Simulating real-time dynamics of hard probes in nuclear matter on a quantum computer - CERN Indico

Simulating real-time dynamics
of hard probes in nuclear
matter on a quantum computer
 James Mulligan
 Lawrence Berkeley National Laboratory

 arXiv: 2010.03571
 Wibe de Jong
 LBNL (Quantum Information)
 Mekena Metcalf
 James Mulligan
 Mateusz Ploskon LBNL (Nuclear Science)
 Felix Ringer
 Xiaojun Yao MIT (Nuclear Science)

 Initial Stages 2021
 Weizmann Institute of Science (virtual)
 Jan 11 2021

Hard probes
 PbPb
Experiments measure how cross-sections of hard probes are 1 dN
 RAA =
 ⟨Ncoll⟩ dN pp
modified in heavy-ion collisions compared to proton-proton collisions

 Jets Heavy quarks
 Jet
 S. ACHARYA et al.
 yields are suppressed due to Heavy quark bound
 PHYSICAL REVIEW C 101, 034911 (2020)
 pairs J/ψ R
 (quarkonium) AA and p
 “energy loss” to the dense medium are “melted” by the J/ψ hot Rmedium
 AA
 R AA

 R AA
 1.4 ALICE R = 0.2 1.4 ALICE R = 0.4
 Pb-Pb 0-10% s NN = 5.02 TeV Pb-Pb 0-10% s NN = 5.02 TeV
 1.2 pp s = 5.02 TeV 1.2 pp s = 5.02 TeV
 | η | < 0.5 p lead,ch > 5 GeV/c | η | < 0.3 p lead,ch > 7 GeV/c
 jet T jet T
 1 1 LBT
 LBT
 SCET
 ALICE 0-10%
 ALICE 0-10% SCET
 Hybrid Model, L = 0 Hybrid Model, L = 0 Correlated uncertainty
 0.8 Correlated uncertainty Hybrid Model, L = 2/(πT ) 0.8 Hybrid Model, L = 2/(πT ) Shape uncertainty
 Shape uncertainty JEWEL, recoils on, 4MomSub JEWEL, recoils on, 4MomSub
 JEWEL, recoils off
 JEWEL, recoils off
 0.6 0.6

 0.4 0.4

 0.2 0.2

 0 0
 0 50 100 0 50 100
 p (GeV/c ) p (GeV/c )
 PRC 101 034911 (2020)
 •
 T,jet T,jet

 James Mulligan, LBNL
 √
 FIG. 7. Jet RAA at sNN = 5.02 TeV for R = 0.2 (left) and R = 0.4 (right) compared to LBT, SCETG , hybrid model, and JEWEL
 Initial Stages 2021
 J/ψ suppression reduced at low pT
 Jan 11, 2021 2
 predictions. The combined "T # uncertainty and pp luminosity uncertainty of 2.8% is illustrated as a band on the dashed line at R = 1.

Hard probes — theory
 In vacuum: calculate scattering of asymptotic states
 using perturbative QCD
 Note that there is no sense of “time evolution”

 In medium: must combine probe evolution with
 hydrodynamic evolution of the QGP
 X.N.Wang

James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 3

Hard probes — theory
 In vacuum: calculate scattering of asymptotic states
 using perturbative QCD
 Note that there is no sense of “time evolution”

 In medium: must combine probe evolution with
 hydrodynamic evolution of the QGP
 X.N.Wang

 In heavy-ion collisions, the modifications of the probe due to its evolution through
 the QGP are typically put in “by hand”, rather than a true real-time evolution

 Medium-modified parton shower
 Majumder PRC 88 (2013)
 Caucal, Iancu, Mueller, Soyez PRL 120 (2018)
 …

James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 4

Real-time dynamics of QCD
 Typical methods in lattice QCD have a sign problem
 and use imaginary instead of real time

