Veriﬁcation of Quantum Computing - SIRTEQ Kick off meeting · for science, technology and business to evaluate and program today’s quantum devices ... design Constraints Noise

Elham Kashefi

Verification of Quantum Computing

University of EdinburghCNRS, Pierre and Marie Curie University

Oxford Quantum Technology HubParis Centre for Quantum Computing

Quantum Software Mission

Develop knowledge and expertise for science, technology and business

to evaluate and program today’s quantum devices

so we can effectively exploit tomorrow’s





- What it is good for ? - Is it working ?





- What it is good for ? - Is it working ? - How much details do I need to know ?

- How could I encode my computation ?

Hardware

QSoft Vision of Quantum Technology

Hardware

Communication Network Computing Device

Hardware

Interface

Verification/BenchmarkingAbstraction/Modeling/Encoding


Hardware


Hardware

Interface

Verification/BenchmarkingAbstraction/Modeling/Encoding

Secrecy Speed

Application


Hardware


Hardware

Interface

Verification/BenchmarkingAbstraction/Modeling

Speed

Application

design Constraints

Noise

Tailor Made Construction


Hardware


Verification/Benchmarking

Secrecy

What is Verification


Sensors and Metrology: Certification of Enhancement



Simulation: Validation




Communications: Adversarial detection




Communications: Adversarial detection

Computations: Correctness

Quantum Era

Quantum Machines

National Investments

Europe 1bn€UK 270M £Netherlands 80M $US, Singapore,Canada

Private Investments

Google, IBM, IntelBig VC foundsStartups Companies: D-Wave

5

Quantum Era

Quantum Machines



Private Investments


5

Quantum Era

Quantum Machines



Private Investments


Target: > 50 qubits Device

5

Quantum Era

Quantum Machines



Private Investments



Feature: Not Simulatable Classically

5

Quantum Era

Quantum Machines



Private Investments




Problem: Testing, Validation, BenchMarking, Certification, Verification …

5

Quantum Era

Quantum Machines



Private Investments




Problem: Testing, Validation, BenchMarking, Certification, Verification …

5

We can BOOTSTRAP a smaller quantum device to test a bigger one



A mechanism that when witness is accepted the outcome is good


A mechanism that when witness is accepted the outcome is not bad



A mechanism that when witness is accepted the outcome is not bad

A mechanism that probability of witness is accepted and the outcome is bad is bounded



A mechanism that prob of witness is acc and outcome is bad is bounded



...

Prover/Device/Eve/NoiseVerifier



⌫

4

random parameters ...

Prover/Device/Eve/NoiseVerifier



⌫

4


Prover/Device/Eve/NoiseVerifier P

⌫ p(⌫) Tr (P ⌫incorrect B(⌫)) ✏

B(⌫)

4

density operator of classical and quantum output



⌫

4


Prover/Device/Eve/NoiseVerifier P


B(⌫)

4

density operator of classical and quantum output

Abort/Acc


proververifier⌫

4

...P


B(⌫)

4



proververifier⌫

4

...P


B(⌫)

4

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect

:= P? ⌦ |accihacc|

1



✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


1

proververifier⌫

4

...P


B(⌫)

4



✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


1

P⌫ p(⌫) Tr (P ⌫

incorrect B(⌫)) ✏

B(⌫)

4

proververifier⌫

4

...P


B(⌫)

4


What is the challenge

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


1

P⌫ p(⌫) Tr (P ⌫


B(⌫)

4

proververifier⌫

4

...P


B(⌫)

4



✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


1

P⌫ p(⌫) Tr (P ⌫


B(⌫)

4

proververifier⌫

4

...P


B(⌫)

4

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦

1



✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


1

P⌫ p(⌫) Tr (P ⌫


B(⌫)

4

proververifier⌫

4

...P


B(⌫)

4

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦

1


How to deal with deviation

P⌫ p(⌫) Tr (P ⌫


B(⌫)

4

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦

1


P⌫ p(⌫) Tr (P ⌫


B(⌫)

4

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦

1

Different toolkits / Different tasks / Different witness / Different properties / Different assumptions / …..


