QUANTUM DEVICES WITH TWO-SIDED OR SINGLE-SIDED DUAL-PURPOSE MAJORANA ZERO MODE JUNCTIONS

Quantum devices with two-sided or single-sided dual-purpose Majorana zero mode (MZM) junctions are described. An example quantum device comprises at least one superconducting island configurable to support at least one pair of Majorana zero modes (MZMs). The quantum device further includes a first conductor configurable to be coupled with at least one MZM of the at least one pair of MZMs, where the first conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state. The quantum device further includes a second conductor configurable to be coupled with the at least one MZM of the at least one pair of MZMs, where the second conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state.

BACKGROUND

Measurement-based Majorana zero mode (MZM) qubits require tuning into the topological phase and qubit measurements. Traditional junctions used with MZM qubits are configured and operated to provide only one of these functions. Accordingly, there is a need for improvements to Majorana zero mode (MZM) junctions.

SUMMARY

In one example, the present disclosure relates to a quantum device comprising at least one superconducting island configurable to support at least one pair of Majorana zero modes (MZMs). The quantum device may further include a first conductor configurable to be coupled with at least one MZM of the at least one pair of MZMs, where the first conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state. The quantum device may further include a second conductor configurable to be coupled with the at least one MZM of the at least one pair of MZMs, where the second conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state.

In another example, the present disclosure relates to a quantum device comprising at least one superconducting island configurable to support at least one pair of Majorana zero modes (MZMs). The quantum device may further include a conductor configurable to be coupled with at least one MZM of the at least one pair of MZMs, where the conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state.

In yet another example, the present disclosure relates to a quantum device comprising at least one superconducting island configurable to support at least one pair of Majorana zero modes (MZMs). The quantum device may further include a first conductor configurable to be coupled with at least one MZM of the at least one pair of MZMs via a first tunable coupling, where the first conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state. The quantum device may further include a first cutter gate for tuning the first tunable coupling. The quantum device may further include a second conductor configurable to be coupled with the at least one MZM of the at least one pair of MZMs via a second tunable coupling, where the second conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state. The quantum device may further include a second cutter gate for tuning the second tunable coupling independent of the first tunable coupling.

DETAILED DESCRIPTION

Examples described in this disclosure relate to quantum devices with two-sided or single-sided dual-purpose Majorana zero mode (MZM) junctions. Quantum devices with MZM qubits require rapidly configuring couplings between different pairs of MZMs for qubit operations and measurement. As used herein, the term qubit refers to any quantum system that can be in a superposition of two quantum states, 0 and 1. Consistent with the present disclosure several examples of quantum devices with two-sided or single-sided MZM dual-purpose junctions that allow MZMs to couple to transport leads or quantum dots in Coulomb blockade are described. These junctions are useful in Majorana-based qubits. When configured for transport measurements, the junctions can be used to tune the qubit using transport signatures of the topological phase. When configured to couple MZMs and quantum dots, the junctions support operation of the measurement-based MZM qubits. Two example families of these junctions include: (1) two-sided junctions that allow an MZM to independently couple to two separate conductors, either of which can be configured to be a transport lead or a quantum dot in Coulomb blockade and (2) single-sided junctions that allow an MZM to couple to just one conductor that can configured to either be a transport lead or a quantum dot in Coulomb blockade. Both junction types are useful for different qubit layouts.

MZM qubits may be built from topological superconducting wires. Example implementations of such qubits includes semiconductor-superconductor heterostructures that are obtained, for instance, by depositing superconductor on a semiconductor two dimensional gas (2DEG) and using gates to define the different regions of the qubits (e.g., topological wires, trivial wires, junctions, and quantum dots). In this scheme, the topological phase supporting MZMs needs to be tuned by appropriately configuring these gates and by applying an external magnetic field. One of the ways to tune such a quantum system into a topological phase is to use transport characteristics of the topological phase to identify the favorable parameter space. Thus, even though transport is not needed for operation of these measurement-based MZM qubits, tunable connections to transport leads are helpful in that they allow one to bring-up the qubit, and subsequently they can be disconnected to allow the qubit to be operated.

The present disclosure describes dual-purpose MZM junctions that allow an MZM to be coupled to either a transport lead or to a quantum dot in Coulomb blockade. Certain measurement-based MZM qubits require tunable MZM junctions. In the idle configuration of the qubit, all junctions are closed and MZMs can only hybridize through the superconductor wire separating them; this leads to exponentially small degeneracy splittings, which is the root of topological protection of these qubits. The operations are performed in a measurement-only scheme by coupling pairs of MZMs through adjacent quantum dots (QDs) and performing measurements on these QDs to read out the qubit state. The qubit thus requires tunable junctions between the MZMs and the quantum dots to support different qubit configurations.