 ∫
 iℒt
 e t → it

 Can instead use the Hamiltonian formulation of QCD
 Large Hilbert space can in principle be simulated by quantum computers
 Theoretical formulation ongoing: gauge choice, difficult color algebra, …
 see e.g. Jordan, Lee, Preskill `11, Preskill `18,
 Klco, Savage et al.`18-`20, Cloet, Dietrich et al. `19

 Quantum computing may allow for a solution of
 the real-time dynamics of QCD

James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 5

Quantum computing
Superposition and entanglement
 2N

 ∑
 | ψ⟩ = ai | ψi⟩ N
 For N qubits, there are 2 amplitudes
 i=1
 e.g. | ψ⟩ = a1 | 000⟩ + a2 | 001⟩ + a3 | 010⟩ + a4 | 011⟩ + a5 | 100⟩ + a6 | 101⟩ + a7 | 110⟩ + a8 | 111⟩

If one can control this high-dimensional space, e.g. with appropriate interference of amplitudes, then
one can potentially achieve exponential speedup of certain computations

 BQP It is expected that quantum computers can solve some
 classically hard problems with exponential speedup

 NP These include a number of highly impactful problems
 P
 such as quantum simulation

 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 6

Quantum devices
Superconducting circuits And a variety of others:
 Trapped ions
 Optical lattice
 Photonics
 … Topological
 … …

 Superconducting circuit qubit coherence times
 have become (100 μs), long enough to 7

 perform (10 − 100) two-qubit operations Fig. 4 Images of four recent devices fabricated at IBM. The device in the top left corner contains 2Q(
 e.g. Kjaergaard et al. `20 is currently being used to study optimal two-qubit gates. The top right corner shows a device with 3
 a parity measurement.40 In the lower left corner is a device with 4Q/4B/4R for demonstrating the [[
 shows a device of 8Q/4B/8R for studying both Z and X parity checks. Inset shows an optical micro

 relaxation quantifies the time it takes for a qubit to decay from its qubit and give rise to
 excited state |1⟩ to the ground state |0⟩ (a bit-flip error) while undesirable effects.59
 dephasing times correspond to p the
 ffiffi time it takes for a quantum For the transmon qubits
 superposition state |+⟩=(|0⟩+|1⟩/ 2 to lose its phase relationship transition frequency of 5–5
 between |0⟩ and |1⟩ (i.e. a phase-flip error). Both quantities play an MHz so that the charge
 important role as shorter times will reduce the accuracy of numerical simulations com
 quantum operations. the qubit design, we aim t
 The first experimental demonstration of a superconducting fF, paired with a JJ critical
 qubit52 is attributed to the group at NEC in 1999, albeit with T2~1 is made quite small (100
 ns. Since this seminal result, many groups around the world defects residing in the tun
 conceived and implemented a variety of superconducting qubits formed by metal pads sp
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 minimize dielectric loss 7 fr
 by varying with the superconducting circuits, for example, by

Quantum devices
Superconducting circuits And a variety of others:
 Trapped ions
 Optical lattice
 Photonics
 … Topological
 … …

 Superconducting circuit qubit coherence times
 have become (100 μs), long enough to 8

 perform (10 − 100) two-qubit operations Fig. 4 Images of four recent devices fabricated at IBM. The device in the top left corner contains 2Q(
 e.g. Kjaergaard et al. `20 is currently being used to study optimal two-qubit gates. The top right corner shows a device with 3
 a parity measurement.40 In the lower left corner is a device with 4Q/4B/4R for demonstrating the [[
 shows a device of 8Q/4B/8R for studying both Z and X parity checks. Inset shows an optical micro

