How quantum finance could alter market engineering

The deploy­ment of quantum tech­no­lo­gies¹ offers prom­ising pro­spects for solv­ing prob­lems with com­plex­ity bey­ond the pro­cessing capa­city of con­ven­tion­al sys­tems. Fin­an­cial insti­tu­tions run up against the lim­it­a­tions of clas­sic­al com­put­ing archi­tec­tures when it comes to optim­ising port­fo­li­os with large num­bers of assets and com­plex con­straints (caps, exclu­sions, etc.), mod­el­ing soph­ist­ic­ated deriv­at­ive products, or pro­ject­ing extreme risk scen­ari­os². These oper­a­tions demand both pre­ci­sion in exe­cu­tion and sig­ni­fic­ant com­pu­ta­tion­al power, driv­ing research toward altern­at­ive paradigms. By lever­aging super­pos­i­tion to pro­cess mul­tiple con­fig­ur­a­tions sim­ul­tan­eously, inter­fer­ence between super­posed states to steer prob­ab­il­it­ies toward the most rel­ev­ant out­comes, and entan­gle­ment to syn­chron­ise inter­de­pend­en­cies between vari­ables, this sys­tem could reshape cur­rent decision-mak­ing meth­ods³.

This shift non­ethe­less requires a care­ful assess­ment of the tan­gible bene­fits, meas­ured against the tech­nic­al and meth­od­o­lo­gic­al con­straints inher­ent to these new tools. Speak­ing with Poly­tech­nique Insights, Lionel Mar­tellini, Pro­fess­or of Fin­ance at EDHEC Busi­ness School and founder and dir­ect­or of the EDHEC Quantum Insti­tute, shares his expert­ise on the integ­ra­tion of these algorithms into secur­ity selec­tion, port­fo­lio con­struc­tion, and risk man­age­ment. His research focuses in par­tic­u­lar on meas­ur­ing the added value of these innov­a­tions with­in fin­an­cial pro­cesses and on the con­di­tions for their viab­il­ity with­in mar­ket struc­tures⁴.

The ques­tion of the matur­ity of these tech­no­lo­gies with­in the fin­an­cial eco­sys­tem remains a crit­ic­al point. It is import­ant to dis­tin­guish the applic­a­tions likely to deliv­er meas­ur­able pro­gress, to identi­fy the factors slow­ing their deploy­ment, and to define the sci­entif­ic mile­stones required before every­day use becomes feas­ible. The gap between cur­rent research cap­ab­il­it­ies and the reli­ab­il­ity require­ments of real-world oper­a­tions thus rep­res­ents the junc­tion between labor­at­ory hypo­theses and the prac­tic­al demands of the industry⁵.

Fin­an­cial mar­kets rely on oper­a­tions with com­pu­ta­tion­al dens­ity that is con­tinu­ously grow­ing. Wheth­er struc­tur­ing multi-asset port­fo­li­os, pri­cing deriv­at­ives with non-lin­ear pro­files, or mod­el­ing stress scen­ari­os, clas­sic­al archi­tec­tures reach a sat­ur­a­tion threshold as the scale of prob­lems expands⁸. In Quantum Spee­dup of Monte Carlo Meth­ods, Ash­ley Montanaro estab­lishes that the quantum amp­litude estim­a­tion algorithm offers a the­or­et­ic­ally sig­ni­fic­ant accel­er­a­tion of Monte Carlo meth­ods, which are essen­tial to deriv­at­ive asset pri­cing and risk man­age­ment. His work demon­strates that, for a giv­en tar­get level of pre­ci­sion, the volume of sim­u­la­tions required bene­fits from a quad­rat­ic reduc­tion com­pared to con­ven­tion­al approaches. This effi­ciency gain opens the door to redu­cing the com­pu­ta­tion­al cost of com­plex fin­an­cial cal­cu­la­tions, provided that fault-tol­er­ant quantum com­puters and mod­els com­pat­ible with the algorith­m’s require­ments are avail­able⁹.

For Lionel Mar­tellini, “a genu­ine quantum advant­age con­sists of improv­ing the return of a port­fo­lio, or redu­cing its risk, in a way that gen­er­ates an eco­nom­ic gain great­er than the addi­tion­al costs induced by the quantum solu­tion.” He con­firms the need to meas­ure the real con­tri­bu­tion of these tech­no­lo­gies bey­ond simple speed gains, spe­cify­ing that “it is essen­tial to con­sider costs before con­clud­ing that a quantum advant­age exists.” Indeed, the invest­ments required for these sys­tems remain substantial.

