engage Quantum

The begin­nings of the aba­cus are thought to be of Sumer­ian ori­gin and date back over 4000 years. Through trade, the con­cepts were spread, var­ied region­al­ly, and are part of the UNESCO imma­te­r­i­al cul­tur­al heritage.

Famous physi­cist Feyn­man was known for his abil­i­ty to per­form writ­ten cal­cu­la­tions extra­or­di­nar­i­ly fast and was chal­lenged to a cal­cu­la­tion con­test by a Japan­ese aba­cus expert. While the aba­cus proved to be the faster method for addi­tion, Feynman’s writ­ten cal­cu­la­tions came out ahead for more com­plex problems.

The mechan­i­cal cal­cu­lat­ing machines of the 17th cen­tu­ry were, by the stan­dards of the time, extreme­ly demand­ing in terms of pre­ci­sion engi­neer­ing, which in some cas­es pre­vent­ed reli­able oper­a­tion and wider distribution

The Pas­ca­line was con­struct­ed by Blaise Pas­cal in 1642 and was long con­sid­ered the first mechan­i­cal adding machine until ref­er­ences to Schickard’s cal­cu­lat­ing machine sur­faced in the 20th cen­tu­ry. This machine (built in 1623) could already add and sub­tract. The design was lost for a long time, but draw­ings of the machine were found in the estate of Johannes Kepler, and a work­ing repli­ca was made in 1960.

The machine designed by Got­tfried Wil­helm Leib­niz and based on the stag­gered-roller prin­ci­ple, could per­form addi­tion, sub­trac­tion, and mul­ti­pli­ca­tion. Parts were demon­strat­ed to the Roy­al Soci­ety in Lon­don in 1673, but the intri­cate pre­ci­sion mechan­ics prob­a­bly pre­vent­ed a com­plete and error-free work­ing mod­el dur­ing Leibniz’s life­time — it was not until 1990 that such an error-free work­ing repli­ca was built. Leib­niz is also of great impor­tance for mod­ern infor­ma­tion pro­cess­ing, for exam­ple through his inves­ti­ga­tions of bina­ry num­bers and the com­bi­na­tion of arith­metic and log­i­cal prob­lems by means of bina­ry numbers.

The orig­i­nal machine would have been a true mas­ter­piece of engi­neer­ing, with over 50000 parts, pow­ered by a steam engine and the size of a small fac­to­ry floor. The pro­gram­ming and sup­ply of data via punched cards was inspired by auto­mat­ed and steam-dri­ven Jacquard looms emerg­ing at the time. Data out­put also took place via punched cards. The pro­gram­ming lan­guage resem­bled today’s assem­bly lan­guages and would have made the ana­lyt­i­cal engine the first Tur­ing-pow­ered machine, since it allowed loops and con­di­tion­al exe­cu­tion. Due to the enor­mous com­plex­i­ty, only indi­vid­ual com­po­nents were built and the machine lat­er fell into oblivion.

Ada Lovelace trans­lat­ed a descrip­tion of the machine by Fred­eri­co Lui­gi Menabrea from French into Eng­lish, which, with Babbage’s encour­age­ment, became a much more detailed trea­tise. She rec­og­nized the pos­si­bil­i­ties of the machine beyond mere cal­cu­la­tions and con­sid­ered pro­cess­ing let­ters or com­pos­ing music. She wrote a descrip­tion of how to cal­cu­late Bernoul­li num­bers and is con­sid­ered the world’s first pro­gram­mer, although Bab­bage him­self also described how to con­trol his machine by giv­ing instruc­tions. Women also often played an essen­tial role in the design of lat­er pro­gram­ming languages.

Boole laid the foun­da­tions of mod­ern math­e­mat­i­cal log­ic by con­sis­tent­ly for­mal­iz­ing clas­si­cal log­ic and propo­si­tion­al log­ic. Nowa­days Boolean log­ic encom­pass­es not only Boole’s orig­i­nal con­cept but also the addi­tions devel­oped by Ernst Schröder, Guiseppe Peano and Ivan Ivanovich She­galkin, among others.