P⌫ p(⌫) Tr (P ⌫


B(⌫)

4

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦

1

Different toolkits / Different tasks / Different witness / Different properties / Different assumptions / …..

Hypothesis Test, Certification, Self Testing, Entanglement detection, Quantum signature, Proof System, Hardware Testing, Post-hoc verification,

Randomised benchmarking, Authentication, Blind Verification

Most General Deviation

cryptographic toolkit

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦Eve,system

1



✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦Eve,system

1

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


�testsubspace

1


Practical Protocols with No assumptions whatsoever


✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦Eve,system

1

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


�testsubspace

1


Practical Protocols with No assumptions whatsoever


✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


⌦Eve,system

1

✓1 00 �1

◆,

✓0 11 0

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(�) := (�+ ✓ + r⇡)✓

1ei✓

◆

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

E(m)

�

P ⌫

incorrect


�testsubspace

1

arXiv:1709.06984

Verification of quantum computation: An overview of existing approaches

Alexandru Gheorghiu, Theodoros Kapourniotis, Elham Kashefi

Classically-controlled QC

arX

iv:0

805.1

002v1 [q

uan

t-ph]

7 M

ay 2

008

Measurement-based classical computation

Janet Anders∗1 and Dan E. Browne†1

1Department of Physics and Astronomy, University College London,Gower Street, London WC1E 6BT, United Kingdom.

(Dated: May 8, 2008)

We study the intrinsic computational power of entangled states exploited in measurement-basedquantum computation. By focussing on the power of the classical computer that controls the mea-surements, we develop a classification of computational resource power, leading naturally to a notionof resource states for measurement-based classical computation. Surprisingly, the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimony-Holt problems emerge naturally as optimal examples.Our work exposes an intriguing relationship between the violation of local realistic models and thecomputational power of entangled resource states.

PACS numbers: 03.67.Lx, 03.65.Ud

Introduction.– Measurement-based quantum computa-tion is an approach to computation radically different toconventional circuit models. In a circuit model, infor-mation is manipulated by a network of logical gates. Inmeasurement-based quantum computation (also knownas “one-way” quantum computation) information is pro-cessed by a sequence of adaptive single-qubit mea-surements on a pre-prepared multi-qubit resource state[1, 2, 3]. A classical computer controls all measurements(see Fig. 1) by keeping track of the outcomes of previousmeasurements and determining the bases for the mea-surements to come. The separation of entangling andsingle-qubit operations leads to significant experimentaladvantages in a number of different systems [4]. Notably,the classical control computer is the only part of themodel where active computation takes place. A strik-ing implication of the measurement-based model is thatentangled resource states can possess an innate computa-tional power. Merely by exchanging single bits with eachof the measurement sites of the resource state (see Fig.1), the control computer is enabled to compute problemsbeyond its own power. For example, by controlling mea-surements on the cluster states the control computer ispromoted to full quantum universality.

Impressive characterization of the necessary propertiesof resource states that enable a computational “boost”to universal quantum computation has already beenachieved [5, 6], however, little is known about the re-quirements for a resource state to increase the power ofthe classical control computer at all. In this paper, we de-velop a framework which allows us to classify the compu-tational power of resource states for a control computerof given power. By doing so, a natural classical ana-logue of measurement-based computation emerges: con-sidering a control computer of restricted computational

∗[email protected]†[email protected]

resource state

control computer

measurement

sites

FIG. 1: The control computer provides one bit of classicalinformation (downward arrows) to each site (circles in the re-source state) determining the choice of measurement basis.After the measurement, one bit of classical information (up-ward arrow), such as the outcome of the binary measurement,is sent back to the control computer.

power what are resource states that enable determinis-tic universal classical computation? Here we show thatsuch resource states exist and that an unlimited supplyof three-qubit Greenberger-Horne-Zeilinger (GHZ) statesimplements this task in an optimal way. Moreover, ourmodel provides a unifying picture drawing together someof the most important results in the study of quantumnon-locality. Specifically, we show that the GHZ prob-lem [7] and the Clauser-Horne-Shimony-Holt (CHSH)construction [8] emerge as closely related to tasks inmeasurement-based classical computation (MBCC), asdoes the Popescu-Rohrlich non-local box [9].