 The dream: universal, fault-tolerant Noisy Intermediate Scale Quantum (NISQ) era
 relaxation quantifies the time it takes for a qubit to decay from its qubit and give rise to
 digital quantum computer excited state |1⟩ to the ground state |0⟩ (a bit-flip error) while
 dephasing timesDecoherence,
 correspond to p the limited
 time it takesnumber
 for a quantum
 undesirable effects.59
 of qubits,
 For the transmon qubits
 ffiffi
 Shor’s and Grover’s algorithm imperfect
 superposition state |+⟩=(|0⟩+|1⟩/gates
 2 to lose its phase relationship transition frequency of 5–5
 between |0⟩ and |1⟩ (i.e. a phase-flip error). Both quantities play an MHz so that the charge
 Quantum error correction important role Aim:
 as achieve
 shorter times quantum
 will reduce advantage
 the accuracy without
 of full
 numerical simulations com
 quantum error correction
 quantum operations. the qubit design, we aim t
 fF, paired with a JJ critical
 The first experimental demonstration of a superconducting
 Shor, Preskill, Kitaev, Zoller … qubit52 is attributed to the group at NEC in Martinis etwith
 1999, albeit al. (2019)
 T2~1 , Zhong
 is madeetquite
 al. (2020)
 small (100
 ns. Since this seminal result, many groups around the world defects residing in the tun
 conceived and implemented a variety of superconducting qubits formed by metal pads sp
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 minimize dielectric loss 8 fr
 by varying with the superconducting circuits, for example, by

A near-term approach: Open quantum systems
Study the real time dynamics of the quantum evolution of
probes in the nuclear medium (LHC/RHIC/EIC)
 Subsystem - Jet/heavy-flavor
 Environment - Nuclear matter

 H(t) = HS (t) + HE (t) + HI (t)

 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 9

A near-term approach: Open quantum systems
Study the real time dynamics of the quantum evolution of
probes in the nuclear medium (LHC/RHIC/EIC)
 Subsystem - Jet/heavy-flavor
 Environment - Nuclear matter

 H(t) = HS (t) + HE (t) + HI (t)

The time evolution is governed by the In the Markovian limit, the subsystem is
von Neumann equation: described by a Lindblad equation
 h i m
 X ✓ ◆
 d (int) (int) (int) d † 1 † 1 †
 ⇢ (t) = i HI (t), ⇢ (t) ⇢S = i [HS , ⇢S ] + Lj ⇢S Lj Lj Lj ⇢S ⇢S L j L j
 dt dt j=1
 2 2
 ⇢S = trE [⇢]

 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 10

Open quantum systems: Quarkonia
The evolution of quarkonia in the QGP can be described by the Lindblad equation
 Akamatsu, Rothkopf et al. `12-`20, Brambilla et al. `17-`20
 Yao, Mueller, Mehen `18-`20, Sharma,Tiwari `20
 “Simple” system:
 reduces to quantum
 mechanics (NRQCD)
 P. Braun-Munzinger and J. Stachel, Nature (2007)

Currently various approximations are considered
 Markovian limit Blaizot, Escobedo `18, Yao, Mehen `18, `20
 Small coupling of system and environment
 Semi-classical transport

 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 11

Open quantum systems: Quarkonia
The evolution of quarkonia in the QGP can be described by the Lindblad equation
 Akamatsu, Rothkopf et al. `12-`20, Brambilla et al. `17-`20
 Yao, Mueller, Mehen `18-`20, Sharma,Tiwari `20
 “Simple” system:
 reduces to quantum Survival probability of the vacuum state
 mechanics (NRQCD)
 P. Braun-Munzinger and J. Stachel, Nature (2007)

Currently various approximations are considered
 Markovian limit Blaizot, Escobedo `18, Yao, Mehen `18, `20
 semiclassical
 Small coupling of system and environment
 Semi-classical transport quantum

 Sharma,Tiwari `20
NRQCD + semiclassical approach vs. full quantum evolution
 Quantum treatment has important phenomenological consequences
 Bjorken expanding QGP T0 = 475 MeV
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 12

Open quantum systems: Jet broadening
 Yao,Vaidya JHEP 10 (2020)
First steps in the direction of jet physics Vaidya 2010.00028

 Soft Collinear Effective Theory
Jet energy Q Forward scattering, Glauber
 gluon exchange

 Markovian master equation describes evolution of jet density matrix:

 where the probability to be in a given momentum state is:

James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 13

Quantum simulation Feynman `81
 Lloyd `96

It is exponentially expensive to simulate an N-body
 N
quantum system on a classical computer: 2 amplitudes!

