KEK素核研物構研 連携研究会 2024
KEK, March 25, 2024

Quantum Computing and Qubit Technology
Development for Particle Physics

ICEPP, The University of Tokyo

Koji Terashi

1Quantum Computing
Quantum computing will offer an intriguing path for paradigm
changes in computational science
A quantum state of an isolated qubit as a complex unit vectoriγiϕ| ψ⟩ = e (cos(θ/2) | 0⟩ + e sin(θ/2) | 1⟩)• Global phase e irrelevant for measurementiϕ• Relative phase e as a unique property in quantum
iγ

| ψ⟩

…

| ψ⟩ → U | ψ⟩ =: | ϕ⟩

0
q1

qn−1

U

…

Unitary operation to transform a quantum state of closed qubit systemnn• n-qubit Unitary operation ➔ 2 × 2 matrix multiplication
n+1• Number of dof’s = 2 − 2
q

| ϕ⟩
2

Quantum Superposition
Superposition as an example
n-qubit register

| 0⟩

| 0⟩

1

2n−1

n

Equal superposition state of 2 computational| x⟩n∑basis states{ | 0⟩, | 1⟩, ⋯, | 2 − 1⟩}
2n
x=0

n

H

⊗n

x

y

10 qubits ➞ 1000 states
50 qubits ➞ 1000 trillion states
300 qubits ➞ states of the number of

all atoms in the UniverseUfxy ⊕ f(x)

1

2n−1

∑
n
2 x=0

| x⟩ | f(x)⟩A single unitary operation, acting as
Uf : | x⟩ | y⟩ → | x⟩ | y ⊕ f(x)⟩, will allow us
to calculate f(x) for all x′s simultaneously(though all f(x) values cannot be obtained )3

Quantum Computational SciencennnQuantum computation as a (gigantic) 2 × 2 matrix multiplication to 2 -dimensional
complex vector
E.g, 64-bit floating-point number / dof

n
32
∼ 48
16
Memory ∼ 1 MiB ∼ 1 TiB 4.85 PiB (Fugaku)

Such gigantic matrix-vector multiplications ubiquitous in simulating quantum
many-body phenomena, which is classically intractable
Prototypical problems in Quantum Chemistry, Condensed Matter Physics andParticle Physics

Realizing quantum advantage for certain problems in these fields— Significant (exponential in some cases) speed up in numerical calculations
over classical counterpart
4

Particle Physics
Fundamental physics to understand properties/dynamics
of elementary particles and nuclear matters
Governedbygauge
theory
U(1)
×
SU(2)
×
SU(3)
‣
Quantum Field Theory (QFT) at cores in HEP theories
Quantum computer may offer advantages:
Simulationofreal-time
dynamics,
matterproperties‣
at finite temperature/density, …
Speed
up
in
some
computational
processing
time‣(e.g, reconstruction, event generation)
5

Qubit Technology as a Sensor
Certain types of qubits work as a probe to nature

Quantum Sensor

What quantum system can work as a quantum sensor?
1. Identified, discretized energy levels (usually 2-levels)
2. Initialization and measurement
3. Coherent manipulation of state
4. Can couple to what we want to measure (e.g, electric/magnetic field, ..)Utilizing sensor response,
e.g, qubit transition energy E or rate Γ,
to what we want to measure

Qubit technologies can offer interesting opportunities to experimentallyprobe nature in different ways from conventional methods
6Outline

Partial review of ICEPP activities on quantum computational scienceand qubit-technology experiment for particle physics

Quantum
machinelearningonclassical/quantum
HEP
data
‣
Quantum
simulationinlatticegauge
theory‣Darkmattersearchwithsuperconducting
qubits‣7

Preparation of Quantum States
Quite often want to produce some desired quantum state, e.g, ground state ofa given Hamiltonian
Hamiltonian H in a diagonal form with eigenvalues λi and eigenvectors | ψi⟩ :

H=

N

∑

λi | ψi⟩⟨ψi |⟨ψi | ψj⟩ = 0 ∀i ≠ j

i=1

For an arbitrary state | ψ⟩,⟨ψ | H | ψ⟩ =

N

∑

2

λi | ⟨ψi | ψ⟩ | ≥ λmin (= smallest-energy eigenvalue)i=1

Equality holds if| ψ⟩ = | ψmin⟩

If one can take | ψ⟩ to be as close as possible to | ψmin⟩,

λmin can be well approximated by ⟨ψ | H | ψ⟩

But how?