In port­fo­lio optim­isa­tion, risk man­age­ment mod­els struggle with the expo­nen­tial growth in asset com­bin­a­tions¹⁰. Tech­niques such as quantum approx­im­ate optim­isa­tion algorithms (QAOA) or QUBO for­mu­la­tions offer pro­spects for explor­ing these data spaces more intel­li­gently, par­tic­u­larly for com­bin­at­or­i­al prob­lems where the object­ive is to identi­fy optim­al con­fig­ur­a­tions under con­straints — these meth­ods hav­ing been spe­cific­ally developed to effi­ciently nav­ig­ate high-dimen­sion­al optim­isa­tion land­scapes¹¹. On the valu­ation side, Mar­tellini notes that “the cent­ral prob­lem con­sists of com­put­ing the expec­ted value of a pay­off under a risk-adjus­ted prob­ab­il­ity, often via Monte Carlo sim­u­la­tions,” and that “the quantum amp­litude estim­a­tion algorithm (QAE) offers a quad­rat­ic gain: the pri­cing error decreases more rap­idly, which reduces the num­ber of tra­ject­or­ies required.” How­ever, fin­an­cial viab­il­ity remains the ulti­mate arbit­er: “On a tech­no­lo­gic­al level, the gain is clear, but the eco­nom­ic advant­age remains to be assessed based on the costs of access­ing quantum com­puters, includ­ing their energy consumption.”

The appeal of quantum pro­cessors for port­fo­lio optim­isa­tion is fully achieved in envir­on­ments char­ac­ter­ised by high dimen­sion­al­ity and shift­ing data struc­tures. “When the para­met­ers are few and sta­tion­ary, clas­sic­al meth­ods suf­fice. Small prob­lems can be solved with simple, low-cost tools,” the expert notes. The util­ity of quantum approaches emerges when the dynam­ic com­plex­ity of data flows over­whelms the capa­city of con­ven­tion­al meth­ods¹².

Nev­er­the­less, research must avoid use cases dis­con­nec­ted from real-world needs. Mar­tellini cau­tions against “com­bin­ing secur­ity selec­tion and port­fo­lio risk-return optim­isa­tion into a single prob­lem. This cre­ates com­bin­at­or­i­al com­plex­ity that makes a quantum advant­age appear arti­fi­cially.” Asset selec­tion must serve clear fin­an­cial object­ives: “It can be motiv­ated by per­form­ance, by com­par­ing the mar­ket price to fair value, or by risk, for example by seek­ing a port­fo­lio with low correlation.”

“Quantum wash­ing” refers to a meth­od­o­lo­gic­al drift con­sist­ing of attrib­ut­ing a quantum advant­age to prob­lems that have been arti­fi­cially over-com­plic­ated. The tend­ency toward “quantum wash­ing” rep­res­ents a bar­ri­er to the cred­ib­il­ity of solu­tions and there­fore to their adop­tion. Indeed, accord­ing to Lionel Mar­tellini, “there is a tend­ency to arti­fi­cially con­struct use cases in order to high­light the advant­ages of quantum com­put­ing. This gives some­what the impres­sion of a solu­tion des­per­ately in search of a prob­lem, or of an over­sized ham­mer look­ing for nails to strike.” This bias can lead to prom­ising but inap­plic­able con­clu­sions. “Even when a prob­lem is real,” he con­tin­ues, “there is a risk of over­stat­ing the sup­posed advant­ages. The bene­fits presen­ted often depend on unstated assump­tions regard­ing the matur­ity of the tech­no­logy or its actu­al cost.”

The integ­ra­tion of quantum com­put­ing into fin­ance runs up against con­straints that go bey­ond raw pro­cessing power, not­ably tech­no­lo­gic­al matur­ity and cyber­se­cur­ity. Con­tem­por­ary machines (NISQ) oper­ate with com­pon­ents that remain unstable. “Cur­rent quantum com­puters are still too lim­ited for large-scale use,” Mar­tellini notes. Real-world bene­fits depend on a more stable tech­no­lo­gic­al hori­zon, known as fault-tol­er­ant¹³.

The fin­an­cial factor is equally sig­ni­fic­ant: “Some machines will cost tens of mil­lions, oth­ers sev­er­al hun­dreds of mil­lions, or even bil­lions,” Mar­tellini points out, adding that “the return on invest­ment of these machines and their energy con­sump­tion — wheth­er in shared or ded­ic­ated cloud usage — will be decis­ive factors.” Fur­ther­more, the hand­ling of sens­it­ive data requires strin­gent encryp­tion pro­to­cols and metic­u­lous over­sight of cloud infrastructures.

As such, the tech­no­logy is best under­stood as a com­ple­ment­ary lay­er to exist­ing sys­tems. “Today, hybrid approaches are the most real­ist­ic path for­ward,” the fin­ance pro­fess­or states. He also men­tions “quantum-inspired sim­u­lat­ors, such as digit­al anneal­ers or tensor net­work-based meth­ods.” These tools allow for exper­i­ment­a­tion without the con­straints of phys­ic­al qubits. Moreover, “while the autonom­ous quantum com­puter remains a medi­um-term object­ive, in the short and medi­um term it is hybrid clas­sic­al-quantum archi­tec­tures that rep­res­ent the most real­ist­ic approach for obtain­ing action­able res­ults.” This trans­ition makes it pos­sible to cap­ture tar­geted gains and explore use cases while keep­ing oper­a­tion­al risks under control.

Aicha Fall