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QUANTUM SUPREMACY :

in

FINANCIAL MARKETS (FOREX)∗

Ignacio Ozcariz†

RQuantech - Geneva (Switzterland)

Criptosasun - Madrid (Spain)

‡

(Dated: November 7, 2019)

The paper presents how to achieve market dominance, implementing the oldest plain vanilla price

arbitrage strategy, using the newest quantum entanglement phenomena.

CONTENTS

I. Introduction. 1

II. Dynamics of FOREX (FX) Market 1

A. High Frequency Trading (HFT) 1

B. Direct Market Access (DMA) 2

C. Strategies 2

1. Latency-Arbitrage 2

2. Regulation (USA) 2

D. Summary 2

III. Quantum Information and Quantum Computation3

A. Introduction (Ref:[1]) 3

B. Quantum State – Vector representation

(Ref:[2]) 3

C. Measurements (Ref:[2]) 3

D. Entanglement (Ref:[2]) 4

IV. Methodology 4

A. Set-up 4

B. Price Communication 4

C. Price Reception and Comparison with current

prices 4

D. Quantum Processes 5

E. Summary 7

V. Implementation 7

A. Structure and Technologies 7

1. Tick-to-Trade 8

2. Communications 8

3. Quantum supremacy 8

B. State of the Art 8

C. Disclaimer 8

VI. Conclusions 8

Acknowledgments 8

References 8

∗Applicable also to any ﬁnancial market

†Also at Universidad Politecnica Madrid. Doctorate Student;

im.ozcariz@alumnos.upm.es

‡i.ozcariz@rquantech.com

I. INTRODUCTION.

“It from bit” symbolizes the idea that every item

of the physical world has at bottom—a very deep

bottom, in most instances — an immaterial source and

explanation; that which we call reality arises in the last

analysis from the posing of yes-or-no questions and the

registering of equipment-evoked responses; in short, that

all things physical are information-theoretic in origin

and that this is a participatory universe.”

– John A. Wheeler, [3]

Thirty years later from this statement it’s time to up-

date it and propose that “It from qubit” could be the

last truth.

This paper will present a novel approach to the

use of quantum techniques that we nickname quantum

supremacy applied to the ﬁnancial markets and particu-

larly to the FOREX market.

We’ll demonstrate that having two entangled devices,

more on the deﬁnition of entanglement in Section 3 of

the paper, it’s possible to achieve a full dominance in the

FOREX using a very simple plain vanilla strategy, price

arbitrage between two far away markets.

II. DYNAMICS OF FOREX (FX) MARKET

Each day, billions of monetary units are exchanged on

the foreign exchange currency market. FX trading is used

to determine currency exchange rates across the world.

While people have been trading currencies for thousands

of years, modern technology has changed the way that

many banks and individual investors do business.

One of the key technologies in the evolution of the

markets has been high frequency trading (HFT) and its

impact in the FX trading has been extraordinary.

A. High Frequency Trading (HFT)

According to the dictionary of ﬁnancial terms of NAS-

DAQ [4]

High Frequency Trading (HFT)

2

Refers to computerized trading using proprietary algo-

rithms. There are two types high frequency trading.

Execution trading is when an order (often a large or-

der) is executed via a computerized algorithm. The pro-

gram is designed to get the best possible price. It may

split the order into smaller pieces and execute at diﬀerent

times.

The second type of high frequency trading is not exe-

cuting a set order but looking for small trading opportu-

nities in the market.

It is estimated that 50 percent of stock trading volume

in the U.S. is currently being driven by computer-backed

high frequency trading. Also known as algo or algorith-

mic trading.

B. Direct Market Access (DMA)

Access to the markets was historically being mediated

by banks or direct brokers at the markets. From the last

decennials of the past century this interrelation has given

pass to the direct access to the markets named DMA

(Direct Market Access).

According to David Polen [5] :

There are two distinct market segments that use DMA

- the human trader and the blackbox. I like to call

this “Human DMA” and “Highfrequency Trading (HFT)

DMA”.