It allows for the ele­gant con­nec­tion of log­i­cal state­ments, which are rep­re­sent­ed by known math­e­mat­i­cal sym­bols, and with which one can cal­cu­late in usu­al form.

Around 1900, the foun­da­tions of quan­tum mechan­ics were laid — among oth­ers by Max Planck, Niels Bohr, Louis de Broglie, Albert Ein­stein, Wern­er Heisen­berg, Paul Dirac and Erwin Schrödinger. These devel­op­ments were hon­ored with sev­er­al Nobel Prizes. Cen­tral to this is their prob­a­bilis­tic view of the world — par­ti­cles, for exam­ple, are not deter­min­is­ti­cal­ly in one place but only with a cer­tain prob­a­bil­i­ty. Like­wise they can be at anoth­er place with a cer­tain prob­a­bil­i­ty. Only a mea­sure­ment deter­mines the place, but also destroys the under­ly­ing quan­tum state.

An imag­i­nary mem­o­ry tape con­tains a series of char­ac­ters, all of which must be tak­en from the so-called input alpha­bet. A machine con­verts these char­ac­ters accord­ing to pre­de­ter­mined rules. These rules change in turn — the machine assumes oth­er ’states’. At each step, it decides not only whether the char­ac­ters are con­vert­ed or not, but also whether a new state is assumed. The states and their changes there­by encode the com­pu­ta­tion­al oper­a­tions — they can be applied to any input. Tur­ing also devel­oped spe­cial­ized com­put­ing machines (the so-called ‘Tur­ing bombs’) to decode Ger­man mil­i­tary ciphers dur­ing World War II.

The Von Neu­mann archi­tec­ture con­sists of dif­fer­ent parts, which tak­en togeth­er imple­ment all func­tions of the Tur­ing machine. A mem­o­ry unit, for exam­ple, con­tains the char­ac­ters that are on the mem­o­ry tape in the Tur­ing machine. It also stores the pro­grams, i.e. the instruc­tion sets cor­re­spond­ing to the states in the Tur­ing machine, and the rules accord­ing to which the states are changed. A con­trol unit trans­mits these instruc­tions to a com­put­ing unit that actu­al­ly phys­i­cal­ly exe­cutes the oper­a­tions. A bus sys­tem ensures com­mu­ni­ca­tion among these ele­ments and with the out­put plant.

Although the von Neu­mann archi­tec­ture is mere­ly an abstrac­tion, it is much more appli­ca­tion-ori­ent­ed and many of its ele­ments can be iden­ti­fied with the com­po­nents of a mod­ern PC: The mem­o­ry plant cor­re­sponds to RAM and hard disk, for exam­ple, and the arith­metic plant to the processor

The Zuse Z4, designed by Kon­rad Zuse in the 1940s, was the first cal­cu­lat­ing machine of this gen­er­a­tion, although it was not entire­ly Tur­ing-com­plete at the time — it could not put into prac­tice all the func­tions that a Tur­ing machine pos­tu­lates. This was achieved by the ENIAC — a device based on elec­tron tubes, diodes and relays, which was devel­oped by the Amer­i­can army. The design­ers went into busi­ness for them­selves some time lat­er and launched the first com­mer­cial com­put­er, the UNIVAC.

A tran­sis­tor can con­trol elec­tri­cal cur­rents and volt­ages applied to its inputs and out­puts by volt­ages applied to oth­er inputs. This gives the pos­si­bil­i­ty to find phys­i­cal equiv­a­lents to the 1 and 0 states of mod­ern dig­i­tal com­put­ers and to real­ize cal­cu­la­tions by the inter­play of transistors.

Elec­tri­cal­ly charged par­ti­cles, such as ions, are sub­ject to forces in elec­tric and mag­net­ic fields. It seems plau­si­ble o not only to set them in motion, but also to stop them — to cap­ture them, so to speak. How­ev­er, the laws of elec­tro­dy­nam­ics do not make it quite so sim­ple, and it was not until 1953 that Wolf­gang Paul suc­ceed­ed in cap­tur­ing ions by using high-fre­quen­cy alter­nat­ing elec­tric fields — radio waves. Orig­i­nal­ly, Paul only want­ed to deter­mine the weights of dif­fer­ent ions. How­ev­er, his inven­tion had resound­ing suc­cess in the field of atom­ic physics, where it had mas­sive sig­nif­i­cance in the run-up to the devel­op­ment of laser cool­ing. From the 1970s onwards, it was increas­ing­ly pos­si­ble to trap ions in these traps and thus to explore the laws of quan­tum optics, in par­tic­u­lar by Hans-Georg Dehmelt, who received the Nobel Prize togeth­er with Paul for this innovation.

