A universal programmable Gaussian Boson Sampler for drug discovery Shang Yu1 2 3 4 Zhi-Peng Zhong1Yuhua Fang5Raj B. Patel2Qing-Peng Li1Wei Liu3 4Zhenghao Li2 Liang Xu1Steven Sagona-Stophel2Ewan Mer2Sarah E. Thomas2Yu Meng3 4Zhi-Peng Li3 4Yuan-Ze

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A universal programmable Gaussian Boson Sampler for drug discovery

Shang Yu∗,1, 2, 3, 4, †Zhi-Peng Zhong∗,1Yuhua Fang∗,5Raj B. Patel,2, ‡Qing-Peng Li,1Wei Liu,3, 4 Zhenghao Li,2

Liang Xu,1Steven Sagona-Stophel,2Ewan Mer,2Sarah E. Thomas,2Yu Meng,3, 4 Zhi-Peng Li,3, 4 Yuan-Ze

Yang,3, 4 Zhao-An Wang,3, 4 Nai-Jie Guo,3, 4 Wen-Hao Zhang,3, 4 Geoﬀrey K Tranmer,5Ying Dong,1Yi-Tao

Wang,3, 4, §Jian-Shun Tang,3, 4, 6, ¶Chuan-Feng Li,3, 4, 6, ∗∗ Ian A. Walmsley,2and Guang-Can Guo3, 4, 6

1Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou, 310000, People’s Republic of China

2Quantum Optics and Laser Science, Blackett Laboratory,

Imperial College London, Prince Consort Rd, London SW7 2AZ, United Kingdom

3CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China

4CAS Center For Excellence in Quantum Information and Quantum Physics,

University of Science and Technology of China, Hefei, 230026, China

5College of Pharmacy, Faculty of Health Science,

University of Manitoba, Winnipeg, MB R3E 0T6, Canada

6Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

Gaussian Boson Sampling (GBS) has the potential to solve complex graph problems, such as

clique-ﬁnding, which is relevant to drug discovery tasks. However, realizing the full beneﬁts of

quantum enhancements requires a large-scale quantum hardware with universal programmability.

Here, we have developed a time-bin encoded GBS photonic quantum processor that is universal,

programmable, and software-scalable. Our processor features freely adjustable squeezing parameters

and can implement arbitrary unitary operations with a programmable interferometer. Leveraging

our processor, we successfully executed clique-ﬁnding on a 32-node graph, achieving approximately

twice the success probability compared to classical sampling. Additionally, we established a versatile

quantum drug discovery platform using this GBS processor, enabling molecular docking and RNA

folding prediction tasks. Our work achieves the state-of-the-art in GBS circuitry with its distinctive

universal and programmable architecture which advances GBS towards real-world applications.

Quantum computing technology has developed rapidly

in recent years [1–5, 8, 9], and an exponential “speed-

up” compared to classical methods has been experimen-

tally demonstrated for certain algorithms [4, 6–9]. Quan-

tum sampling tasks, like boson sampling [10–12], have

proven to be challenging to solve on classical computers

within a reasonable time frame, but can be implemented

and solved eﬃciently on photonic processors [1, 13]. As

a variant of boson sampling, Gaussian Boson sampling

(GBS) [14] uses squeezed light as the input states mak-

ing it easier to scale and therefore shows great capacity to

demonstrate quantum advantage in optical systems [8, 9].

The prospect of achieving quantum advantage has mo-

tivated the discovery of several real-world applications,

such as dense graph searching [15, 16], molecular vibronic

spectra calculations [5, 17], and molecular docking [18].

In these tasks, a GBS device should be programmable

and scalable to a large number of modes [5, 8]. How-

ever, it is a challenging task [16] due to the experimental

complexity involved in preparing a large number of in-

dividually addressable input states and phase-shifters to

achieve universal programmability [5, 8].