With Human DMA, the extreme is a buy-side that has

traders manually executing trades and looking at market

data over the Internet-

With HFT DMA, the extreme is a blackbox co-located

at the exchange. One market segment is sub-millisecond

and the other is more than tens of milliseconds - some-

times hundreds of milliseconds.

C. Strategies

About the strategies used by the black-boxes, in 2014

the Security and Exchange Commission (SEC) appears to

emphatically say that two strategies, order anticipation

and momentum ignition, are manipulative and illegal.

The SEC writes [6]:

“Directional strategies generally involve establishing a

long or short position in anticipation of a price move

up or down. The Concept Release requested comment

on two types of directional strategies – order anticipa-

tion and momentum ignition – that ‘may pose particular

problems for long-term investors’ and ‘may present seri-

ous problems in today’s market structure.’

An order anticipation strategy seeks to ascertain the

existence of large buyers or sellers in the marketplace and

then trade ahead of those buyers or sellers in anticipation

that their large orders will move market prices (up for

large buyers and down for large sellers).

A momentum ignition strategy involves initiating a se-

ries of orders and trades in an attempt to ignite a rapid

price move up or down.

As noted in the Concept Release[7], any market partic-

ipant that manipulates the market has engaged in con-

duct that already is illegal. The Concept Release focused

on the issue of whether additional regulatory tools were

needed to address illegal practices, as well as any other

practices associated with momentum ignition strategies.”

1. Latency-Arbitrage

Going down to the technicalities, Latency Arbitrage is

an important concept when discussing High Frequency

Trading, and refers to the fact that diﬀerent people and

ﬁrms receive market data at diﬀerent times.

These time diﬀerences, known as latencies, may be as

small as a billionth of second (a nanosecond), but in the

world of high speed trading, such diﬀerences can be cru-

cial. So crucial, in fact, that trading ﬁrms pay lots of

money to be located closer to exchanges’ servers– each

foot closer saves one nanosecond.

Latency arbitrage occurs when high frequency trading

algorithms make trades a split second before a competing

trader, and then resell the stock seconds later for a small

proﬁt.

2. Regulation (USA)

The previous Congress dealt with potential regulation

of HFT (US Congress HFT Overview of Recent Devel-

opments 2016)[8]. We very brieﬂy refer here to the Tes-

timony on Regulatory Reforms to Improve Equity Mar-

ket Structure by Stephen Luparello, director, Division

of Trading and Markets, U.S. Securities and Exchange

Commission, Before the Senate Committee on Banking,

Housing and Urban Aﬀairs Subcommittee on Securities,

Insurance and Investment. This declaration was made

March 3, 2016.

Luparello said SEC staﬀ was developing a recommen-

dation for the SEC to consider addressing the use of ag-

gressive, destabilizing trading strategies that could exac-

erbate price volatility.

Until today regulation is still a working process.

D. Summary

It can be extremely challenging to earn a proﬁt when

trading currency. In many cases, investors can lose sig-

niﬁcant sums of money. Exchange rates can be impacted

by a variety of factors. This can include economic condi-

tions, politics, weather, shipping conditions, piracy, tech-

nology advances and more.

Many HFT programs are installed in specialized data

centres located near an exchange (Co-location). Since the

speed of execution is limited by the speed of light, many

programmers and investors try to minimize the amount

3

of time it takes for an order to be executed. This is

possible by minimizing the amount of time it takes data

to travel between the operator premises and an exchange.

Most HFT programs are designed to proﬁt from very

small price diﬀerences in a currency. In many cases, a

program will make a proﬁt of only a few cents per trade.

However, millions of these types of trades every day can

yield a signiﬁcant proﬁt.

Our approach in this paper we’ll be to use the oldest

strategy, price arbitrage between two locations, proﬁt-

ing the quantum supremacy. (The spooky action at a

distance; in Einstein words).

III. QUANTUM INFORMATION AND

QUANTUM COMPUTATION

A. Introduction (Ref:[1])

a. Quantum computing fundamentals. All comput-

ing systems rely on a fundamental ability to store and

manipulate information. Current computers manipulate

individual bits, which store information as binary 0 and

1 states. Quantum computers leverage quantum mechan-

ical phenomena to manipulate information. To do this,

they rely on quantum bits, or qubits.

b. Quantum Properties. Three quantum mechan-

ical properties — superposition, entanglement, and

interference — are used in quantum computing to

manipulate the state of a qubit.