The best configuration of such a dual-purpose MZM junction may depend upon the type of qubit design under consideration. A two-sided dual-purpose junction (e.g., two-sided dual-purpose junctions described with respect toFIGS.1-8) contacts the MZM on both sides of the superconducting wire. As such, a two-sided dual-purpose MZM junction connects the MZM to two conductors, each of which can either be configured to be a transport lead or a quantum dot in Coulomb blockade. Either side of the junction is independently tunable, which can be achieved through designated cutter gates. The junction can be tuned so that both sides of the junction are completely pinched off, for instance in the qubit configuration when that MZM is not being measured. The two-sided dual-purpose MZM junctions can have a single layer gate configuration, a dual layer gate configuration, or a combination of these two configurations. Moreover, the gates corresponding to the MZM junctions may also be formed in more than two layers.

A single-sided dual-purpose junction (e.g., single-sided dual-purpose junctions described with respect toFIGS.9-13) contacts the MZM on just one side of the wire; it thus couples the MZM to a single conductor, which can be configured to function either as a transport lead or as a quantum dot in the Coulomb blockade regime. The coupling to the conductor is controlled through a designated cutter gate, which can be fully pinched off when that MZM is not being measured. One benefit of a single-sided dual-purpose junction is that there is a single-type of MZM junction that needs to be optimized for the qubit. Having one such type of junction can simplify experiments. Another benefit is that when the conductor is in Coulomb blockade but the cutter gate to the transport lead is in the tunneling regime, the electron-electron interactions in the conductor can remove unwanted bound states in the junction through level repulsion, resulting in better controllability. Just as not all designs can support two-sided dual-purpose MZM junctions, not all designs can support single-sided dual-purpose MZM junctions. As with the two-sided dual-purpose MZM junctions, a single-sided dual-purpose MZM junction can have a single layer gate configuration, a dual layer gate configuration, or a combination of these two configurations. Moreover, the gates corresponding to the MZM junctions may also be formed in more than two layers.

FIG.1is a block diagram of a quantum device100with two-sided dual-purpose Majorana zero mode (MZM) junctions in accordance with one example. Quantum device100may include topological superconductors (e.g.,110,140, and170) that are coupled via a trivial superconductor180(e.g., a qubit backbone). The combination of the topological superconductors and the backbone may be referred to as a superconducting island. Each of superconductors110,140,170,180may be formed as nanowires. As an example, superconductors110,140,170, and180may be formed as superconductor wires (e.g., indium arsenide (InAs) wires) coated by a superconductor (e.g., aluminum (Al)). Ends of topological superconductors110,140, and170may further be coupled via semiconducting regions130and150. In one example, the terms topological and trivial refer to the phase of the superconductor and even a single superconducting nanowire can have sections that are tuned using electrostatic gates to form topological or trivial superconducting sections.

With continued reference toFIG.1, quantum device100is operated such that Majorana zero modes (MZMs)112and114are formed at the ends of topological superconductor110, MZMs142and144are formed at the ends of topological superconductor140, and MZMs172and174are formed at the ends of topological superconductor170. MZM junctions corresponding to the MZMs may allow for the tunable coupling of MZMs to each other or to transport leads. As an example, quantum device100is shown as having a two-sided dual-purpose MZM junction120, which connects the MZM (e.g., MZM114) to two conductors, either of which can be configured to be in a grounded state or in a Coulomb blockade state. Either side of the junction is independently tunable, which can be achieved through designated cutter gates. The junction can be tuned so that both sides of the junction are completely pinched off, for instance in the qubit configuration when that MZM is not being measured. MZM junction120includes cutter gates125and127, a region adjacent quantum dot132, and a region adjacent transport lead134. Depending on the voltages applied to cutter gates125and127, respectively, the region adjacent to quantum dot132and the region adjacent to transport lead134may be tuned. Advantageously, having two-sided dual-purpose MZM junctions (e.g., MZM junction120) that can couple MZMs to transport leads facilitates the tuning of superconductors110,140, and170of quantum device100into topological phase. Moreover, the same two-sided dual-purpose MZM junctions also allow MZMs to be disconnected from transport leads (e.g., transport lead134acting as one conductor) and be connected to quantum dots (e.g., quantum dot132acting as the other conductor) in Coulomb blockade, which is needed for qubit measurement. AlthoughFIG.1shows quantum device100as including a certain number of components arranged and coupled in a certain way, quantum device100may include fewer or additional components arranged and coupled differently. As an example,FIGS.2and3show additional block diagrams of quantum device200and another quantum device300with two-sided dual-purpose MZM junctions.