Framework for measurement-based computation.– Firstwe need to cast measurement-based quantum computa-tion in a framework which assumes as little as possibleabout the physical properties of the computational re-source. The model consists of the following components(see Fig. 1): 1) a control computer, with a specified com-putational power; 2) n measurement-sites, which mayshare pre-existing entanglement, or correlation, but maynot communicate during the computation 3) limited com-munication between control computer and sites - duringthe computation each measurement site receives a singlebit from the control computer and sends back a singlebit in return. It is emphasized that we place no restric-

control computer

resource state

measurement site

Program is encoded in the classical control computer

Computation Power is encoded in the quantum entanglement

7

MBQC - Cluster State - Gate Teleportation

Hiding Program

arX

iv:0

805.1

002v1 [q

uan

t-ph]

7 M

ay 2

008










resource state

control computer

measurement

sites




control computer

resource state

measurement site

8

Hiding Program

arX

iv:0

805.1

002v1 [q

uan

t-ph]

7 M

ay 2

008










resource state

control computer

measurement

sites




control computer

resource state

measurement site

single encrypted qubit +

classical bits

8

Hiding Program

arX

iv:0

805.1

002v1 [q

uan

t-ph]

7 M

ay 2

008










resource state

control computer

measurement

sites




control computer

resource state

measurement site


classical bits

8

✓1 00 eib⇡/2

◆✓1 00 eia⇡/2

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(m) = (m+ ✓ + r⇡ , |0i+ ei✓|1i)

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓

Xi = PRi + ✓i Ri 2R ZQ ✓ 2R [A Suitably Small Range]

1

Hiding Program

arX

iv:0

805.1

002v1 [q

uan

t-ph]

7 M

ay 2

008










resource state

control computer

measurement

sites




control computer

resource state

measurement site


classical bits

8

✓1 00 eib⇡/2

◆✓1 00 eia⇡/2

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(m) = (m+ ✓ + r⇡ , |0i+ ei✓|1i)

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓


1

Computing via Teleportation

Hiding Program

arX

iv:0

805.1

002v1 [q

uan

t-ph]

7 M

ay 2

008










resource state

control computer

measurement

sites




control computer

resource state

measurement site

Informationally Secure Perfect Privacy

Server learns nothing about client’s input/output/function


classical bits

8

✓1 00 eib⇡/2

◆✓1 00 eia⇡/2

◆✓1 00 e�i(a�b)⇡/2

◆✓1�1

◆=

✓1 00 e�i(a^b)⇡

◆✓1�1

◆

Z

�2 = f(r1, r2, ✓2,�2)

m

E(m) = (m+ ✓ + r⇡ , |0i+ ei✓|1i)

E(m2) = m+ PR2 + ✓2

E(m1) ⇤ E(m2) = E(m1 ⇤m2)