The very first inputs into com­put­ers were made with punch cards. Imprac­ti­cal, not user-friend­ly, and heav­i­ly depen­dent on the par­tic­u­lar com­put­er mod­el, these sys­tems were replaced start­ing in 1957 by pro­gram­ming lan­guages. These are­for­mal­ized lan­guages that are eas­i­er for humans to parse and under­stand, and which are used to write pro­grams that were then trans­lat­ed into machine lan­guage by a com­pil­er and exe­cut­ed. IBM intro­duced For­tran for its com­put­er sys­tems in 1957. At the same time, Grace Hop­per devel­oped FLOW-MATIC, the pre­cur­sor lan­guage to COBOL, for Rem­ing­ton Rand’s UNIVAC computer.

Then, as now, the solu­tion to improv­ing com­put­ers was well known: More cir­cuits, more com­po­nents. Con­ven­tion­al design required vast quan­ti­ties of vac­u­um elec­tron tubes, relays, tran­sis­tors and oth­er elec­tron­ic com­po­nents. How­ev­er, Jack Kil­by noticed that with the inven­tion of the tran­sis­tor, it had become pos­si­ble to make all the nec­es­sary com­po­nents from semi­con­duc­tors. He suc­ceed­ed in pro­duc­ing a quite com­plex cir­cuit from one cast, with quite small com­po­nents on a ger­ma­ni­um chip. Although sil­i­con quick­ly proved to be the supe­ri­or mate­r­i­al, Kil­by nev­er­the­less received the Nobel Prize in Physics in 2000.

By the end of the 1960s, com­put­ers were already wide­spread as large-scale devices. Sev­er­al com­pa­nies then began to devel­op oper­at­ing sys­tems to allow mul­ti­ple users to use the com­put­ers simul­ta­ne­ous­ly and to run pro­grams con­cur­rent­ly. To pre­vent the lat­ter from get­ting in each other’s way, it was nec­es­sary to orga­nize resource usage. UNIX was devel­oped by the famous Bell Labs for this pur­pose. Microsoft’s DOS oper­at­ing sys­tem became the cor­ner­stone of the company’s suc­cess a few years lat­er. Today, Win­dows shares the mar­ket with MacOS and Android (on cell phones) — but the UNIX suc­ces­sor LINUX is also still wide­ly used.

Based on the exploita­tion of dis­crete ener­gy lev­els and tran­si­tion wave­lengths in atoms and the Doppler effect, two pro­pos­als were inde­pen­dent­ly pub­lished in 1975 by Theodor Hän­sch and Arthur L. Schawlow, and Dave J. Wineland and Hans G. Dehmelt, on how to cool free or trapped atoms with laser light. All four authors lat­er received a Nobel Prize, but none for their con­tri­bu­tion to laser cool­ing: Schawlow in 1981, Dehmelt in 1989, Hän­sch in 2005, Wineland in 2012. Laser cool­ing allowed ground­break­ing devel­op­ments, such as the Bose Ein­stein con­den­sa­tion. Or the world’s most accu­rate atom­ic clocks.

Some Nobel lau­re­ates men­tioned here not only helped shape the research that led to this company’s found­ing, but also the founders of ele­Qtron them­selves: Prof. Christof Wun­der­lich received his PhD in the group of Theodor W. Hän­sch and did post­doc­tor­al research in the group of Serge Haroche before inves­ti­gat­ing new con­cepts for quan­tum com­put­ers with ions togeth­er with Peter E. Toschek and Wern­er Neuhauser. Dr. Michael Johan­ning did research as a Post­Doc in the group of William D. Phillips.