FIG.4is a block diagram of a quantum device400with two-sided dual-purpose MZM junctions in accordance with another example. Quantum device400may include topological superconductors (e.g.,410and440) that are coupled via a trivial superconductor470(e.g., a qubit backbone). The combination of the topological superconductors and the backbone may be referred to as a superconducting island. Each of superconductors410,440, and470, may be formed as nanowires. As an example, superconductors410,440, and470may be formed as superconductor wires (e.g., indium arsenide (InAs) wires) coated by a superconductor (e.g., aluminum (AI)). Ends of topological superconductor410may further be coupled via semiconducting regions462and464. Ends of topological superconductor440may further be coupled via semiconducting regions482and484. Ends of trivial superconductor470may be coupled via semiconducting regions492and494. In one example, the terms topological and trivial refer to the phase of the superconductor and even a single superconducting nanowire can have sections that are tuned using electrostatic gates to form topological or trivial superconducting sections.

With continued reference toFIG.4, quantum device400is operated such that Majorana zero modes (MZMs)412and414are formed at the ends of topological superconductor410and MZMs442and444are formed at the ends of topological superconductor440. MZM junctions corresponding to the MZMs may allow for the tunable coupling of MZMs to each other or to transport leads. As an example, quantum device400is shown as having a two-sided dual-purpose MZM junction420, which connects the MZM (e.g., MZM412) to two conductors, one of which is a transport lead422and the other one of which (quantum dot436) can either be configured to be in a grounded state, thus acting as a transport lead, or in the Coulomb blockade state. Either side of the junction is independently tunable, which can be achieved through designated cutter gates. The junction can be tuned so that both sides of the junction are completely pinched off, for instance in the qubit configuration when that MZM is not being measured. MZM junction420includes cutter gates424and426, and a region adjacent quantum dot436and a region adjacent transport lead422. Depending on the voltages applied to cutter gates424and426, respectively, the region adjacent to quantum dot436(acting as one conductor) and the region adjacent to transport lead422(acting as the other conductor) may be tuned. Moreover, the region adjacent quantum dot436can either be configured to be grounded when the cutter gate454opens the connection to the transport lead452, or the quantum dot436can be configured to be in Coulomb blockade when the cutter gate454is fully pinched off.

Still referring toFIG.4, quantum device400is shown as having another two-sided dual-purpose MZM junction450that includes cutter gates456and458, and region adjacent quantum dots436and476. Depending on the voltages applied to cutter gates456and458, respectively, the region adjacent to quantum dots436and476may be tuned. Quantum dots436and476may be configured to be grounded or in Coulomb blockade by tuning cutter gates454and474, respectively to the adjacent transport leads452and472. Advantageously, having two-sided dual-purpose MZM junctions (e.g., MZM junction420and MZM junction450) that can couple MZMs to transport leads facilitates the tuning of superconductors410and440of quantum device400into the topological phase. Moreover, the same two-sided dual-purpose MZM junctions also allow MZMs to be disconnected from transport leads (e.g., transport lead422, transport lead452, or transport lead472) and be connected to quantum dots (e.g., quantum dot436or quantum dot476) in Coulomb blockade, which is needed for qubit measurement. AlthoughFIG.4shows quantum device400as including a certain number of components arranged and coupled in a certain way, quantum device400may include fewer or additional components arranged and coupled differently.

The two-sided dual-purpose MZM junctions described above may be implemented using various example gate configurations. Example gate configurations described herein relate to a layout for a two-dimensional electron gas (2DEG) qubit where the superconducting wires are formed on the underlying 2DEG. As part of this example configuration, gates are used to deplete the 2DEG in most of the plane, and to configure quantum dots and tunable junctions in the regions of interest. In one example, the 2DEG underlying the gates may be manufactured by forming a series of layers of semiconductors on a substrate (e.g., using any of indium phosphide (InP) substrate, indium arsenide (InAs), indium antimonide (InSb), mercury cadmium telluride (HgCdTe), or any appropriate combination of materials selected from groups II, III, IV, V, or VI of the periodic table, or any ternary compounds of three different atoms of materials selected from groups II, III, IV, V, or VI of the periodic table). As an example, the 2DEG may further include a buffer layer (e.g., an indium aluminum arsenide (InAlAs) layer) formed over the substrate. The 2DEG may further include a quantum well layer (e.g., an indium arsenide (InAs) layer) formed over the buffer layer, and another buffer layer formed over the quantum well layer. Each of these layers may be formed using molecular-beam epitaxy (MBE). As an example, the MBE related process may be performed in an MBE system that allows the deposition of the appropriate materials in a vacuum. Topologically active areas may be defined by depositing a metal layer (e.g., aluminum (AI)) and using electrostatic gates and an applied magnetic field to tune into the topological phase.