8

State Preparation with Variational Method
Strategy:|ψ⟩Consideracertaininitial
state
0
‣

Z
Y
Rj (θj2)Rj (θj1)
Parameterized unitary, e.g, U(θ) =
∏
j

|
|
|
ψ(θ)⟩
=
U(θ)
ψ
⟩
ψ
⟩
Generate
a
trial
state
by
applyingaunitary
to
U(θ)
0
0
‣
|
|
λ(θ)
:=
⟨ψ(θ)
H
ψ(θ)⟩
Calculate
‣
λ(θ)
θ
Find
the
smallest
value
of
by
varyingtheparameter‣θ → θ*
Quantumλ(θ*) = ⟨ψ(θ*) | H | ψ(θ*)⟩ ∼ ⟨ψmin | H | ψmin⟩ = λmin
Classical

Quantum-Classical hybrid algorithm

Find optimized parameter θ* by repeating
the calculation of λ(θ) using quantum
computer and parameter update usingclassical computer9Quantum Machine Learning
State preparation/manipulation is a central task in quantum machine learning
Learning classical data x
E.g, images, digitized detector signals

Quantum Neural Network

ρ(x)

U(θ)

…

U(x)

…

…

c

| 0⟩

c
cv

c

Classification, Regression10Equivariant Quantum Machine Learning

Zhelun Li (PD)

Symmetry often provides a useful resource in machine learninge.g, Convolution for translational symmetry

Symmetryubiquitousinphysics,e.g,
Lorentzsymmetry,
Permutation
symmetry,…
‣‣ Not obvious to incorporate general (continuous) symmetries in quantum setting

Investigate a generic QNN architecture to efficiently encode rotational
and permutational symmetries‣ Inner products as inputs (e.g, inner products of particle 4-vectors)→ Weyl’s theorem‣ Twirling method to make quantum gates invariant against input permutation→ L. Schatzki et al., npj Quantum Inf. 10, 12 (2024)11

Equivariant Quantum Machine Learning

Fully symmetric circuit• Rotations handled by dot products• Permutations handled by twirling.

Fully symmetric circuit
Rotationshandledbyinnerproducts‣‣ Permutations handled by twirling

Zhelun Li (PD)Particle decay

Better performances with less parameters.
Requires the use of non-linearity;• The usual technique of measuring a subset of qubits won’t work.
• Need an non-linearity that respects the symmetry.
Particle decay
2
We use an ad-hoc one: ℒ(θ, b) = ( f(θ, b) − y) = ( − | fQ(θ) −•Lorentz symmetry in particle decays.

H → ZZ → 4-leptons classification asa benchmark• SO(3+1).
• Typically useful in High energy particle classification.
• Found in many state of the art classical ML algorithms.
• Hard to convolute but easy to take inner products.

14‣ Lorentz symmetry in particle decay
Reconstructed
Higgs
mass
to
be
‣

permutation invariant
Ad-hocnon-linearity
after
quantum‣
measurement:L(θ, b) = [− | fQ(θ) − b | − y]202More details in write-up under preparation 12
21

Barren Plateau
Hilbert space grows exponentially in number of qubits
Known that the training of variational quantum algorithm (parameterized quantum circuit)generally becomes difficult with the system size
J. R. McClean et al., Nat. Commun. 9, 4812 (2018)

Cost function†

C(θ) = tr[OU(θ)ρU (θ)]

C(θ)

∂C(θ)
Eθ∼uniform=0[ ∂θi ]∂C(θ)−nVθ∼uniform= 𝒪(b )[ ∂θi ](b > 1)

Vanishing gradientNqubits

Barren Plateau (BP) problem
13

Barren Plateau from Data Encoding
Learning classical data requires the data to firstencode into quantum state
Quantum Neural Network
E.g, images, digitized detector signals

ρ(x)

UQNN

…

U(x)

…

…

c

| 0⟩

c
cv

c

14

Barren Plateau from Data Encoding 問題設定
はじめに

Kensuke Kamisoyama (M2)

量子コンピューター
変分量子アルゴリ
ズム

Learning classical data requires the data to firstencode into quantum state
量子機械学習バレンプラトー

研究概要

Examine how data-encoding unitary U(x)can cause BP with BP-free QNN circuit
方法と結果
まとめ
補足

以下の定理 [Cerezo et al., 2021] を解析に用いた。

Theoremθν は、上の図で h 番目のブロックに含まれるパラメータ(h)は、 ρi = Trh [ρi ] と最大混合状態の間の Hilbert Schm

きる。

(h)
s
Varθ [∂θν ℓi (θ) ] = rn,s × DHS ( ρi , I/2

上曽山 健介, 永野 廉人, 寺師 弘二 (東京大学)