Time-bin encoding of Gaussian states is an eﬀective

means of achieving scale and programmability [9, 16, 19–

21]. First, it is resource eﬃcient where only one squeezed

source and one detector are required [16]. Second, time-

∗These authors contributed equally to this work

bin operation provides phase stability and exhibits com-

parable losses with other approaches [22]. Furthermore,

time-bin interferometers shows ﬂexibility in reconﬁgura-

tion since it can realize arbitrary-dimension linear trans-

formations with the same setup. Recently, quantum

computational advantage with a programmable time-bin-

encoded GBS [9] machine has been demonstrated albeit

whilst sacriﬁcing universality to avoid the accumulation

of loss.

This prompts us to consider a universal and pro-

grammable time-bin GBS machine that can fulﬁll var-

ious practical tasks. Besides, the GBS algorithm can

potentially be applied to many important problems and

enhance their performance, for example, the complete

subgraph (clique) ﬁnding task [23, 24]. Some structural-

based drug design methods, like molecular docking or

protein folding prediction, can be interpreted as such a

problem of ﬁnding the maximum weighted clique in their

corresponding graph models [18, 25, 26]. This indicates

that a universal programmable GBS machine equipped

with freely adjustable squeezers and interferometer can

be utilized for the above tasks and extend the range of

practical applications based on graph theory. Inspired

by this prospect, we built a scalable, universal, and pro-

grammable time-bin GBS machine in this work, and

make a signiﬁcant stride towards using GBS in drug dis-

covery applications.

Programmable GBS machine and sampling results—

The GBS machine shown in Fig. 1, called Abacus, can

be divided into four main parts which we now describe.

arXiv:2210.14877v3 [quant-ph] 7 Mar 2024

SLM

ppKTP

waveguide

EOM0

EOM2 EOM1

EOMa

EOMb

AOM

spatial

reshaper

to detector from QPU

SNSPDs

trigger signal

PBS HWP mirror lens

RAP CL coupler

filtergratingBS

≈7.5m delayline

encoding graphs into GBS

A=αG+βI

graph G

decomposition

unitary

operation U

squeezing

parameters ri

signal send

to EOM0

signal

send to

EOM 1, 2

......

signal send

to EOM0

objective

lens

0.0

2.5

5.0

7.5

×10-3

Norm. probability ( )

10.0

7.5

5.0

2.5

0250 500 750 1000 1250

1820 output distributions, from {1,2,3,4}, {1,2,3,5},...to {13,14,15,16}

1500 1750

Experiment

Theory

0.0

4.0

6.0

8.0

2.0

4.0

6.0

×10-3

Norm. probability ( )

2.0

8.0

0 100 200 300 400 500

496 output distributions, from {1,2}, {2,3},...to {31,32}

Experiment

Theory

22 23

Weight of six-node cliques

0.15

0.10

0.05

0.00

Probabilities

7.957.587.216.846.696.576.325.83

FIG. 1: a, Universal programmable time-bin encoded GBS machine. The GBS machine consists of four main parts:

(1) Squeezed state preparation, (2) Quantum processing unit, (3) Quantum sequential access memory (QuSAM), and (4)

Detection. The control system including three arbitrary wave generators is omitted for clarity. Abbreviations: PBS: polar-

ization beam splitter, HWP: half-wave plate, RAP: right-angle prism mirrors, RF: roof prism mirror, CL: cylindrical lens,

BS: beam splitter. See Methods and Supplementary Information for details. band c, Gaussian boson sampling results

b, Probability distribution of all 496 two-photon detection events in a 32-mode experiment. c, Probability distribution of

all 1820 four-photon detection events in a 16-mode experiment. The horizontal axis labels output distributions in increasing

order {(1,2),(1,3),...,(31,32)}or {(1,2,3,4),(1,2,3,5),...,(13,14,15,16)}from left to right d, Finding the maximum

weighted clique in a 32-node graph. The normalized average probabilities of the six-node cliques in the graph G32 is shown

at the bottom with the corresponding graph shown above. Labels beside the nodes denote the corresponding order, and the

weight of the nodes is represented by their size. The probabilities are calculated from ten individual experiments each with

around 300 samples. The bars represent the GBS experimental results, and the squares are the corresponding classical uniform

sampling data. Evidently, the maximum weighted clique can be found with higher success probability by using GBS machine

(shown as the red bar). The error-bars are obtained from standard deviations.