D(m) = m� bm/P eP � ✓


1

Computing via Teleportation

Unconditionally Secure Quantum Cloud in Theory

Broadbent, Fitzsimons and Kashefi, FOCS09

Unconditionally Secure Quantum Cloud in Theory

Universal Blind Quantum Computing: QKD + Teleportation

Broadbent, Fitzsimons and Kashefi, FOCS09

Verifiable Quantum Cloud in Theory

Aharonov, Ben-Or, and Eban, ICS 2010 Fitzsimons and Kashefi, 2012

Verifiable Quantum Cloud in Theory

Verifiable Universal Blind Quantum Computing: QKD + Teleportation + Test

Aharonov, Ben-Or, and Eban, ICS 2010 Fitzsimons and Kashefi, 2012

c

d

Quarter/Half-wave Plate

Polarization Controller

Filter

Polarizing Beam Splitter

BBO crystal

Bob

Alice

b

a

2

4

1

3θ 3 θ 2

S. Barz, E. Kashefi, A. Broadbent, J. Fitzsimons, A. Zeilinger, P. Walther Science 2012

Photonic Implement

Hybrid Architecture

Hybrid Architecture

arXiv:1611.10107

Private quantum computation: An introduction to blind quantum computing

Joseph F. Fitzsimons

Global Directions on Verification

via Hiding : Cloud-based Crypto App Distributed Network



via Proof System : Quantum Simulation




via Hypothesis Testing : Bench Marking Quantum Supremacy





- EPSRC UK - NRF Singapore- USAirforce - EU QFlagship





- EPSRC UK - NRF Singapore- USAirforce - EU QFlagship

- Number Crunching- Noise Handling- Architecture Adaptation - New Methods Development

Verification Status

Verification Status

Trust Worthy Quantum Information TyQi17 Paris

- It exists- It is expanding

Verification Status

Trust Worthy Quantum Information TyQi17 Paris

- It exists- It is expanding

- The overhead depends on the level of trust

Single server price of trust

Protocols: [Gheorghiu, Kashefi, Wallden ’15], [Hajdusek,Perez-Delgado, Fitzsimons ’15], [Gheorghiu, Wallden, Kashefi ’15]

aaaaaaaaaaaMeasurements

Entanglement

TrustedSemi-trusted

(i.i.d.)Untrusted

Trusted O(N) O(N4logN) O(N13log(N))Untrusted O(N4logN) O(N4logN) O(N64)

Bounds are not tight!

Assuming untrusted entanglement...

Untrusted measurements ! device independence

Trusted measurements ! one-sided device independence

Elham Kashefi (joint work with A. Gheorghiu and P. Walden) Price of Trust

Verification Status

Verification Status

Robust and Efficient Fault Tolerant Verification of various architectures is possible

Verification Challenge


Standardisation ??? Given the unknown nature of the emerging devices

- uniform platform versus tailored made




- Academic versus Industry’s need

Objective improvements




- Academic versus Industry’s need

Objective improvements

VeriQloud spinoff of LIP6

Certifiable Quantum Advantage


Computational Problem Quantum Hardware Verification Technique


Boson Sampling Photonics Hardware Noise Certification




IQP Cold Atoms Blind Verification





Randomised Circuit Superconducting Hypothesis Test





Randomised Circuit Superconducting Hypothesis Test


Trace Estimation NMR Blind Verification

Instantaneous quantum poly-time machine


Only use two qubit commuting gates


Only use two qubit commuting gates

• Almost Classical Verifier

• Certify the machine is capable of computing IQP

IQP Hypothesis Test - Theory


Theory Step 1

If IQP computation was classically simulatable then PH collapses


Theory Step 1


Theory Step 2

Hide Test Round among the Sampling Round


Theory Step 1


Theory Step 2


5

��

��

��

��

��

��

��

��

FIG. 4: Schematic of a quantum computation with verification sub-routines.

Whereas the laws of physics have been tested in vari-ous limits - small or large scales, high or low energies -the boundary of high computational complexity is mostlyunexplored. So, it is even imaginable that quantummechanics might break down at some scale of complex-ity [22].

On the experimental side, current quantum comput-ers [23] are limited to the processing of a few qubits,which does not allow yet to solve problems which are in-tractable using classical computers. In the future whenlarge-scale quantum computers might be available [24–27], the verification of quantum computations and quan-tum simulations will be a crucial task [28].

Thus, our demonstration might have implications fornew quantum computing experiments as well as on thefoundations of quantum physics.