量子機械学習におけるデータ符号化回路の構造と勾配消失の関係

15

Barren Plateau from Data Encoding 問題設定
はじめに

Kensuke Kamisoyama (M2)

量子コンピューター
変分量子アルゴリ
ズム

Learning classical data requires the data to firstencode into quantum state
量子機械学習バレンプラトーはじめに
研究概要

量子コンピューター

Examine how data-encoding unitary U(x)can cause BP with BP-free QNN circuit
方法と結果

変分量子アルゴリ
ズム

まとめ

量子機械学習補足
バレンプラトー

研究概要

Analytically evaluate the gradient of cost function
using Hilbert-Schmidt distance
方法と結果

回路の構造
2 用いた回路の構造

まとめ

9/14
補足

2 結果: 層数の設定

上限が量子ビット数に対して指数関数的に落ちないための以下の定理 [Cerezo et al., 2021] を解析に用いた。

9/14
Theorem

(h)
s
Var
[∂
dU
D
(ρ
,
𝕀/2
)
!θ sℒ(θ)] ≤(h)(h) Af s× rn,s ×θHSx(D(ρHSDHS (ρx , I/2 ) は、下図の各青色ゲートブロックがユニタリ
2 デザイン
U DHS, I/2Uνx) dU
は、下図の各青色ゲートブロックがユニタリ
2 デザインx :=∫𝕌θは、上の図でh
番目のブロックに含まれるパラメータνxになると仮定)

ー

(h)
は、
ρ
=
Tr
[ρ
]
と最大混合状態の間のHilbertSchmiihRandomTensor Network
Integrator(RTNI)[Fukuda
et al.,D2019]
を用いて、DHS を解析
or Network
Integrator(RTNI)[Fukuda
et al.,
2019] を用いて、HS を解析

Derived necessary condition on data的に計算した。その際、入力回路(x) に次の二つの構造を仮定した:。その際、入力回路
U (x) に次の二つの構造を仮定した:
encoding
unitaryU to
avoid Barren
Plateau

きる。

(h)sVarθ [∂θν ℓi (θ) ] = rn,s × DHS ( ρi , I/2

上曽山 健介, 永野 廉人, 寺師 弘二 (東京大学)

量子機械学習におけるデータ符号化回路の構造と勾配消失の関係

α, γ > 0 β > 1

ALT

ALT

MPS

MPS

D̄HS ≥ β

−L

≥ n

−γ

γ
L ≤
log n
( log β ) 16

Learning Quantum Data
Directly learn quantum states without classical measurement, e.g,
Extract
entanglement
properties
ofaquantum
system‣Determineclassical
parametersthat
controlaphysical
system(e.g,
Hamiltonianparameters)‣
E.g, quantum state from another quantum system

Quantum sensor
| 1⟩
| 0⟩

ρx

QNN

…

Wave function…

Quantum Neural Network

| 1⟩
| 0⟩
17

Learning Quantum Data
Learn physical properties of quantum states generated with HEP quantum simulation
CLTime-evolved states(1 + 1)d ℤ2
gauge theory

Multi-particle states
Parton shower

PL

FCL

VQE

Phase recognitiontime
evolution

gauge theoryCL<latexit sha1_base64="jaSWaoRRCL83YcxubK87MhQ70kQ=">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</latexit>⇢out

CT-symmetry
phasesPhase recognitionρ⇢inin<latexit sha1_base64="SbCQ6p+NmbmH7bO4WAnB9t9ihQ8=">AAACbHicbVHBTtwwEPWGFuhSKNDeUKWoKxCnVYJa2iMSl94KUhdW2qzQxJmAtbaT2hPo1soXcG0/jp/gG+ps9tBAR7L09N6M3ptxWkphKYoeesHKi5era+uv+huvN7febO/sXtiiMhxHvJCFGadgUQqNIxIkcVwaBJVKvExnp41+eYvGikJ/p3mJUwXXWuSCA3nq/NvV9iAaRosKn4N4CQZsWWdXO71RkhW8UqiJS7B2EkclTR0YElxi3U8qiyXwGVzjxEMNCu3ULZLW4b5nsjAvjH+awgX774QDZe1cpb5TAd3Yp1pD/ldLDcyQOu7uZ2vaTUT5l6kTuqwINW8D5ZUMqQib84SZMMhJzj0AboTfKeQ3YICTP2LXUXXdSMx+tUyDpPCJzNz9qEC3Sj/ReMcLpUBnLslEntcuaRYxymV17T8ifnr25+DiaBgfDz+dfxycHC6/ZJ3tsQ/skMXsMzthX9kZGzHOkN2z3+xP7zF4F+wF79vWoLececs6FRz8BRVJv+s=</latexit><latexit sha1_base64="pBeuFsYwPtgD3lAc/RB1z+HQ3WE=">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</latexit>