1. Superposition

Superposition refers to a combination of states we

would ordinarily describe independently. To make

a classical analogy, if you play two musical notes at

once, what you will hear is a superposition of the

two notes.

2. Entanglement

Entanglement is a famously counter-intuitive quan-

tum phenomenon describing behavior we never see

in the classical world. Entangled particles behave

together as a system in ways that cannot be ex-

plained using classical logic.

3. Interference

Finally, quantum states can undergo interference

due to a phenomenon known as phase. Quantum

interference can be understood similarly to wave

interference; when two waves are in phase, their

amplitudes add, and when they are out of phase,

their amplitudes cancel.

B. Quantum State – Vector representation

(Ref:[2])

What then is a qubit?

Just as a classical bit has a state – either 0 or 1 – a qubit

also has a state. Two possible states for a qubit are the

states |0iand h1|, which as you might guess correspond

to the states 0 and 1 for a classical bit.

Notation like | i and h | is called the Dirac notation,

and we’ll be seeing it often, as it’s the standard notation

for states in quantum mechanics. The diﬀerence between

bits and qubits is that a qubit can be in a state other than

|0ior h1|. It is also possible to form linear combinations

of states, often called superpositions:

|ψi=α|0i+β|1i(1)

FIG. 1. Qubit Bloch Sphere representation

The numbers αand βare complex numbers, although

for many purposes not much is lost by thinking of them

as real numbers. Put another way, the state of a qubit

is a vector in a two-dimensional complex vector space.

The special states |0iand h1|are known as computational

basis states and form an orthonormal basis for this vector

space.

We can examine a bit to determine whether it is in

the state 0 or 1. For example, computers do this all the

time when they retrieve the contents of their memory.

Rather remarkably, we cannot examine a qubit to deter-

mine its quantum state, that is, the values of αand β.

Instead, quantum mechanics tells us that we can only ac-

quire much more restricted information about the quan-

tum state. When we measure a qubit we get either the

result 0, with probability |α|2, or the result 1, with prob-

ability |β|2.Naturally, |α|2+|β|2= 1, since the probabil-

ities must sum to one. Geometrically, we can interpret

this as the condition that the qubit’s state be normalized

to length 1. Thus, in general a qubit’s state is a unit

vector in a two-dimensional complex vector space.

C. Measurements (Ref:[2])

Suppose we have two qubits. If these were two classical

bits, then there would be four possible states, 00, 01, 10,

and 11. Correspondingly, a two qubit system has four

computational basis states denoted |00i,|01i,|10i,

|11i.

4

A pair of qubits can also exist in superpositions of these

four states, so the quantum state of two qubits involves

associating a complex coeﬃcient – sometimes called an

amplitude – with each computational basis state, such

that the state vector describing the two qubits is

|ψi=α00|00i+α01 |01i+α10|10i+α11 |11i(2)

Similar to the case for a single qubit, the measurement

result x (= 00, 01, 10 or 11) occurs with probability

|αx|2, with the state of the qubits after the measure-

ment being |xi. The condition that probabilities sum to

one is therefore expressed by the normalization condition

that Px∈{0,1}2|αx|2= 1,where the notation x∈ {0,1}2

means ‘the set of strings of length two with each let-

ter being either zero or one’. For a two-qubit system,

we could measure just a subset of the qubits, say the

ﬁrst qubit, and you can probably guess how this works:

measuring the ﬁrst qubit alone gives 0 with probability

|α00|2+|α01 |2, leaving the post-measurement state

|ψi=α00|00i+α01 |01i

p|α00|2+|α01 |2(3)

Note how the post-measurement state is re-normalized

by the factor p|α00|2+|α01|2so that it still satisﬁes the

normalization condition, just as we expect for a legiti-

mate quantum state.

D. Entanglement (Ref:[2])

An important two qubit state is the Bell state or EPR

pair, β00, that we’ll make use in our methodology section.