FIG.5shows a top view500of an example single layer gate configuration for MZM junction420associated with quantum device400ofFIG.4. MZM512corresponds to MZM412ofFIG.4. Topological superconductor portion516corresponds to a portion of topological superconductor410ofFIG.4.FIG.5further shows a trivial superconductor portion514next to MZM512. Individual gates described as part of the single layer gate configuration may serve more than one purpose. As an example, certain cutter gates may both deplete the 2DEG under them, and control the tunnel coupling in the uncovered adjacent junction to them. Similarly, QD plunger gates may deplete the 2DEG under the gate, and control the quantum dot tuning in the uncovered semiconductor region adjacent to them. Gate520may perform the functions of a trivial superconductor plunger gate and a depletion gate. Gate522may perform the functions of a topological superconductor plunger gate and a depletion gate. Gate528may perform the function of a QD side plunger gate and a depletion gate. Gates524,526, and530may be configurable as depletion gates to remove electrons from selected areas of the underlying 2DEG. Gates542,544, and552are configurable as side cutter gates. Transport leads562and564may also act as accumulating gates. Cutter gate542(corresponding to cutter gate424ofFIG.4) may be used to control the coupling of the MZM (e.g., MZM512) to transport lead portion562(corresponding to transport lead422ofFIG.4). Cutter gate544(corresponding to cutter gate426ofFIG.4) may be used to control the coupling of the MZM (e.g., MZM512) to the adjacent quantum dot (e.g., quantum dot436ofFIG.4), whose density is controlled by the quantum dot/plunger gate528. Thus, either side of the junction is independently tunable, which is achieved through designated cutter gates. The junction can be tuned so that both sides of the junction are completely pinched off, for instance in the qubit configuration when that MZM is not being measured. Cutter gate552may be used to control the coupling of the MZM (e.g., MZM512) to another transport lead564. Similar gate configurations may be used with the other quantum devices (e.g., quantum devices100,200, and300described earlier). AlthoughFIG.5shows a certain gate configuration corresponding to an MZM junction, other gate configurations may also be used to implement the functionality of the MZM junction.

FIG.6shows a top view600of an example dual layer gate configuration for MZM junction420associated with quantum device400ofFIG.4. MZM612corresponds to MZM412ofFIG.4. Topological superconductor portion616corresponds to a portion of topological superconductor410ofFIG.4.FIG.6further shows a trivial superconductor portion614next to MZM612. Gate620may perform the functions of a trivial superconductor plunger gate and a depletion gate. Gate622may perform the function of a topological superconductor plunger gate and a depletion gate. Gates624and628may be configurable as depletion gates to remove electrons from selected areas of the underlying 2DEG. Gates620,622, and624may be formed in a first layer. Gate628may be formed in a second layer, different from the first layer, to control the density of quantum dot436ofFIG.4. Gates642,644, and652are configurable as cutter gates and these gates may be formed in a second layer, different from the first layer. Cutter gate642(corresponding to cutter gate424ofFIG.4) may be used to control the coupling of the MZM (e.g., MZM612) to transport lead portion662(corresponding to transport lead422ofFIG.4). Cutter gate644(corresponding to cutter gate426ofFIG.4) may be used to control the coupling of the MZM (e.g., MZM612) to the adjacent quantum dot (e.g., quantum dot436ofFIG.4) under QD plunger gate628. Cutter gate652may be used to control the coupling of transport lead portion664to the quantum dot under QD plunger gate628. Thus, either side of the MZM junction is independently tunable using cutter gates642and644, and the conductor on one side of the junction is configurable to be in Coulomb blockade or grounded using cutter gate652. The MZM junction can be tuned so that both sides of the junction are completely pinched off, for instance in the qubit configuration when the MZM is not being measured. Similar gate configurations may be used with the other quantum devices (e.g., quantum devices100,200, and300described earlier). AlthoughFIG.6shows a certain gate configuration corresponding to an MZM junction, other gate configurations may also be used to implement the functionality of the MZM junction.