O(De)confinement
phases of matter

Lagrangianparameter
determination

partonshowerGround States(1 + 1)d U(1)PL

Quantum Convolutional Neural Network
L. Nagano, KT et al., Phys. Rev. Res. 5, 043250 (2023)
18

QML to Quantum Data (I)(1 + 1)d U(1) Gauge Theory (Schwinger Model)
21θZk + (−1)
ω
m
θ
j
0.5
(Xj Xj+1 + YjYj+1) +(−1) Zj
H=J
+
+
∑ (∑
∑
∑
2π
2
2π
2
2
)
j=0
k=0
j=0
j=0
Ns−2

j

k

Ns−2

Ns−2

‣ Non-trivial properties such as chiral condensate, though the model is simple
Phasetransition
at
due
to
topological
term
θ
=
π,
m/g
=
m
/g
≈
0.33
c
‣

0

Phase transitionin m-θ plane≈ 0.33m/g∞

Quantum data generation and classification
Physicalparameters:
N
=
N
=
8,
ag
=
2,
θ
=
π
s
‣
‣ Generate ground states | ψGS(m)⟩ using VQE withinparameter range of m/g ∈ [−2,2]‣ Phase recognition as aclassification with label:+1 (m > mc)
ym ={−1 (m < mc)

Upool

Uconv
Uconv

Upool

Uconv
Uconv

Uconv
Uconv

Uconv

Upool

Uconv

Upool

Upool

Uconv

Uconv
Uconv

Upool

Upool

19

QML to Quantum Data (II)Deconfinement

Confinement(1 + 1)d ℤ2 Gauge Theory
Ns−1

Ns−2

Ns−1

J
m
j
H=−
(XjZj,j+1Xj+1 + YjZj,j+1Yj+1) −f ∑ Xj,j+1 + ∑ (−1) Zj
2
2 ∑
j=0
j=0
j=0

‣ Confinement ( f ≠ 0) and Deconfinement ( f = 0) phases
depending on the presence of background electric field

Quantum data generation and classification
N
=
2N
=
4,
J
=
1,
T
=
2
Physicalparameters:s‣−iH(m,f )T| ψ0⟩‣ Generate time-evolved states | ψ(m, f )⟩ = e

Matter siteusing Suzuki-Trotter decomposition withinm ∈ [0,2], f ∈ {0,3}‣ Phase recognition as aclassification with label:+1 ( f ≠ 0)ym ={−1 ( f = 0)

Upool

Uconv
Uconv

Upool

Uconv

Uconv

Upool

Uconv

20

Quantum Simulation• (conventional) lattice QFT• Hamiltonian simulation• discretize spacetime• discretize space→using Monte Carlo method• no sign problem!
Z
Hamiltonian simulation as a useful computational
resource
withnear-term
QC
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Lattice gauge theory forcalculating
non-perturbative physics
sign problem• infamousneed exponential resources…
•• topological term
Conventional LGT simulation• real-time dynamics, etc.

‣ Discretize spacetime‣ MC sampling−Sfor phase-space
integrals of e

Sign problem with• non-zero density, temperature• topological term, etc.