But a quantum computer can naturally simulate a quantum system

 State preparation
 Time evolution
 Measurement
 Evolution in time steps Δt = t/Ncycle

 Time evolution of closed systems
 Quantum simulation of the Schrödinger equation
 The evolution is unitary and time reversible

James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 14

Non-unitary evolution
In open quantum systems, the subsystem evolution is non-unitary
 m
 X ✓ ◆
 d † 1 † 1 †
 ⇢S = i [HS , ⇢S ] + Lj ⇢S Lj Lj Lj ⇢S ⇢S L j L j
 dt j=1
 2 2

The Stinespring dilation theorem

 Any allowed quantum operation can be written as a unitary evolution acting on a larger
 space (after coupling to appropriate ancilla), and reducing back to the subsystem
 †
 V U V
 † †
 V V =1 V V 6= 1

 | ai
 ...

 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 15

Quantum simulation of open quantum systems
 G
 Toy model setup G
 g
 g

 Two-level system in a thermal environment q̄ g
 S
 G g
 e.g. bound/unbound J/ψ, cc̄
 E
 g
 E q̄ q E
 HS = Z q g
 2 q
 q̄

 HI = gX ⌦ (x = 0)
 Quantum circuit: Lindblad evolution

 Pauli matrices X, Y, Z, interaction strength g
 Lindblad operators †
 0 L0 L1 0 †
 ...
 Lj ⇠ g(X ⌥ iY ) L0 0 0 0
 J=
 j = 0, 1 L1 0 0 0
 0 0 0 0
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 16

Quantum circuit synthesis
Approximate unitary operations with a
compiled circuit of one- and two-qubit gates
 ...

 Optimization problem w/unitary loss function
 qsearch compiler
 Siddiqi et al. `20 10 CNOT gates/cycle

 Single qubit

 CNOT

Error mitigation
 Readout error
 Constrained matrix inversion Unfolding
 Nachman, Urbanek, de Jong, Bauer `19
 Gate error
 Zero-noise extrapolation of CNOT noise using Random Identity Insertions
 He, Nachman, de Jong, Bauer `20
James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 17

Quantum simulation of open quantum systems
 arXiv: 2010.03571
 Real-time evolution
 G
 G g

 P0(t) describes fraction that remains in “bound state” q̄ g
 g

 Similar to t-dependent RAA S
 G g

 E
 g
 q̄ q E
 q g
 tt [fm/c]
 [fm/c] (T
 (T =
 = 300
 300 MeV)
 MeV) q̄ q
 00 55 10
 10 15
 15 20
 20 25

 1.2
 1.2 IBM Q Vigo, Ncycle = 1, g = 0.3
 Uncorrected Simulator, Ncycle = 1
 1.1
 1.1 Readout corrected Simulator, Ncycle = 3
 Readout + RIIM corrected Runge ° Kutta
 1.0
 1.0
 (t)
 P0(t)

 Thermal equilibrium
 0

 0.9
 0.9
 P

 0.8
 0.8

 0.7
 0.7

 0.6
 0.6
 00 10
 10 20
 20 30
 30 40
 tt [1/T
 [1/T]]
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 18

Quantum simulation of open quantum systems
 arXiv: 2010.03571
 Real-time evolution
 G
 G g

 P0(t) describes fraction that remains in “bound state” q̄ g
 g

 Similar to t-dependent RAA S
 G g

 E
 g
 q̄ q E
 q g
 tt [fm/c]
 [fm/c] (T
 (T =
 = 300
 300 MeV)
 MeV) q̄ q
 00 55 10
 10 15
 15 20
 20 25