(1) Tunable squeezed state source. The pump light from

a mode-locked pulsed laser (80MHz, 773nm, ∼150 fs) is

reduced in repetition rate to 40 MHz by an acoustic-

optic modulator (AOM). The electro-optic modulator

(EOM0) and PBS are used to adjust the pump energy

of each pulse. This controls the squeezing degree (ri) of

the squeezed vacuum states in each time-bin. The spec-

tral mode of the pump light is modulated by a spatial

light modulator (SLM), two gratings and cylindrical lens

(CL). Then, spectrally uncorrelated two-mode squeezed

light can be generated by pumping the periodically poled

KTP (ppKTP) waveguide [27–29]. Following interference

at a 50:50 beamsplitter (BS), a series of individually ad-

dressable single-mode squeezed states (SMSSs) can be

eﬃciently prepared [30]. (2) Quantum processing unit.

The SMSSs are then sent into a time-bin interferometer,

which is programmed for a speciﬁc unitary operation.

This is achieved according to Clements’ architecture [31],

which is realized by a group of Mach-Zehnder interferom-

eters (MZIs) consists of two fast optical switches EOMa

and EOMb, a 7.5 m delay line (to combine or sepa-

rate two adjacent time bins), and a linear transforma-

tion T(θ, φ) achieved by EOM1 and EOM2. Since the

optical path before and after T(θ, φ) pass through the

same low-loss free-space delay line, the phase stability of

the setup is well guaranteed, and the non-uniform loss

expected in the ﬁber-loop scheme [32] is mitigated. (3)

Quantum sequential access memory (QuSAM). In each

loop of evolution, the quantum memory is achieved by

a 180-meter-long optical ﬁbre delay line. The QuSAM

ensures that the last time-bin has completed the opera-

tion in one cycle before the ﬁrst time bin enters into next

cycle. With a 4f beam-shaper system, we can eﬃciently

couple the light from free space into single-mode optical

ﬁber, and realize a low-loss time-bin memory (with total

eﬃciency of ≈94%) by reshaping the spatial mode of

the beam. (4) Detection module. The experiment is re-

quired to be run with collision-free detections. After the

linear transformation, the photonic time-bin modes are

sent into superconducting nanowire single photon detec-

tor (SNSPDs), and the output photons on each time-bin

can be measured.

As illustrated in Fig. 1(a), this time-bin encoded GBS

machine enables us to expand the number of modes arbi-

trarily, and freely set the required squeezing parameters

and linear transformation matrix for the tasks with a se-

ries of EOMs. Thus, this universal and programmable

architecture supports arbitrary GBS circuits to be run

on this machine. As a concrete example, beneﬁting from

these merits, the adjacency matrix Aof a graph Gcan

be encoded into this GBS machine by decomposing L(A)

(Laplacian of graph G) after a suitable rescaling, as shown

in the inset of Fig. 1(a).

The validation of Abacus can be demonstrated by the

sampling results from two random GBS circuits with dif-

ferent dimensions. The normalized photon sampling dis-

tribution probabilities are shown in Fig. 1(b) and (c). In

Fig. 1(b), a 32-mode random interferometer is chosen,

and only four squeezers are turned on (r1−3,32 = 2.23)

here. The statistical results of all two-photon detec-

tion events are plotted, and the total variation distance

(TVD) between experimental and theoretical results is

0.054. Similarly, the four-photon distribution pattern is

shown in Fig. 1(c), which is carried out on a 16-mode

GBS with all 16 squeezers turned on and rmax = 1.8

(here, TVD is 0.175). We also use the modiﬁed likeli-

hood ratio test introduced in [33] to exclude the thermal

state and distinguishable photon hypotheses, and these

details can be found in Supplementary Information II.G.