<latexit sha1_base64="ivpsGTs47kQGohL2u7T5/w95Z0U=">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</latexit>(xi )Hamiltonian LGT simulation| (0)i<latexit sha1_base64="9OqwEp0dKJnIxWgEPTyA4qy5e78=">AAACdHichVFNLwNRFD0d3/XRYiNhISaV2jS3IoiVsLH0VW2i0syMp146X5mZNqH8AX/AwooQET/Dxh+w8BPEkrCxcDudRGhwJ2/eeefdc9957+quKf2A6DGmtLV3dHZ198R7+/oHEsnBoS3fqXqGyBmO6XgFXfOFKW2RC2RgioLrCc3STZHXK8uN/XxNeL507M3gwBU7lla25Z40tICpUjJxVHR9maapoqfZZVOUkiplKIzxVpCNgIooVp3kNYrYhQMDVVgQsBEwNqHB528bWRBc5nZQZ85jJMN9gWPEWVvlLMEZGrMV/pd5tR2xNq8bNf1QbfApJg+PleNI0QPd0Avd0y090cevtephjYaXA571pla4pcTJyMb7vyqL5wD7X6o/PQfYw3zoVbJ3N2QatzCa+trh6cvGwnqqPkkX9Mz+z+mR7vgGdu3VuFoT62eIcwOyP5+7FWxNZ7KzmZm1GXVxKWpFN0YxgTS/9xwWsYJV5MKenOESV7E3ZUxRlVQzVYlFmmF8CyXzCbbcj8A=</latexit>‣ Discretize space −iHt
‣ Directly simulate e| (t)i<latexit sha1_base64="8f4fz0sCFKOUffUHfXtpx0UMtmY=">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</latexit>t

No sign problem• still need exponential resource• infinite Hilbert spaces for gauge dof’s
t=0<latexit sha1_base64="teYGQ80MFADQNKd6qBdcKdf4ZVA=">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</latexit>

time<latexit sha1_base64="iyOUMBAm3uzpya9oaZwF4R/wcnU=">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</latexit>

Simulation of real-time phenomena, e.g, out-of-equilibrium dynamics, particle
scattering, is a promising example of quantum enhanced applications
21

Quantum Dynamics Simulation

L. Nagano, A. Bapat, C. W. Bauer,
Phys. Rev. D 108, 034501 (2023)

Simulation of quench dynamics in (1 + 1)d U(1) LGT (Schwinger model)
Schwinger model Hamiltonian:
j

N−2

k

2

N−2

N−2

Zk + (−1)
θ
ω
m
j
H=J
+
+
(Xj Xj+1 + YjYj+1) +(−1) Zj
∑ (∑
∑
∑
2
2π
2
2
)
j=0
k=0
j=0
j=0

Particle creation due to strong external
electric
fieldOF➡
effectQUENCHDYNAMICS
THESchwinger
SCHWINGER MODEL
VIA …BAPAT, and BAUER
PHYS. REV. D 108, 034501 (2NAGANO,<latexit sha1_base64="4DasnCr2GrD9bNoY3vU5Iu6L4t4=">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</latexit>

(t)

(a)

✓⇤

(

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q=0

q>0

<latexit sha1_base64="p7raHduhqn/B62XLK+jGapHK2ks=">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</latexit><latexit sha1_base64="YXttslw/BTyJ8kbn4z0zykI7CZ0=">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</latexit>

Particle creation| (t)i ⇡ | ( (t))i<latexit sha1_base64="R9MAr9f7vYvidpDYZ464AYmJX9s=">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</latexit>|<latexit sha1_base64="MHTvUsnr2asUrfXbht/CkNAjdig=">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</latexit>

GS i ⇡ |( ⇤ )it<latexit sha1_base64="iyOUMBAm3uzpya9oaZwF4R/wcnU=">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</latexit>

VQE

VQS

(c)

Ground statewith VQE

Time-evolution
with VQSFirst step towards more complex, non-trivial simulation
with increasing system volume(

FIG. 3. Fidelity between states from VQS and ED for N ¼ 4, a · g ¼ 1.0, m=g ¼ 1.0, q ¼ 2.0. Solid curves/error bands sho
medians and 25–75 percentiles of 20 samples: (left) dependence of the number of layers L ∈ f1; 2; 3g with δt ¼ 0.01 fixed, (dependence of a time increment δt ∈ f0.01; 0.02; 0.04g with L fixed.

(1) State preparation via VQE: One approximates

B. Quench dynamics via VQS 22

Qubits as Quantum Sensor
Superconducting qubits potentially a powerful probe to nature
∼
μeV
Low
threshold()
attemperature𝒪(mK)‣
Coherent
manipulation
withinor
longercoherence
time
𝒪(100
μs)
‣

‣ Robust measurement with non-demolition technique
EDM: μ ∼ Qd

Josephson
Junctiond = 𝒪(100 μs)

Strong coupling to electromagnetic field6

𝒪(10 ) stronger than single atom23

代表的な波ダークマター (2Dark Matter Search with Direct Qubit Excitation

Wave-like DM, e.g, Axion, Dark Photon with mass ∼ 𝒪(μeV − meV)Chen, welletmotivatedal.