 1.2
 1.2 IBM Q Vigo, Ncycle = 1, g = 0.3
 Uncorrected Simulator, Ncycle = 1 The algorithm converges to Lindblad
 1.1
 1.1 Readout corrected Simulator, Ncycle = 3 evolution with a small number of cycles
 Readout + RIIM corrected Runge ° Kutta
 1.0
 1.0
 (t)
 P0(t)

 Thermal equilibrium
 0

 0.9
 0.9
 P

 0.8
 0.8

 0.7
 0.7

 0.6
 0.6
 00 10
 10 20
 20 30
 30 40
 tt [1/T
 [1/T]]
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 19

Quantum simulation of open quantum systems
 arXiv: 2010.03571
 Real-time evolution
 G
 G g

 P0(t) describes fraction that remains in “bound state” q̄ g
 g

 Similar to t-dependent RAA S
 G g

 E
 g
 q̄ q E
 t [fm/c] (T = 300 MeV) q g
 0 5 ttt [fm/c]
 10 (T
 [fm/c]
 [fm/c] (T=
 (T 15300
 == 300MeV)
 300 MeV)
 MeV)
 20 25 q̄ q
 000 5555 10
 10
 10 15
 15
 15
 15 20
 20
 20
 20 25
 25
 25
 1.2 IBM Q Vigo, Ncycle = 1, g = 0.3
 1.2 IBM
 1.2
 1.2 IBMQ
 IBM QQVigo,
 Vigo,N
 Vigo,
 Uncorrected NN cycle=
 cycle
 cycle ==1,
 1,1,ggg=
 ==0.3
 0.3
 0.3 Simulator, Ncycle = 1
 1.1 Uncorrected
 Uncorrected
 Readout corrected
 Uncorrected Simulator,
 Simulator,N
 Simulator, NN cycle=
 cycle
 cycle ==1113 IBM Q Vigo device
 1.1
 1.1
 1.1 Readout
 Readoutcorrected
 Readout corrected
 + RIIM corrected
 corrected Simulator, N
 Simulator,
 Simulator, NN
 Runge ° Kutta cycle=
 cycle
 cycle ==333
 1.0
 Readout
 Readout+
 Readout ++RIIM
 RIIMcorrected
 RIIM corrected
 corrected Runge
 Runge °°°Kutta
 Kutta
 P0(t)

 Thermal
 Runge equilibrium
 Kutta
 1.0
 1.0
 1.0
 Thermal
 Thermalequilibrium
 (t)

 Thermal equilibrium
 P0(t)

 0.9 equilibrium
 00

 0.9
 0.9
 0.9
 P

 0.8
 0.8
 0.8
 0.8
 0.7
 0.7
 0.7
 0.7
 0.6
 0.6
 0.6 0 10 20 30 40
 0.6
 000 10
 10
 10 t2020[1/T ]
 20 30
 30
 30
 30 40
 40
 40
 ttt [1/T
 [1/T]] ]
 [1/T
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 20

Quantum simulation of open quantum systems
 arXiv: 2010.03571
 Real-time evolution
 G
 G g