Add Caslav’s statement: In our implementation, weassume the correctness of quantum mechanics forthe verification of quantum resources. Without thisassumption, a full demonstration would require thetwo entangled photons to be sent far apart from eachother in two distant laboratories of the prover whereonly in the very last instant of the computation theverifier gives the measurement instructions to theprover. By this means, no classical computers couldmimic the output of the computation.

ACKNOWLEDGEMENTS

Please add Acknowledgements

The authors are grateful to D. Aharonov and S. Aaron-son for discussions. We acknowledge support from...

AUTHOR CONTRIBUTION

S.B. designed and performed the experiments, acquiredthe experimental data, carried out theoretical calcula-tions and the data analysis, and wrote the manuscript.E.K. and J.F. carried out theoretical calculations, con-tributed the proofs, and edited the manuscript. C.B.provided theoretical analysis and wrote the manuscript.P.W. edited the manuscript and supervised the project.

[1] D. Deutsch, Proc. R. Soc. A 400, 97 (1985),http://rspa.royalsocietypublishing.org/content/400/1818/97.full.pdf+html,URL http://rspa.royalsocietypublishing.org/

content/400/1818/97.abstract.[2] D. Deutsch and R. Jozsa, Proc. R. Soc. A 439, 553

(1992).[3] L. K. Grover, in Proceedings of the 28th Annual ACM

Symposium on the Theory of Computing (1996), pp. 212–219.

[4] P. W. Shor, SIAM J. Comput. 26, 1484 (1997), first pub-lished in 1995.

[5] A. W. Harrow, A. Hassidim, and S. Lloyd, Phys. Rev.Lett. 103, 150502 (2009).

[6] D. Aharonov, M. Ben-Or, and E. Eban, arXiv:0810.5375(2008).

[7] D. Aharonov and U. Vazirani, arXiv:1206.3686 (2012).[8] A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceed-

ings of the 50th Annual Symposium on Foundations ofComputer Science (2009), pp. 517–526.

[9] S. Barz, E. Kashefi, A. Broadbent, J. Fitzsimons,A. Zeilinger, and P. Walther, Science 335, 303 (2012).

[10] R. Feynman, Int. J. Theor. Phys. 21, 467 (1982), URLhttp://dx.doi.org/10.1007/BF02650179.

[11] J. Watrous, arXiv:0804.3401 (2008).[12] L. Babai, in Proceedings of the seventeenth annual ACM

Test Run

SamplingSampling

Sampling

SamplingSampling

Test Run


Theory Step 1


Theory Step 2


5

��

��

��

��

��

��

��

��

FIG. 4: Schematic of a quantum computation with verification sub-routines.

Whereas the laws of physics have been tested in vari-ous limits - small or large scales, high or low energies -the boundary of high computational complexity is mostlyunexplored. So, it is even imaginable that quantummechanics might break down at some scale of complex-ity [22].

On the experimental side, current quantum comput-ers [23] are limited to the processing of a few qubits,which does not allow yet to solve problems which are in-tractable using classical computers. In the future whenlarge-scale quantum computers might be available [24–27], the verification of quantum computations and quan-tum simulations will be a crucial task [28].

Thus, our demonstration might have implications fornew quantum computing experiments as well as on thefoundations of quantum physics.

Add Caslav’s statement: In our implementation, weassume the correctness of quantum mechanics forthe verification of quantum resources. Without thisassumption, a full demonstration would require thetwo entangled photons to be sent far apart from eachother in two distant laboratories of the prover whereonly in the very last instant of the computation theverifier gives the measurement instructions to theprover. By this means, no classical computers couldmimic the output of the computation.

ACKNOWLEDGEMENTS

Please add Acknowledgements

The authors are grateful to D. Aharonov and S. Aaron-son for discussions. We acknowledge support from...

AUTHOR CONTRIBUTION

S.B. designed and performed the experiments, acquiredthe experimental data, carried out theoretical calcula-tions and the data analysis, and wrote the manuscript.E.K. and J.F. carried out theoretical calculations, con-tributed the proofs, and edited the manuscript. C.B.provided theoretical analysis and wrote the manuscript.P.W. edited the manuscript and supervised the project.