もういっそ直接励起
Coherent
electric
field
generatedbyphotons‣

converted from DM (e.g, dark photon)
Directly
drive
Qubit
as
a
DM-induced
microwave‣ DMから転換した光子由来のコヒーレントな電場
Dark photon DM

A′

Qubitのドライブパルス

EX

µ

γ

arXiv: 2212.03884

|e>

=

X

Dark p(質量固ℏω = mDM 磁場がか○ 新しいU(1)Q'|g>○ Dark photon := 光子とちょっとだけ混ざ○ 磁場かけてないAxion探索実験で探せる

直接励起はnaiveには筋が良いはず

opulation (a.u.)Superconducting
qubitsasanattractive
probe
due
to
○ そもそもqubit-photon結合は強い
S. Chen et al.,
(実験初期のベンチマークに利用されが
well-motivated
DM
mass
in
~GHz
range
PRL 131, 211001 (2023)‣ µqubit ~106 × µatom
strongcouplingofsuperconducting
qubitstophotons‣24

(

Cu for decent cavity
Al, Nb for high quality

tuations also makes it hard toby milling machineSuperconducting Qubit(b) Capacitive coupling via coupler

wo coupled systems takes a

)
Nb

(25)
10 μm

C2

+
LJ
第 9 章 量子実験系における種々の結合

(d)

I1

3

IC1

3
2
1

e10 QHO

v
-

Cs

CJ

5

(

L1 L2
(d)
-32

(

I2

x4

HEMT

e2

125

TransmonQubit Resonator Filter

M12

5

(e)

(d)
4
3
2
1

Excitation probability

4

Cr

]

4

1

IC2

Cr

(c)

5
5
Direct inductive coupling(c)Transmon

E

IC2

1 mm

-20/2 10 mK
0
/2
- /2
0
- /2
/2
- 9.6:- /2 LC 0共振器とトランズモンの結合系
図Ecco
EccoSuperconducting phase,Superconducting phase,Superconducting
phase,
(f)
LPF
LPF
1 mm
-20
√
0

という Hamiltonian を得る。ここで量子ビットの周波数は h̄ωq = 8EC EJ −EC であり、Inductive
coupling
via
coupler(d)Si

he Hamiltonians of the individ)h could be any combination of
40 μm

(b)

2

(c)

Physical design (3D Resonator)

30mm M1C+ H2 + Hint ,

Lr

Lr

Cs

(d)

0

0
/2
Superconducting phase,i

Excitation probability

citive and inductive
- /2

C1

3D cavity + qubit

Cg2

Comp.
subspace

QHO

Resonator

Energy [

1
0

LJ
CJ

Energy [

2

IC1

(a)

]

]
Energy [

3

(c)

gr2

Cg1

Energy [t between individual quantum
+
Lr
Cr
v
engineer an interaction
Hamilees of freedom in those indi)(b)
ction,
we discussthephysical5
ts representation in the qubit
4pling to form 2-qubit gates isiComp.
subspace

(a)

Qubit

]

2D cavity + qubit

engineering

gr1

IC1

2 μm Al/AlOx/Al e1400 nm

L1

非調和性を表す
αJTWPAq = −EC /h̄ を導入した。典型的なパラメータとしては、ωq ≃ 10 GHz、
ICC
Mα2C
EJ /EC ≥ 50、
q ∼ −200 MHz ほどである。
Cu
DUT
一見すると Josephson エネルギー EJ が電荷エネルギー EC よりも大きいという仮定
Cryoperm
は、Josephson 接合が非線形インダクタとして働くということから非線形性が大きいことIC2L2を意味するようにも思えるが、実は θ の係数にも EJ /EC の因子があるように、非線形性
eC
e2が小さくなることを意味することが分かる。
これは nC の真空ゆらぎ δnC = (EJ /8EC )1/4を考えるとより直観的になる。EJ /EC が小さいときには δnC は小さく、Cooper 25
対が 0

D~ GHz|0>|1>
Qubit Fabrication,
Frequency Modulation⇒Transmon excite

0.1% - 10% excitationin the unexplored region

Create our own qubits and cavity for the experiment

Fabricationofour
superconducting
transmon
Al
Cavity Transmon
Maketransmons by
selvesReadout test

Scan DM mass by modulating qubit frequency[ µV ]

Fabrication• Single shot readout test
|0>
4
|1>
Using
SQUID with external
magnetic
field• Error rate
値要修正

250 µm7 cm
400 µm2

Q

Josephson
Junction

20 µm
Line width:
350 nm𝒪(100nm × 100nm)