 P0(t) describes fraction that remains in “bound state” q̄ g
 g

 Similar to t-dependent RAA S
 G g

 E
 g
 q̄ q E
 t [fm/c] (T = 300 MeV) q g
 0 5 ttt [fm/c]
 10 (T
 [fm/c]
 [fm/c] (T=
 (T 15300
 == 300MeV)
 300 MeV)
 MeV)
 20 25 q̄ q
 000 5555 10
 10
 10 15
 15
 15
 15 20
 20
 20
 20 25
 25
 25
 1.2 IBM Q Vigo, Ncycle = 1, g = 0.3
 1.2 IBM
 1.2
 1.2 IBMQ
 IBM QQVigo,
 Vigo,N
 Vigo,
 Uncorrected NN cycle=
 cycle
 cycle ==1,
 1,1,ggg=
 ==0.3
 0.3
 0.3 Simulator, Ncycle = 1
 1.1 Uncorrected
 Uncorrected
 Readout corrected
 Uncorrected Simulator,
 Simulator,N
 Simulator, NN cycle=
 cycle
 cycle ==1113 IBM Q Vigo device
 1.1
 1.1
 1.1 Readout
 Readoutcorrected
 Readout corrected
 + RIIM corrected
 corrected Simulator, N
 Simulator,
 Simulator, NN
 Runge ° Kutta cycle=
 cycle
 cycle ==333
 1.0
 Readout
 Readout+
 Readout ++RIIM
 RIIMcorrected
 RIIM corrected
 corrected Runge
 Runge °°°Kutta
 Kutta Including CNOT gate error correction
 P0(t)

 Thermal
 Runge equilibrium
 Kutta
 1.0
 1.0
 1.0
 Thermal
 Thermalequilibrium
 (t)

 Thermal equilibrium
 P0(t)

 equilibrium
 0.9 gives good agreement
 00

 0.9
 0.9
 0.9
 Random Identity Insertion Method (RIIM)
 P

 0.8
 0.8
 0.8
 0.8 Bauer, He, de Jong, Nachman `20
 0.7
 0.7
 0.7
 0.7
 0.6
 0.6
 0.6
 0.6
 0 10 20 30 40 Proof of concept
 000 10
 10
 10 t2020[1/T ]
 20 30
 30
 30
 30 40
 40
 40
 ttt [1/T
 [1/T]] ]
 [1/T
 James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 21

Summary
 Real-time evolution of hard probes in heavy-ion collisions can be formulated
 as an open quantum system, and encoded in a quantum algorithm

 Allows to go beyond semiclassical approximations in current models

Proof of concept that these systems can be simulated on
current and near-term quantum computers
 NISQ era digital quantum computing

Future steps:
 Extension toward QCD
 Explore different digital/analog devices
 More efficient quantum algorithms and error mitigation
James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 22

Backup

James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 23

be executed simultaneously a

 Quantum advantage
alibrated and benchmarked
ystem level using a powerful
 inally, we used component-
rformance of the whole sys-
mation behaves as expected REPORTS

 Last year Last month
 Cite as: H.-S. Zhong et al., Scienc
 10.1126/science.abe8770 (2020)
ompare our quantum proces-
uters in theArticle
 task of sampling