FIG.7shows a top view700of an example single layer gate configuration for MZM junction450associated with quantum device400of FIG.4. MZM712corresponds to MZM414ofFIG.4. Topological superconductor portion714corresponds to a portion of topological superconductor410ofFIG.4.FIG.7further shows a trivial superconductor portion716next to MZM712. Trivial superconductor portion716corresponds to a portion of trivial superconductor470ofFIG.4. As noted earlier, individual gates described as part of the single layer gate configuration may serve more than one purpose. As an example, certain cutter gates may both deplete the 2DEG under them, and control the tunnel coupling in the uncovered adjacent junction to them. Similarly, QD plunger gates may deplete the 2DEG under the gate, and control the quantum dot tuning in the uncovered semiconductor region adjacent to them. Gate720may perform the functions of a topological superconductor plunger gate and a depletion gate. Gate722may perform the functions of a trivial superconductor plunger gate and a depletion gate. Gates724,728,730, and732may be configurable as depletion gates to remove electrons from selected areas of the underlying 2DEG. Gates742,744,762, and764are configurable as side cutter gates. Each of gates726and734may perform the functions of a QD side plunger gate and a depletion gate. Transport leads772and774may also act as accumulating gates. Cutter gate744(corresponding to cutter gate454ofFIG.4) may be used to control the coupling of the quantum dot (e.g., quantum dot436ofFIG.4) adjacent to QD plunger gate734to transport lead portion774(corresponding to transport lead452ofFIG.4). Cutter gate764(corresponding to cutter gate474ofFIG.4) may be used to control the coupling of the quantum dot (e.g., quantum dot476ofFIG.4) adjacent to QD plunger gate726to transport lead portion772(corresponding to transport lead472ofFIG.4). Cutter gate742(corresponding to cutter gate458ofFIG.4) may be used to control the coupling of the MZM (e.g., MZM712) to the adjacent quantum dot (e.g., quantum dot476ofFIG.4), whose density is controlled by QD plunger gate726. Cutter gate762(corresponding to cutter gate456ofFIG.4) may be used to control the coupling of the MZM (e.g., MZM712) to the adjacent quantum dot (e.g., quantum dot436ofFIG.4), whose density is controlled by QD plunger gate734. Thus, either side of the junction is independently tunable, which is achieved through designated cutter gates. The junction can be tuned so that both sides of the junction are completely pinched off, for instance in the qubit configuration when that MZM is not being measured. Similar gate configurations may be used with the other quantum devices (e.g., quantum devices100,200, and300described earlier). AlthoughFIG.7shows a certain gate configuration corresponding to an MZM junction, other gate configurations may also be used to implement the functionality of the MZM junction.

FIG.8shows a top view800of an example dual layer gate configuration for MZM junction450associated with quantum device400ofFIG.4. MZM812corresponds to MZM412ofFIG.4. Topological superconductor portion814corresponds to a portion of topological superconductor410ofFIG.4.FIG.8further shows a trivial superconductor portion816next to MZM812. Trivial superconductor portion816corresponds to trivial superconductor470ofFIG.4. Gate820may perform the functions of a topological superconductor plunger gate and a depletion gate. Gate824may perform the function of a trivial superconductor plunger gate and a depletion gate. Gates822, and826may be configurable as depletion gates to remove electrons from selected areas of the underlying 2DEG. These gates may be formed in a first layer. Each of gates832and854may perform the function of a QD plunger gate and may act as a depletion gate or an accumulation gate. In this example, gates832and854are formed in a second layer, different from the first layer. Gates842,844,852, and856are configurable as cutter gates and these gates may be formed in a second layer, different from the first layer. Cutter gate844(corresponding to cutter gate454ofFIG.4) may be used to control the coupling of the quantum dot (e.g., quantum dot436ofFIG.4) under QD plunger gate832to transport lead portion864(corresponding to transport lead452ofFIG.4). Cutter gate856(corresponding to cutter gate474ofFIG.4) may be used to control the coupling of the quantum dot (e.g., quantum dot476ofFIG.4) under QD plunger gate854to transport lead portion862(corresponding to transport lead472ofFIG.4). Cutter gate842(corresponding to cutter gate458ofFIG.4) may be used to control the coupling of the MZM to the adjacent quantum dot (e.g., quantum dot476ofFIG.4). Cutter gate852(corresponding to cutter gate456ofFIG.4) may be used to control the coupling of the MZM to the adjacent quantum dot (e.g., quantum dot436ofFIG.4). Thus, the conductor on either side of the junction is configurable to be grounded or in Coulomb blockade using cutter gates844and856, and either side of the junction to the MZM is independently tunable using cutter gates842and852. The junction can be tuned so that both sides of the junction are completely pinched off, for instance in the qubit configuration when that MZM is not being measured. Similar gate configurations may be used with the other quantum devices (e.g., quantum devices100,200, and300described earlier). AlthoughFIG.8shows a certain gate configuration corresponding to an MZM junction, other gate configurations may also be used to implement the functionality of MZM junction.