β00 =|00i+|11i

√2(4)

This innocuous-looking state is responsible for many sur-

prises in quantum computation and quantum informa-

tion. The Bell state has the property that upon mea-

suring the ﬁrst qubit, one obtains two possible results: 0

with probability 1/2, leaving the post-measurement state

|φ´i=|00i, and 1 with probability 1/2, leaving |φ´

i=|11i.

As a result, a measurement of the second qubit al-

ways gives the same result as the measurement of the

ﬁrst qubit. That is, the measurement outcomes are cor-

related.

These correlations have been the subject of intense in-

terest ever since a famous paper by Einstein, Podolsky

and Rosen, in which they ﬁrst pointed out the strange

properties of states like the Bell state. EPR’s insights

were taken up and greatly improved by John Bell, who

proved an amazing result: the measurement correlations

in the Bell state are stronger than could ever exist be-

tween classical systems. These results were the ﬁrst inti-

mation that quantum mechanics allows information pro-

cessing beyond what is possible in the classical world.

This “amazing” correlation will be at the base of our

Quantum Supremacy over the FOREX market.

IV. METHODOLOGY

A. Set-up

Market strategy will be made in the FOREX market

over London and New York markets based on the pair

EUR/USD. Let’s name the price of this pair P.

For the implementation of our strategy we’ll use the

Alice and Bob characters invented by Ron Rivest, Adi

Shamir, and Leonard Adleman in their 1978 paper ”A

method for obtaining digital signatures and public-key

cryptosystems. In our scenario we suppose that A and

B (also known as Alice and Bob) are two market ma-

chines located (collocated) in London (Alice) and New

York (Bob).

Initially, at the start of the market session, both ma-

chines shared several entangled pair of qubits (2N). Let’s

name for the ﬁrst interchange the qubits Aq1,Aq2 for

Alice and Bq1,Bq2 for Bob.

Aq1,Bq1 are a pair of Bell’s qubits β00 and the same for

the other pair Aq2,Bq2.

Let’s establish a reference via the GPS clock shared by

both parties, using 20 Hz cycle, so each 50 milliseconds,

and name this time reference T0.

B. Price Communication

At this time A and B sends the current price Pof its

market to the other. Taking in account the 7,000 Kilo-

metres distance the time taken to the signal to arrive to

the other end is approx. (ﬁbre-optics or radio transmis-

sion could made diﬀerences in the ﬁnal time), 43 mil-

liseconds. Let’s name these prices P l0(London Price)

and P n0(New York price) at T0.

The potential outcomes that A and B will have regard-

ing the prices at T0are:

1. P l0=P n0State φ0(London equal price than New

York)

2. P l0> P n0State χ0(London greater price than

New York)

3. P l0< P n0State ψ0(London lesser price than New

York)

An arbitrage strategy could be established in the states

χand ψbut not in φ.

We’ll introduce a 5 milliseconds guard time to cover

potential delays of the signal due to any circumstances.

C. Price Reception and Comparison with current

prices

At T0+48 msec. that we’ll consider as T1, A and B had

new prices of Pat their respective markets. Let’s name

these new prices P l1(London) and P n1(New York).

5

FIG. 2. Initial Price States

It’s obvious that if the price in London is greater than

in NY (state χ0) a very simple strategy consists to buy

the pair in NY and to sell it in London that will carry on

a proﬁt in the transaction. The same occurs if London

is lesser than in NY (state ψ0). In his case the strategy

consists to sell the pair in NY and to buy it in London

and the strategy will carry also on a proﬁt.

To be successful in this strategy we need:

1. The prices when both parties received the infor-

mation regarding the other partner side have not

changed to the opposite condition. So for example,

at time T1,P l1> P n1

2. Both parties can communicate the other side the

condition 1 satisﬁed in its leg of the market.

The second condition allows that both parties go forward

in the buy/sell process doing the transactions concur-

rently.

Logically a further “classical” communication regard-

ing condition 2 will introduce a new delay of 43 millisec-

onds allowing the markets to change its positions during

the delay and removing any potential beneﬁt.

At this point we’ll introduce the Quantum Supremacy

mechanism based on the qubits shared previously be-

tween A and B.