The Apple II, along with com­pet­ing mod­els from Com­modore and Tandy, rep­re­sents the first com­mer­cial­ly suc­cess­ful per­son­al com­put­er. Its rel­a­tive­ly wide­spread dis­tri­b­u­tion enabled com­mer­cial soft­ware providers to find a mass mar­ket for the first time. The large num­ber of avail­able pro­grams in turn increased its appeal, and four years lat­er led to indus­try giant IBM also enter­ing the PC market.

The com­bi­na­tion of ion traps and laser cool­ing allowed the cre­ation of Coulomb crys­tals in which ions arrange them­selves in reg­u­lar struc­tures. Some­thing sim­i­lar had been observed before on charged dust par­ti­cles. Thus, in 1980, Wern­er Neuhauser, Mar­tin Hohen­statt and Peter Toschek were able to take a pho­to of a sin­gle ion, some­thing that co-founders of quan­tum mechan­ics such as Heisen­berg and Schrödinger had dis­missed as infea­si­ble only 20 years earlier.

By allow­ing eas­i­ly con­trol­lable ions to inter­act with each oth­er in the same way as elec­trons would in a sol­id, for exam­ple, it would be pos­si­ble to recre­ate this sol­id, so to speak. This con­cept, then called the quan­tum sim­u­la­tor, is con­sid­ered one of the ori­gins of the idea of the quan­tum computer.

Almost all real phys­i­cal sys­tems con­sist of a mul­ti­tude of small­er par­ti­cles whose inter­ac­tion with each oth­er deter­mines the mea­sur­able prop­er­ties of that sys­tem. To under­stand the sys­tems, one could cal­cu­late the prop­er­ties — but doing so with­out approx­i­ma­tions is near­ly impos­si­ble. For exam­ple, a sys­tem con­sist­ing of 30 par­ti­cles, each of which can indi­vid­u­al­ly assume two states (qubit), has about a bil­lion states — so describ­ing it accu­rate­ly is almost impos­si­ble. Feynman’s idea was to adjust well-con­trol­lable phys­i­cal sys­tems such that they behave sim­i­lar­ly to the sys­tem of inter­est — and to sim­u­late it in this way. The com­put­er here would be the adjustable phys­i­cal sys­tem that relies on quan­tum effects itself — a quan­tum simulator.

Like oper­at­ing sys­tems, mod­ern net­work tech­nolo­gies owe their exis­tence to the need of var­i­ous com­put­er users to share resources and, if pos­si­ble, to con­trol com­put­ers remote­ly. ARPANET was intro­duced as a net­work of var­i­ous Amer­i­can uni­ver­si­ties over the tele­phone net­work in 1969. The WWW also has its ori­gins in an aca­d­e­m­ic field: to give uni­ver­si­ties around the world access to the high-ener­gy physics data mea­sured and stored at the CERN physics research cen­ter. There, it was devel­oped between 1985 and 1989 by Tim Berners-Lee.

Since the pro­pos­al for a CNOT quan­tum gate with stored ions by Cirac and Zoller in 1995, sev­er­al groups world­wide have been work­ing on the imple­men­ta­tion of this con­cept. Ini­tial­ly, focused high­ly sta­ble laser sources were used to con­trol indi­vid­ual ions and thus qubits. Their mutu­al repul­sion allows the cre­ation of entan­gled states: here, the state of both ions is ran­dom when mea­sured by itself, but both ions are always found in the same state, for example.

The sta­bil­i­ty of laser sources at this lev­el is an enor­mous tech­ni­cal chal­lenge, and the real­iza­tion of CNOT gates with ions by Blatt’s and Wineland’s groups in 2003 is tes­ti­mo­ny to the high lev­el of con­trol and sta­bil­i­ty that has been achieved in these groups. The con­trol of small quan­tum sys­tems was rec­og­nized with the Nobel Prize in 2012.

Oth­er plat­forms have also been pro­posed and used to demon­strate quan­tum algo­rithms. One out­stand­ing exper­i­ment was the effi­cient fac­tor­iza­tion of the num­ber 15 by using a mol­e­cule in which the nuclear spins were used as quan­tum reg­is­ters and con­trolled with radio fre­quen­cy puls­es (nuclear mag­net­ic res­o­nance — NMR). Despite these ear­ly suc­cess­es, this plat­form was known to be non-scal­able because ensem­ble aver­ages are mea­sured here, result­ing in poor scal­ing of the sig­nal-to-noise ratio as the reg­is­ter size increases.