These show that Abacus can perform the sampling tasks

with high ﬁdelity.

Finding the maximum weighted clique with GBS—Not

only can GBS be used to demonstrate quantum advan-

tage in the laboratory [8, 9], as a near-term speciﬁc-

function quantum computer, it can also be used in solv-

ing certain problems in real-world applications. Here, we

ﬁrst use Abacus to solve the max clique decision prob-

lems, which are NP-hard problems in graph theory, and

plays a crucial role in many applications [25].

Clique refers to all the maximal complete subgraphs

in a graph G, and clique-ﬁnding is a problem with a

complexity which scales exponentially with the number

of nodes. Here, we use Abacus to ﬁnd the maximum

weighted clique in a graph. A 32-node weighted graph

G32 is artiﬁcially constructed here (details are shown in

Supplementary Information IV), and the essential step is

encoding G32 onto our GBS machine. Using the method

introduced in Ref. [18, 24], we perform Takagi-Autonne

decomposition to the Laplacian of graph Gwith appro-

priate re-scaling, and obtain the unitary operation U

and squeezing parameters riwhich are required to be

programmed on the GBS (see the Methods for details).

Then, we control the AOM chopper with an arbitrary

waveform generator (AWG) to pump the ppKTP waveg-

uide with 32 sequential pulses. EOM0 is used to adjust

rifor each time-bin, and U, the unitary operation, is

achieved by adjusting the input voltages of EOM1 and

EOM2 in the time-bin interferometer. After the map-

ping G32 onto Abacus, around 300 ﬁve-(or more)-photon

sampling results are then collected in each experiment.

Using these sampling data, we can ﬁnd the cliques with

nodes corresponding to the 30-time post-processed sam-

pling results (see details in Methods). Fig. 1(d) dis-

plays all six-node cliques and their corresponding prob-

abilities. The maximum weighted clique stands out as

the most probable among them. In comparison to clas-

sical sampling with the same post-processing iterations,

GBS demonstrates a signiﬁcantly higher probability of

successfully ﬁnding the maximum weighted clique, ap-

proximately twice as much. This indicates that GBS can

perform the clique-ﬁnding task with high eﬃciency [18].

Molecular docking with GBS —If the graph is con-

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AuniversalprogrammableGaussianBosonSamplerfordrugdiscoveryShangYu∗,1,2,3,4,†Zhi-PengZhong∗,1YuhuaFang∗,5RajB.Patel,2,‡Qing-PengLi,1WeiLiu,3,4ZhenghaoLi,2LiangXu,1StevenSagona-Stophel,2EwanMer,2SarahE.Thomas,2YuMeng,3,4Zhi-PengLi,3,4Yuan-ZeYang,3,4Zhao-AnWang,3,4Nai-JieGuo,3,4Wen-HaoZhang,3,4Geoffrey...

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A universal programmable Gaussian Boson Sampler for drug discovery Shang Yu1 2 3 4 Zhi-Peng Zhong1Yuhua Fang5Raj B. Patel2Qing-Peng Li1Wei Liu3 4Zhenghao Li2 Liang Xu1Steven Sagona-Stophel2Ewan Mer2Sarah E. Thomas2Yu Meng3 4Zhi-Peng Li3 4Yuan-Ze.pdf

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A universal programmable Gaussian Boson Sampler for drug discovery Shang Yu1 2 3 4 Zhi-Peng Zhong1Yuhua Fang5Raj B. Patel2Qing-Peng Li1Wei Liu3 4Zhenghao Li2 Liang Xu1Steven Sagona-Stophel2Ewan Mer2Sarah E. Thomas2Yu Meng3 4Zhi-Peng Li3 4Yuan-Ze

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