 Quantum supremacy using a programmable
circuit11,13,14. Random circuits
 ecause they do not possess
 Quantum computational advantage using photons
 superconducting processor
uarantees of computational Han-Sen Zhong1,2*, Hui Wang1,2*, Yu-Hao Deng1,2*, Ming-Cheng Chen1,2*, Li-Chao Peng1,2,
tangle a set of quantum bits Yi-Han Luo1,2, Jian Qin1,2, Dian Wu1,2, Xing Ding1,2, Yi Hu1,2, Peng Hu3, Xiao-Yan Yang3,
e-qubit and two-qubit logi- Wei-Jun Zhang3, Hao Li3, Yuxuan Li4, Xiao Jiang1,2, Lin Gan4, Guangwen Yang4, Lixing You3,
cuit’s output produces a set Qubit Martinis et al. (2019)
 Adjustable coupler Zhen Wang3, Li Li1,2, Nai-Le Liu1,2, Chao-Yang Lu1,2, Jian-Wei Pan1,2†
100, …}. Owing to quantum
 1
 Science (2020)
 Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui
 of the bitstrings resembles
 https://doi.org/10.1038/s41586-019-1666-5
 b Frank Arute , Kunal Arya , Ryan Babbush , Dave Bacon , Joseph C. Bardin , Rami Barends ,
 1 1 1 1 1,2 1
 230026, China. 2CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology
y light interference Rupak Biswas3, Sergio Boixo1, Fernando G. S. L. Brandao1,4, David A. Buell1, Brian Burkett1,
 Received: 22in laser
 July 2019 of China, Shanghai 201315, China. 3State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology,
 Yu Chen1, Zijun Chen1, Ben Chiaro5, Roberto Collins1, William Courtney1, Andrew Dunsworth1,
ch more likely to occur than Chinese Academy of Sciences, Shanghai 200050, China. 4Department of Computer Science and Technology and Beijing National Research Center for Information
 Accepted: 20 September 2019 Edward Farhi1, Brooks Foxen1,5, Austin Fowler1, Craig Gidney1, Marissa Giustina1, Rob Graff1, Science and Technology, Tsinghua University, Beijing 100084, China.
bility distribution becomes Keith Guerin1, Steve Habegger1, Matthew P. Harrigan1, Michael J. Hartmann1,6, Alan Ho1,
 Published online: 23 October 2019 *These authors contributed equally to this work.
of qubits (width) and number Markus Hoffmann1, Trent Huang1, Travis S. Humble7, Sergei V. Isakov1, Evan Jeffrey1,
 Zhang Jiang1, Dvir Kafri1, Kostyantyn Kechedzhi1, Julian Kelly1, Paul V. Klimov1, Sergey Knysh1,
 †Corresponding author. Email: pan@ustc.edu.cn
 Alexander Korotkov1,8, Fedor Kostritsa1, David Landhuis1, Mike Lindmark1, Erik Lucero1,
 is working properly using a Dmitry Lyakh9, Salvatore Mandrà3,10, Jarrod R. McClean1, Matthew McEwen5, Quantum computers promises to perform certain tasks that are believed to be intractable to classical
ng11,12,14, which compares how Anthony Megrant1, Xiao Mi1, Kristel Michielsen11,12, Masoud Mohseni1, Josh Mutus1, computers. Boson sampling is such a task and is considered as a strong candidate to demonstrate the
ntally with its corresponding Ofer Naaman1, Matthew Neeley1, Charles Neill1, Murphy Yuezhen Niu1, Eric Ostby1,
 quantum computational advantage. We perform Gaussian boson sampling by sending 50 indistinguishable
 on a classical computer. For Andre Petukhov1, John C. Platt1, Chris Quintana1, Eleanor G. Rieffel3, Pedram Roushan1,
 Nicholas C. Rubin1, Daniel Sank1, Kevin J. Satzinger1, Vadim Smelyanskiy1, Kevin J. Sung1,13, single-mode squeezed states into a 100-mode ultralow-loss interferometer with full connectivity and
 strings {xi} and compute the Matthew D. Trevithick1, Amit Vainsencher1, Benjamin Villalonga1,14, Theodore White1, random matrix—the whole optical setup is phase-locked—and sampling the output using 100 high-
 1,13,14
 (see also Supplementary Z. Jamie Yao1, Ping Yeh1, Adam Zalcman1, Hartmut Neven1 & John M. Martinis1,5* efficiency single-photon detectors. The obtained samples are validated against plausible hypotheses
mulated probabilities of the exploiting thermal states, distinguishable photons, and uniform distribution. The photonic quantum
 10 mm computer generates up to 76 output photon clicks, which yields an output state-space dimension of 1030
 The promise of quantum computers is that certain computational tasks might be
 and a sampling rate that is ~1014 faster than using the state-of-the-art simulation strategy and
 executed exponentially faster on a quantum processor than on a classical processor1. A
 (1) supercomputers.
 Fig. 1 | The Sycamorefundamental
 processor. challenge
 a, Layout of is to build a high-fidelity
 processor, processor capable of running quantum
 showing a rectangular