D. Quantum Processes

At the moment T1we’ll have, related to the potential

movements of the market, the next conditions:

Alice side:

If State χ0

1. Condition GO:P l1≥P l0. The market is in the

same or more favourable conditions that in T0

2. Condition NO-GO:P l1< P l0. The market is in

less favourable conditions that in T0

If State ψ0

1. Condition GO:P l1≤P l0. The market is in the

same or more favourable conditions that in T0

2. Condition NO-GO:P l1> P l0. The market is in

less favourable conditions that in T0

FIG. 3. Alice at T1

Bob side:

If State χ0

1. Condition GO:P n1≤P n0. The market is in the

same or more favourable conditions that in T0

2. Condition NO-GO:P n1> P n0. The market is in

less favourable conditions that in T0

6

If State ψ0

1. Condition GO:P n1≥P n0. The market is in the

same or more favourable conditions that in T0

2. Condition NO-GO:P n1< P n0. The market is in

less favourable conditions that in T0

FIG. 4. Bob at T1

The manipulations of the qubits that Alice and Bob will

make with their qubits depending of the previous condi-

tions are:

Alice makes a measure in Aq1that is:

1. State φ0– Do nothing

2. States χ0and ψ0– and Condition GO Vmakes

a measure using M=|1ih1|

3. States χ0and ψ0– and Condition NO-GO V

makes a measure using M=|0ih0|

FIG. 5. Alice Measurement

Bob makes a measure in Bq2that is:

1. State φ0– Do nothing

2. States χ0and ψ0– and Condition GO Vmakes

a measure using M=|1ih1|

3. States χ0and ψ0– and Condition NO-GO V

makes a measure using M=|0ih0|

FIG. 6. Bob Measurement

7

Taking in consideration the characteristics of the measure

processes described in the Section (3), after the measure

of Alice and Bob of their qubits Aq1and Bq2with the

Matrix |1ih1|the qubits will ﬁnish in the state |1iand

after the measure of Alice and Bob of their qubits with

the Matrix |0ih0|the qubit will ﬁnish in the state |0i.

Going now to the entanglement properties presented

also in Section III.D, instantaneously to the above-

mentioned measures, the entangled qubits of Alice and

Bob, Aq2and Bq1will pass to the states |1iand |0iif

their pairs had ﬁnished in these states. (Remember the

properties of the Bell state β00 ).

A measure by Alice or Bob to these qubits will allow

to determine the GO or NO-GO condition of his part-

ner with probability 1, without the need of any classic

information exchange between them.

FIG. 7. Quantum Entanglement

E. Summary

Summarizing at the end of the process Alice and Bob

will have each of them the conditions GO or NO-

GOcorresponding to both partner positions.

So, two GO conditions will allow to settle from both

parties the Buy/Sell transaction making the correspond-

ing proﬁt.

FIG. 8. Trade Summary

Taking in account that ﬁrst measurement with the cho-

sen matrix is made at T1exact (∆T < 100 nanoseconds),

the second measurement would be made at T1+ 1 mi-

crosecond to have the assurance that the ﬁrst measure-

ment has already taken place by the other party.

In this condition the trade is settle by both parties at

T1+2 microseconds using machines that perform Tick to

Trade in this 1 microsecond delay.

Trade is close and next cycle will start at T0+ 50 mil-

liseconds as the new T0.

To close this section let us, using the dynamics of the

market as presented in Section II, to make a quick and of

course not very serious calculation of the potential that

the above strategy could bring over this pair.

Considering that the GO conditions are established by

a minimum 1 pip (0.01%), price diﬀerence between the

positions, and these GO conditions have a probability

of 10% (minimum), the 20 Hz cycle gives us 2 trades

successful each second. Having 10 hours market trading,

he total number of successful trades are 72,000. With the

previous 1 pip proﬁt per trade we obtain 7.2% proﬁt per

day over the nominal amount of the transactions.

V. IMPLEMENTATION

A. Structure and Technologies

The previous devised strategy could be implemented

under the structure of a Hedge Fund (HF) under the cat-

egory of extremely technological High Frequency Trad-

ing.

The base as presented is the arbitration of one pair

(EUR / USD) at FOREX markets between New York

and London.