FIG.9is a block diagram of a quantum device900with single-sided dual-purpose Majorana zero mode (MZM) junctions in accordance with one example. Quantum device900may include topological superconductors (e.g.,910,940, and970) that are coupled via a trivial superconductor980(e.g., a qubit backbone). The combination of the topological superconductors and the backbone may be referred to as a superconducting island. Each of superconductors910,940, and970may be formed as nanowires. Trivial superconductor980may be formed as a network of nanowires. As an example, superconductors910,940,970, and980may be formed as superconductor wires (e.g., indium arsenide (InAs) wires) coated by a superconductor (e.g., aluminum (Al)). One end of topological superconductors910,940, and970may further be coupled via a semiconducting region930. In one example, the terms topological and trivial refer to the phase of the superconductor and even a single superconducting nanowire can have sections that are tuned using electrostatic gates to form topological or trivial superconducting sections.

With continued reference toFIG.9, quantum device900is operated such that Majorana zero modes (MZMs)912and914are formed at the ends of topological superconductor910, MZMs942and944are formed at the ends of topological superconductor940, and MZMs972and974are formed at the ends of topological superconductor970. A single-sided dual-purpose junction contacts the MZM on just one side of the wire; it thus couples the MZM to a single conductor, which can be configured to function either as a transport lead or as a quantum dot in the Coulomb blockade regime. As an example, quantum device900is shown as having a single-sided dual-purpose MZM junction920, which connects MZM914to a conductor, which can be configured to be in a grounded state or in a Coulomb blockade state. MZM junction920includes a cutter gate924and a region adjacent quantum dot932. Depending on the voltage applied to cutter gate924, the region adjacent to quantum dot932may be tuned. The coupling to the conductor (e.g., the quantum dot) is controlled through a designated cutter gate (e.g., cutter gate924), that can be fully pinched off when that MZM is not being measured. A benefit of a single-sided dual-purpose junction (e.g., MZM junction920) is that there is a single-type of junction that needs to be optimized for the qubit, which can be simpler for experiments. AlthoughFIG.9shows quantum device900as including a certain number of components arranged and coupled in a certain way, quantum device900may include fewer or additional components arranged and coupled differently. As an example,FIG.10shows an additional block diagram of another example of quantum device1000with single-sided dual-purpose MZM junctions.

FIG.11is a block diagram of a quantum device1100with single-sided dual-purpose MZM junctions in accordance with one example. Quantum device1100may include topological superconductors (e.g.,1110and1140) that are coupled via a trivial superconductor1130(e.g., a qubit backbone). The combination of the topological superconductors and the backbone may be referred to as a superconducting island. Trivial superconductors (e.g., trivial superconductors1150and1160) may abut topological superconductors (e.g.,1110and1140) as shown inFIG.11. Each of superconductors1110,1130,1140,1150, and1160may be formed as nanowires. As an example, superconductors1110,1130,1140,1150, and1160may be formed as superconductor wires (e.g., indium arsenide (InAs) wires) coated by a superconductor (e.g., aluminum (Al)). In one example, the terms topological and trivial refer to the phase of the superconductor and even a single superconducting nanowire can have sections that are tuned using electrostatic gates to form topological or trivial superconducting sections.

With continued reference toFIG.11, quantum device1100is operated such that Majorana zero modes (MZMs)1112and1114are formed at the ends of topological superconductor1110and MZMs1142and1144are formed at the ends of topological superconductor1140. Cutter gates formed in semiconducting regions (e.g., semiconducting regions1180and1190) adjoining the MZMs may allow for the tunable coupling of MZMs to each other or to transport leads. A single-sided dual-purpose junction contacts the MZM on just one side of the wire; it thus couples the MZM to a single conductor, which can be configured to function either as a transport lead or as a quantum dot in the Coulomb blockade regime. As an example, quantum device1100is shown as having a single-sided dual-purpose MZM junction1120that includes cutter gates1125,1127, and1129, and a quantum dot1132that results in a coupling of MZM1112to transport lead1134. Depending on the voltage applied to cutter gate1125, the region adjacent to quantum dot1132may be tuned. The coupling to the conductor (e.g., the quantum dot) is controlled through a designated cutter gate (e.g., cutter gate1125), that can be fully pinched off when that MZM is not being measured. A benefit of a single-sided dual-purpose junction (e.g., MZM junction1120) is that there is a single-type of MZM junction that needs to be optimized for the qubit, which can be simpler for experiments. AlthoughFIG.11shows quantum device1100as including a certain number of components arranged and coupled in a certain way, quantum device1100may include fewer or additional components arranged and coupled differently.