Substrate: Sp, Si

Capacitance pad: Nb, Al

Laser

Nakazono-san (M1)

0

-2

J1

-4

× 480

2( ~ 5 56

𝜙ext

ResistCapacitancepad

NbOsin 2If+,-.
-2

0

Plasm Nb

Sp

Watanabe-san (M1)246 [ µV ]I→Osin 2If+,-.K + P =Gsin 2If+,-.K + Mcos 2If+,-.K

Cu cavity• Noise of readout pulse

Resist

150 nmJ2|0> as |1>: ~ 15%
eﬀ
EJ (ϕext) =• Judged |0> or |1>
2 by phase2change
of ϕ
EJ1
+ EJ2
+ 2E
E
cos
J1 J2
ext
readout pulse-6

Error source
1.2 μm|1> as |0>: ~ 20%

SQUID

Nb

Nb

Sp

Sp

• Transmon lifetime, in |1> as |0>•

QubitsExcited transmon may de-excite before
readout

F$beamWork at 500nm
Clean
ResistRoom

Josephson
Junction

ResistNb

480 qubits
on Wafer

Al

Dicing

500nm
Nb

Nb

• Residual thermal excitation, in |0> as |1>•

Transmon & cavity was in fridge•

Temp. of transmon &magnetic
cavity >>fieldtemp.
fridge ~10 mK ?
byofelectric
current

NbTi coil

値要修正

26

Purcell filtergQubit Readout
andExperimentκ
Qubit
Purcell filter

κ
Res.

g

Qubit

Qubit stateRes. read out through the cavity
CHIP

CHIP
Cavity frequency shifts dependingon thequbit status (➞ Dispersive readout)

(b)

(c)

1.0

|S
|
(a.u.)
11|S | (a.u.)

(b)

(c)

1.0

κ/2
κ/2

0.5
0.5

11

2χ/2
2χ/2

θ θ

θθ(rad)(rad)∼ 1 μs∼ 20 ns

Excited with probability pge

4× 𝒪(10 )𝒪(100 μs)f01
ϵτpge ≃ 0.12 × κ cos Θ( 10−11 ) ( 1 GHz ) ( 100 μs )2--

Qubit Readout

Qubit Initialization|S11|S
| 11|

0.0
0.0
00

-2
-2

Experimental procedure for DM detection

2

2

2

ρDM
C
d
( 0.1 pF ) ( 100 μm ) ( 0.45 GeV/cm3 )
2

-2

-2

-1

0

1

2

-1
0
1
2
Frequency, ωRF - ωr (a.u)

Frequency, ωRF - ωr (a.u)

Initialize qubits to | 0⟩, wait and measure

|
1⟩
Count
the
occurrence
of
state
in
‣
4

𝒪(10 ) measurements

27

Expected Sensitivity for Direct Qubit Excitation
S. Chen et al., PRL 131, 211001 (2023)

Possible to probe into unexplored region
even with the excitation rate of 0.1%-10%
Expected noise sources of | 0⟩ → | 1⟩
transition
Thermalnoise:‣p∼e−ℏω/kBT∼ 0.01% − 1 % @ 30 mK∼
0.1%
Readouterror:‣
Dark blue: nq = 1 @ 1 mK / year
Light blue: nq = 100 @ 1 mK / year
Dashed lines: 30 mK

28

Status of Direct Qubit Excitation Experiment[mV]| 0⟩ state| 1⟩ stateClassification of | 0⟩ and | 1⟩ states||
Preparethequbitsinorstates0⟩1⟩‣‣ Determine the centers of gravities by measuring
the states (200 times)
Assignlabel
bycheckingthe
distancefrom
the‣centers for new measurements

Q

Measured error rates:| 0⟩ → | 1⟩ : ∼ 5 %| 0⟩ center| 1⟩ centerI➡ Possibly due to thermal excitation[mV]

5 % thermal error roughly corresponds to ∼ 133 mK
Measure the true temperature of qubits| 1⟩ → | 0⟩ : ∼ 35 %➡ Possibly due to energy relaxation

Aiming at T1 ∼ 100 μs (currently ∼ 5 μs)

29

Dark Matter Search in Cavity Haloscope Experiment
キャビティハロスコープ実験

Cavity haloscope as a powerful technique to search for wave-like DM
photons from DM with a mass resonant to the cavity frequency‣ Accumulating
キャビティハロスコープ実験
Manyphotons
creating
EM
mode
in
the
cavity‣out voltage by antenna~10 mK
microwave‣ lRead
世界最高感度に到達している有力な検出方法
l 空洞共振器 (Cavity)に光子を溜め, 高周波で検Cavity出frequency to be varied to scan over a wide