MAGIC (MAg­net­ic Gra­di­ent Induced Cou­pling) allows con­trol of qubits with sta­t­ic mag­net­ic fields and scal­able radio fre­quen­cy fields as wide­ly used in com­mu­ni­ca­tions. The con­cept was invent­ed by founder Christof Wun­der­lich and exper­i­men­tal­ly researched and fur­ther devel­oped in his Siegen research group. The MAGIC con­cept com­bines the advan­tages of indi­vid­u­al­ly con­trol­lable ions with the scal­a­bil­i­ty and con­trol of microwave puls­es from NMR.

Based on the ear­ly suc­cess­es of NMR-based sys­tems and the excel­lent qual­i­ty in con­trol and state mea­sure­ment of sin­gle ions, the ques­tion aris­es whether the NMR approach is not applic­a­ble to ions. Indeed, the quan­tum states of ions can be con­trolled coher­ent­ly, i.e. with full preser­va­tion of quan­tum infor­ma­tion, by radiofre­quen­cy puls­es. How­ev­er, two phys­i­cal facts stand in the way of this approach:

High-fre­quen­cy fields can­not be focused on sin­gle, close­ly spaced ions because of their long wavelength.

The momen­tum of high-fre­quen­cy pho­tons is too small to excite oscil­la­tion of the ions, which is used to cre­ate entan­gled states.

In Prof. Christof Wunderlich’s con­cept, these two prob­lems are solved by adding inho­mo­ge­neous mag­net­ic fields. His group has been work­ing on the demon­stra­tion and appli­ca­tion of robust quan­tum gates with sin­gle ions since the very beginnings.

Both were hon­ored for their ground­break­ing research on the analy­sis and con­trol of indi­vid­ual quan­tum sys­tems, which they pur­sued con­sis­tent­ly over decades. Wineland spe­cial­ized pri­mar­i­ly in the con­trol of ions with laser light, while Haroche inves­ti­gat­ed the inter­ac­tion between microwave pho­tons and uncharged atoms.

What they both had in com­mon was that they suc­ceed­ed in observ­ing fun­da­men­tal quan­tum effects and con­trol­ling them almost at will. This includes, for exam­ple, an imple­men­ta­tion of Schrödinger’s cat — Erwin Schrödinger’s famous thought exper­i­ment, which leads to a super­po­si­tion (i.e. simul­ta­ne­ous exis­tence) of two clas­si­cal­ly dis­tin­guish­able states.

The ele­Qtron GmbH was found­ed on May 12, 2020. Founders on the phys­i­cal-tech­ni­cal side are Prof. Dr. Christof Wun­der­lich and PD. Dr. Michael Johan­ning, who have been inten­sive­ly and suc­cess­ful­ly pur­su­ing the quan­tum infor­ma­tion approach with ions, mag­net­ic fields and high-fre­quen­cy puls­es for years on both the con­cep­tu­al and exper­i­men­tal side. The eco­nom­ic com­pe­tence is con­tributed by Hill GmbH, rep­re­sent­ed by Prof. Dr. Mar­tin Hill, Dr. Rain­er Baum­gart and the Siegerland­fonds, rep­re­sent­ed by Dr. Susanne Kolb.

We are pur­su­ing two major goals in par­al­lel: on the one hand, to devel­op a scal­able and freely pro­gram­ma­ble quan­tum com­put­er, and on the oth­er hand, to build a soon-to-be-avail­able quan­tum com­put­er spe­cial­ized for spe­cif­ic solu­tions. By 2025, we will lay the foun­da­tions for the first goal. Beyond that, we will have com­plet­ed a quan­tum com­put­er suit­ed for opti­miza­tion problems.

MAGIC quan­tum com­put­ers are avail­able for a large num­ber of indus­tri­al and aca­d­e­m­ic prob­lems and will rev­o­lu­tion­ize both busi­ness and science.