The single-sided dual-purpose MZM junctions described above may be implemented using various example gate configurations. Example gate configurations described herein relate to a layout for a two-dimensional electron gas (2DEG) qubit where the superconducting wires are formed on the underlying 2DEG. As part of this example configuration, gates are used to deplete the 2DEG in most of the plane, and to configure quantum dots and tunable junctions in the regions of interest. In one example, the 2DEG underlying the gates may be manufactured by forming a series of layers of semiconductors on a substrate (e.g., using any of indium phosphide (InP) substrate, indium arsenide (InAs), indium antimonide (InSb), mercury cadmium telluride (HgCdTe), or any appropriate combination of materials selected from groups II, III, IV, V, or VI of the periodic table, or any ternary compounds of three different atoms of materials selected from groups II, III, IV, V, or VI of the periodic table). As an example, the 2DEG may further include a buffer layer (e.g., an indium aluminum arsenide (InAlAs) layer) formed over the substrate. The 2DEG may further include a quantum well layer (e.g., an indium arsenide (InAs) layer) formed over the buffer layer, and another buffer layer formed over the quantum well layer. Each of these layers may be formed using molecular-beam epitaxy (MBE). As an example, the MBE related process may be performed in an MBE system that allows the deposition of the appropriate materials in a vacuum. Topologically active areas may be defined by depositing a metal layer (e.g., aluminum (Al)) and using electrostatic gates and an applied magnetic field to tune into the topological phase.

FIG.12shows a top view1200of an example single-layer gate configuration for single-sided dual-purpose MZM junction1120associated with quantum device1100ofFIG.11. MZM1212corresponds to MZM1112ofFIG.11. Trivial superconductor portion1214corresponds to a trivial superconductor1150ofFIG.11and topological superconductor portion1216corresponds to topological superconductor1110ofFIG.11. Transport lead portion1218corresponds to transport lead1134ofFIG.11. As noted earlier, individual gates described as part of the single layer gate configuration may serve more than one purpose. As an example, certain cutter gates may both deplete the 2DEG under them, and control the tunnel coupling in the uncovered adjacent junction to them. Similarly, QD plunger gates may deplete the 2DEG under the gate, and control the quantum dot tuning in the uncovered semiconductor region adjacent to them. Gate1220may perform the functions of a trivial superconductor plunger gate and a depletion gate. Gates1222,1224, and1226may be configurable as depletion gates to remove electrons from selected areas of the underlying 2DEG. Gate1228may perform the functions of a QD side plunger gate and a depletion gate. Gate1230may perform the functions of a topological superconductor plunger gate and a depletion gate. Gates1242,1244, and1252are configurable as side cutter gates. Transport lead1218may also act as an accumulating gate. Cutter gate1244(corresponding to cutter gate1129ofFIG.11) may be used to control the coupling of the MZM (e.g., MZM1112) to transport lead portion1218(corresponding to transport lead1134ofFIG.11). Cutter gate1252(corresponding to cutter gate1127ofFIG.11) may be used to control the coupling of the MZM (e.g., MZM1212) to transport lead portion1218(corresponding to transport lead1134ofFIG.11). Cutter gate1242(corresponding to cutter gate1125ofFIG.11) may be used to control the density of the adjacent quantum dot (e.g., quantum dot1132ofFIG.11). Similar gate configurations may be used with the other quantum devices with single-sided dual-purpose MZM junctions (e.g., quantum device900ofFIG.9and quantum device1000ofFIG.10described earlier). AlthoughFIG.12shows a certain gate configuration corresponding to an MZM junction, other gate configurations may also be used to implement the functionality of the MZM junction.

FIG.13shows a top view1300of an example dual-layer gate configuration for single-sided dual-purpose MZM junction1120associated with quantum device1100ofFIG.11. MZM1312corresponds to MZM1112ofFIG.11. Trivial superconductor portion1314corresponds to a trivial superconductor1150ofFIG.11and topological superconductor portion1316corresponds to topological superconductor1110ofFIG.11. Transport lead portion1318corresponds to transport lead1134ofFIG.11. Gate1320may perform the functions of a trivial superconductor plunger gate and a depletion gate. Gate1322may be configurable as a depletion gate to remove electrons from selected areas of the underlying 2DEG. Gate1324may perform the functions of a topological superconductor plunger gate and a depletion gate. Gates1320,1322, and1324may be formed in a first layer. Gates1326and1328may also be configurable as QD plunger gates that are formed in a second layer, different from the first layer. Gates1342,1344, and1352are configurable as cutter gates and these gates may be formed in a second layer, different from the first layer. Cutter gate1344(corresponding to cutter gate1129ofFIG.11) may be used to control the coupling of the quantum dot under QD plunger gate1326to transport lead portion1318(corresponding to transport lead1134ofFIG.11). Cutter gate1352(corresponding to cutter gate1127ofFIG.11) may be used to control the coupling between two adjacent quantum dots. Cutter gate1342(corresponding to cutter gate1125ofFIG.11) may be used to control the coupling to the adjacent quantum dot (e.g., quantum dot1132ofFIG.11). Similar gate configurations may be used with the other quantum devices with single-sided dual-purpose MZM junctions (e.g., quantum device900ofFIG.9and quantum device1000ofFIG.10described earlier). AlthoughFIG.13shows a certain gate configuration corresponding to an MZM junction, other gate configurations may also be used to implement the functionality of the MZM junction.