~K

CavityHEMT

増幅

Amplifier

増幅

DM mass range
Inserting metal rods in ADMX
experiment‣ lE.g,信号が非常に微弱なため,複数段階で信号増幅…(HEMT,
Not easy常温アンプ,
due to thermal
noise,
EM
field
leakage
JPA,…)

γ

本研究では未使用

l Cavityの共振周波数

Analyzer

探索DMの質量対応

γ’
Room Temperature30

Varying Cavity Frequency

周波数変調の手法
CavityLamb shift in cavity frequency due to strong coupling of superconducting qubits
to cavity
Cavity周波数変調の手法
SQUID型トランズモ
Varying cavity SQUID型Qubitに対し,
frequency by changing
superconducting
qubit
frequency
10 μm
コイルによってループを貫く磁束を増減させる
SQUID型トランズモン量子ビット→QubitのインダクタンスLjが変化
2
2
10 μm
SQUID型Qubitに対し,コイルによってループを貫く磁束を増減させるℏgg→Qubitの共振周波数が変化
Cavity周波数変調の手法
Jaynes-Cummings†→QubitのインダクタンスLjが変化
H
=
ω
+
σ
+
ℏ
ω
+
σ
a
a
周波数変調…
qzcz→detuningΔが変化
Hamiltonian →Qubitの共振周波数が変化
2
Δ
Δ
(
)
[
]
SQUID型トランズモン量子ビット→Cavityの共振周波数が変調
Δ10 μm:= | ωq − ωc | JJ
周波数変調…
→detuningΔが変化

SQUID型Qubitに対し, コイルによってループを貫く磁束を増減させる→QubitのインダクタンスLjが変化→Cavityの共振周波数が変調→Qubitの共振周波数が変化
SQUID型トランズモン量子ビット
周波数変調…
→detuningΔが変化→Cavityの共振周波数が変調せる

Qubit frequency

SQUID
10 μm

3.2
3.2
cmcm

3.2 cmCavity frequency

JJ
JJ

width
幅2 mm
2 mm

幅2 mm幅2 mm

JJ
次ページから周波数変調の検証

31

次ページから周波数変調の検証
7実証実験の手順

Status of Cavity Haloscope Experiment
実証実験の手順

コイルに流れる電流値を変更
コイルに流れる電流値を変更
Experimental
procedure
to measure cavity frequency
繰り返し1) Vary the current on the coil繰り返し2) Measurethetransmission
rate
S
21
透過率(S21)を測定
3) Repeat 1)-2)
steps
透過率(S21)を測定

結果→変調を確認

結果→変調を確認

Confirmed that the cavity frequency did vary
変調が大きくなると,ピークが崩れ始める
変調が大きくなると,ピークが崩れ始める
Peak
shapes distorted due to worsened Q factors‣(Qualityfactor悪化)(Qualitypossible
factor悪化)
Currently
tochange
while
∼
10
MHz
‣

Frequency vs Current vs S21
Frequency vs Current vs S21

maintaining high-Q value

Q値を保ったまま実効的に観測可能な量
Q値を保ったまま実効的に観測可能な量→10 MHz→10 MHz
シミュレーション75MHz
シミュレーション75MHz→Qubitによる緩和, lossを一部考慮していない→Qubitによる緩和, lossを一部考慮していない

32

Summary
Partially reviewed ICEPP activities on quantum computational science andqubit-technology experiment for particle physics
Quantum
machinelearningonclassical/quantum
HEP
data
‣
Quantum
simulationinlatticegauge
theory‣Darkmattersearchwithsuperconducting
qubits‣• Quantum computational science is a promising area with practicalapplications for quantum computers, aiming at achieving quantum
advantage in future• New opportunities in technology development and scientific discovery(e.g, DM search with superconducting qubits)

33

Summary
Partially reviewed ICEPP activities on quantum computational science andqubit-technology experiment for particle physics
Quantum
machinelearningonclassical/quantum
HEP
data
‣
Quantum
simulationinlatticegauge
theory‣Darkmattersearchwithsuperconducting
qubits‣• Quantum computational science is a promising area with practicalapplications for quantum computers, aiming at achieving quantum
advantage in future• New opportunities in technology development and scientific discovery(e.g, DM search with superconducting qubits)

Looking forward to further discussion and collaboration opportunities!!
34