a lower two-qubit gate count. With the chem-
3
摘要:

ChemicallyAwareUnitaryCoupledClusterwithabinitioCalculationsonSystemModelH1:ARefrigerantChemicals'ApplicationOctober27,2022I.T.Khan,M.Tudorovskaya,J.J.M.Kirsopp,D.Mu~nozRamoQuantinuum,TerringtonHouse,13{15HillsRoad,CambridgeCB21NL,UnitedKingdomP.Warrier,D.K.Papanastasiou,R.SinghHoneywellAdvancedMate...

收起<<
Chemically Aware Unitary Coupled Cluster with ab initio Calculations on System Model H1 A Refrigerant Chemicals Application.pdf

共12页,预览3页

还剩页未读, 继续阅读

声明:本站为文档C2C交易模式,即用户上传的文档直接被用户下载,本站只是中间服务平台,本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私,请立即通知玖贝云文库,我们立即给予删除!
分类:图书资源 价格:10玖币 属性:12 页 大小:1.33MB 格式:PDF 时间:2025-04-30

开通VIP享超值会员特权

  • 多端同步记录
  • 高速下载文档
  • 免费文档工具
  • 分享文档赚钱
  • 每日登录抽奖
  • 优质衍生服务
/ 12
客服
关注