In conclusion, the present disclosure relates to a quantum device comprising at least one superconducting island configurable to support at least one pair of Majorana zero modes (MZMs). The quantum device may further include a first conductor configurable to be coupled with at least one MZM of the at least one pair of MZMs, where the first conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state. The quantum device may further include a second conductor configurable to be coupled with the at least one MZM of the at least one pair of MZMs, where the second conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state.

Each of the first conductor and the second conductor may be configurable to be coupled to the at least one MZM of the at least one pair of MZMs via a tunable coupling. The first conductor may be configurable to be coupled via a first coupling and the second conductor may be configurable to be coupled via a second coupling, and each of the first coupling and the second coupling may be independently tunable. The first conductor may be configurable as a transport lead when in the grounded state or as a quantum dot when in the Coulomb blockade state. The second conductor may be configurable as a transport lead when in the grounded state or as a quantum dot when in the Coulomb blockade state.

The quantum device may further include a two-dimensional electron gas (2DEG), where a set of gates formed on the 2DEG is configurable to control the tunable coupling. Each of the set of gates may be formed in a single layer. Alternatively, or additionally, a first subset of the set of gates may be formed in a first layer and a second subset of the set of gates may be formed in a second layer, different from the first layer.

In another example, the present disclosure relates to a quantum device comprising at least one superconducting island configurable to support at least one pair of Majorana zero modes (MZMs). The quantum device may further include a conductor configurable to be coupled with at least one MZM of the at least one pair of MZMs, where the conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state.

The conductor may be configurable to be coupled to the at least one MZM of the at least one pair of MZMs via a tunable coupling. The conductor may be configurable as a transport lead when in the grounded state or as a quantum dot when in the Coulomb blockade state.

The quantum device may further include a two-dimensional electron gas (2DEG), where a set of gates formed on the 2DEG is configurable to control the tunable coupling. Each of the set of gates may be formed in a single layer. Alternatively, or additionally, a first subset of the set of gates may be formed in a first layer and a second subset of the set of gates may be formed in a second layer, different from the first layer. The quantum device may further comprise a cutter gate for tuning the tunable coupling.

In yet another example, the present disclosure relates to a quantum device comprising at least one superconducting island configurable to support at least one pair of Majorana zero modes (MZMs). The quantum device may further include a first conductor configurable to be coupled with at least one MZM of the at least one pair of MZMs via a first tunable coupling, where the first conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state. The quantum device may further include a first cutter gate for tuning the first tunable coupling. The quantum device may further include a second conductor configurable to be coupled with the at least one MZM of the at least one pair of MZMs via a second tunable coupling, where the second conductor is configurable to be in at least one of a grounded state or a Coulomb blockade state. The quantum device may further include a second cutter gate for tuning the second tunable coupling independent of the first tunable coupling.

The first conductor may be configurable as a transport lead when in the grounded state or as a quantum dot when in the Coulomb blockade state. The second conductor may be configurable as a transport lead when in the grounded state or as a quantum dot when in the Coulomb blockade state.

The quantum device may further include a two-dimensional electron gas (2DEG), where a set of gates formed on the 2DEG is configurable to control the tunable coupling. Each of the set of gates may be formed in a single layer. Alternatively, or additionally, a first subset of the set of gates may be formed in a first layer and a second subset of the set of gates may be formed in a second layer, different from the first layer.

It is to be understood that the systems, devices, methods, and components described herein are merely examples. In an abstract, but still definite sense, any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or inter-medial components. Likewise, any two components so associated can also be viewed as being “operably connected,” or “coupled,” to each other to achieve the desired functionality. Merely because a component, which may be an apparatus, a structure, a device, a system, or any other implementation of a functionality, is described herein as being coupled to another component does not mean that the components are necessarily separate components. As an example, a component A described as being coupled to another component B may be a sub-component of the component B, the component B may be a sub-component of the component A, or components A and B may be a combined sub-component of another component C.

Although the disclosure provides specific examples, various modifications and changes can be made without departing from the scope of the disclosure as set forth in the claims below. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of the present disclosure. Any benefits, advantages, or solutions to problems that are described herein with regard to a specific example are not intended to be construed as a critical, required, or essential feature or element of any or all the claims.