8

Technologies for the implementation will be forefront

in these three domains:

1. Tick-to-Trade

Tick-to-Trade in the order of 1 microsecond (1 µsec).

The current (posted) fastest time is 98 nanoseconds. So,

we can be 10 times slower to the top performers of the

table regarding this technology.

2. Communications

Communications between London and New York us-

ing existing Fibre-optics links or in a further step radio

waves over the Atlantic. Satellite connectivity with Low

Orbit Satellites could also be considered. In any case

our 43-msec. mark is easily achievable from any of these

technologies.

3. Quantum supremacy

Quantum supremacy in execution, through the entan-

glement mechanisms between the devices co-located with

the execution computers at the premises of the FOREX

markets in London and New York.

B. State of the Art

The markets of London and New York will be the

launching ones due to its maximum volume and relia-

bility. Also initially as described in the paper we can op-

erate over one pair. There’s no reason to think in further

expansions of the operations to other places and other

pairs, in which the HF can operate.

It’s clear that the hurdle for the expansion, and for the

launch of course, will be the availability of the devices

that will support the quantum supremacy.

As today, November 2019, the availability of qubits en-

tangled in diﬀerent locations to perform quantum com-

munication is one of the hottest applications. The main

beneﬁt for Quantum Communication is in the Quantum

Key Distribution (QKD) processes and currently is a

matter of normal business. In July last year, Alberto

Boaron of the University of Geneva, Switzerland, and

colleagues reported distributing secret keys using QKD

over a record distance of more than 400 kilometres of op-

tical ﬁber, at 6.5 kilobits per second. In contrast, com-

mercially available systems, such as the one sold by the

Geneva-based company ID Quantique, provide QKD over

50 kilometres of ﬁbre.

The critical issue for all the current developments is

the distance that the photons as carriers of the quantum

information could achieve.

C. Disclaimer

The companies of the Author, RQuanTech (Geneva)

and Criptosasun (Madrid), are working in a device that

would implement the entanglement of qubits at the dis-

tances required by the setup of the methodology dis-

cussed in Section IV and the implementation presented

in Section V

Taking in account that this development is a work in

progress we can not now assure that the milestones pro-

posed will be achieved.

VI. CONCLUSIONS

It’s clear that Quantum Supremacy will not only dis-

rupts ﬁnancial markets nor all the other markets in the

world.

Regarding the current quarrel between IBM and

Google over the claim of the later, Ethan Siegel has

written in Forbes magazine[9], “Progress in the world

of quantum computing is astounding, and despite the

claims of its detractors, systems with greater numbers of

qubits are undoubtedly on the horizon. When successful

quantum error-correction arrives (which will certainly re-

quire many more qubits and the necessity of addressing

and solving a number of other issues), we’ll be able to

extend the coherence timescale and perform even more

in-depth calculations”

ACKNOWLEDGMENTS

The Author wish to acknowledge the support of the

teams of RQuanTech and Criptosasun for their full sup-

port with the corrections and marvelous ideas.

[1] IBM, (2019), https://www.ibm.com/quantum-

computing/.

[2] I. L. Nielsen, Michael A.; Chuang, Quantum Computa-

tion and Quantum Information: 10th Anniversary Edition

(Cambridge University Press, 2010).

[3] J. A. Wheeler, Information, physics, quantum: the search

for links, in Complexity, entropy, and the physics of in-

formation (Westview Press, 1990).

[4] NASDAQ, (2019), https://www.nasdaq.com/glossary/h/high-

frequency-trading.

[5] D. Polen, Fix Globlal 2-12, 23 (2010).

[6] SEC, (2014), https://wallstreetonparade.com/2014/04/did-

the-sec-admit-that-it-knows-the-stock-market-is-rigged/.

[7] S. of SEC, Equity Market Structure Literature Review.

Part II: High Frequency Trading (U.S. Securities and Ex-

change Commission, 2014).

9

[8] R. S. M. Shorter, High Frequency Trading: Overview

of Recent Developments (Congressional Research Service,

2016).

[9] E. Siegel, Forbes Magazine 10-19, 27 (2019).