he probability of bitstring xi 53-qubit superconducting circuit device
 algorithms
 array of 54 qubits (grey), in an exponentially
 each connected
 couplers (blue). Theprocessor
 inoperablewith
 to its fourlarge
 programmable
 qubit
 computational
 nearest neighbours space.
 is outlined. b,superconducting
 Photograph of the
 with Here we report the use of a
 qubits2–7 to create quantum states on
 Photonic device — special-purpose
 and the average is over the Sycamore chip. 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). The Extended Church-Turing Thesis is a foundational tenet A very recent experiment on a 53-qubit processor has
 rrelated with how often we
 n there are no errors in the
 Algorithm: sampling of random circuits
 Measurements from repeated experiments sample the resulting probability
 distribution, which we verify using classical simulations. Our Sycamore processor takes
 Algorithm: boson sampling
 in computer science, which states that a probabilistic Turing
 machine can efficiently simulate any process on a realistic
 generated a million noisy (~0.2% fidelity) samples in 200 s
 (8), while a supercomputer would take 10,000 years. It was
 abilities is exponential (see connectivity was about
 chosen 200toseconds
 be forward-compatible
 to sample one instance with
 of aerror
 quantum correc-
 circuit a million times—our physical device (1). In the 1980s, Richard Feynman observed soon argued that the classical algorithm can be improved to

 (103) times faster than best classical Claim: (10 ) times faster than
 14
ng from this distribution will tion using the surface
 benchmarks
 26
 code . currently
 A key systems
 indicate engineering advance
 that the equivalent taskof
 forthis
 a state-of-the-art classical that many-body quantum problems seemed difficult for cost only a few days to compute all the 253 quantum proba
 mpling from the uniform device is achieving high-fidelitywould
 supercomputer single- takeand two-qubit 10,000
 approximately operations, not dramatic increase in
 years. This classical computers due to the exponentially growing size of bility amplitudes and generate ideal samples (9). Thus, if the
duce FXEB = 0. Values of FXEB just in isolation but alsocompared
 speed while performing
 to all knownaclassical
 realisticalgorithms
 computation with
 is an experimental realization of the quantum state Hilbert space. He proposed that a quan- competition were to generate a much larger size of samples
 supercomputers
ity that no error has occurred simultaneous gatequantum
 operations
 anticipated
 on many
 supremacy
 computing
 8–14
 qubits. We discuss
 for this specific
 paradigm.
 the highlights
 computational task, heralding a much- best classical supercomputers
 tum computer would be a natural solution.
 A number of quantum algorithms have since been de-
 for example, ~1010, the quantum advantage would be re
 versed provided with sufficient storage. This sample-size
 P(xi) must be obtained from below; see also the Supplementary Information.
 vised to efficiently solve problems believed to be classically dependence of the comparison—an analog to loopholes in
, and thus computing FXEB is In a superconducting circuit, conduction electrons condense into a
 hard, such as Shor’s factoring algorithm (2). Building a Bell tests (10)—suggests that quantum advantage would re
 macy. However, with certain
 James Mulligan, macroscopic
 LBNL quantum state, such that currents and voltages behave Initial
 In the early 1980s, Richard Feynman proposed that a quantum computer In reaching this milestone, we show that quantum speedupStages
 is achiev- 2021 fault-tolerant quantum computer to run Shor’s Janalgorithm,
 11, 2021 quire long-term competitions between faster classical25simu
 titative fidelity estimates of quantum mechanically2,30. Our processor uses transmon qubits6, which

Readout error mitigation
 Constrained matrix inversion Unfolding
 Nachman, Urbanek, de Jong, Bauer `19

 Prepare states by applying bit-flip
 X gates and read out

 ibmq_vigo device

James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 26

Error mitigation
 Readout error
 Constrained matrix inversion Unfolding
 Nachman, Urbanek, de Jong, Bauer `19
 Gate error
 Zero-noise extrapolation of CNOT noise using Random Identity Insertions
 He, Nachman, de Jong, Bauer `20

 Circuit 1 …

 …
 Circuit 2 …

 Circuit 3 …
 …
James Mulligan, LBNL Initial Stages 2021 Jan 11, 2021 27