[1] D. Deutsch, Proc. R. Soc. A 400, 97 (1985),http://rspa.royalsocietypublishing.org/content/400/1818/97.full.pdf+html,URL http://rspa.royalsocietypublishing.org/

content/400/1818/97.abstract.[2] D. Deutsch and R. Jozsa, Proc. R. Soc. A 439, 553

(1992).[3] L. K. Grover, in Proceedings of the 28th Annual ACM

Symposium on the Theory of Computing (1996), pp. 212–219.

[4] P. W. Shor, SIAM J. Comput. 26, 1484 (1997), first pub-lished in 1995.

[5] A. W. Harrow, A. Hassidim, and S. Lloyd, Phys. Rev.Lett. 103, 150502 (2009).

[6] D. Aharonov, M. Ben-Or, and E. Eban, arXiv:0810.5375(2008).

[7] D. Aharonov and U. Vazirani, arXiv:1206.3686 (2012).[8] A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceed-

ings of the 50th Annual Symposium on Foundations ofComputer Science (2009), pp. 517–526.

[9] S. Barz, E. Kashefi, A. Broadbent, J. Fitzsimons,A. Zeilinger, and P. Walther, Science 335, 303 (2012).

[10] R. Feynman, Int. J. Theor. Phys. 21, 467 (1982), URLhttp://dx.doi.org/10.1007/BF02650179.

[11] J. Watrous, arXiv:0804.3401 (2008).[12] L. Babai, in Proceedings of the seventeenth annual ACM

Test Run

SamplingSampling

Sampling

SamplingSampling

Test RunBlind Quantum Computing

IQP Hypothesis Test - Practice

NQIT: Photon/Ion Traps

Noise Model



Noise Model



Simulator of Quantum Computing

Noise Model



Simulator of Quantum Computing

HT is very fragile

Interface

Verification Hypothesis Test

Classical Client ?Abstraction/Modeling

QCloud, QMultiPartySampling

Quantum Simulation ?

Application

design Constraints ?

Noise ?

Tailor Made Construction ?

Where we stand

Hardware ?

Real Network ? Computing Device ?

The Edinburgh-Paris Team

Development Deployment

Q-enhancedCloud

In the lab

Certification Multi-party QC

Research

Verification

The Edinburgh-Paris Team

Development Deployment

Q-enhancedCloud

In the lab

Certification Multi-party QC

Research

Verification

Alexandru Cojocaru

Andru Gheorghiu

Daniel Mills

Luka Music

Ulysse Chabaud

Tom Douce

Interns:

Ieva Cepaite Iskren Vankov Phivos Sofokleous Kelsey Horan Léo Colisson

Petros Wallden

Ellen Derbyshire

Brian Coyle

Other collaborators

Theory

Experiment

Damian Markham (LIP6)Joe Fitzsimons (SUTD)

Anna Pappa (UCL)Anne Broadbent (Ottawa)Vedran Dunjko (Innsbruck) Anthony Leverrier (INREA)Animesh Datta (Warwick)

Theodoros Kapourniotis (Warwick)

Stefanie Barz (Vienna,Oxford)Philip Walther (Vienna)Ian Walmsley (Oxford)

Other collaborators

Theory

Experiment

Damian Markham (LIP6)Joe Fitzsimons (SUTD)

Anna Pappa (UCL)Anne Broadbent (Ottawa)Vedran Dunjko (Innsbruck) Anthony Leverrier (INREA)Animesh Datta (Warwick)

Theodoros Kapourniotis (Warwick)

Stefanie Barz (Vienna,Oxford)Philip Walther (Vienna)Ian Walmsley (Oxford)

Documents

Veriﬁcation of Quantum Computing - SIRTEQ Kick off meeting · for science, technology and business to evaluate and program today’s quantum devices ... design Constraints Noise