A method of tuning a quantum information processing system

Abstract

A method of tuning a circuit portion of a quantum information processing circuit, the circuit portion including a first qubit (210) coupled to a second qubit (200). The first qubit includes a first Josephson junction (212) and an inductive circuit element (216), and the second qubit includes a second Josephson junction (202). The method includes measuring the anharmonicity of the first qubit and the anharmonicity of the second qubit; followed by annealing the circuit portion to change the anharmonicity of the first qubit. The annealing causes the anharmonicity of the first qubit to approach the same magnitude as and opposite sign to the anharmonicity of the second qubit.

Description

[0001] 175067 / 01

[0002] A Method of Tuning a Quantum Information Processing System

[0003] This invention relates to a method of tuning a quantum information processing system, in particular to tuning superconducting circuit portions for quantum information processing systems.

[0004] In a superconducting circuit implementation of a quantum computer, the base unit of quantum computing, a qubit (quantum bit) can be implemented physically in a number of different ways. Typically, one or more Josephson junctions are combined with capacitors and / or inductors, to form a high quality anharmonic circuit, the lowest quantised energy levels of which are used as the qubit. It is useful for the qubit to have a high anharmonicity, such that the lowest quantised energy levels can be addressed without exciting the qubit to higher-order energy levels.

[0005] The most commonly used superconducting qubit is the transmon, which uses a Josephson junction shunted by a capacitor to create a non-linear oscillator, which is insensitive to charge noise. Insensitivity to charge noise makes the transmon less likely to decohere, such that it can remain in a superposition of states and be used for quantum computation.

[0006] In order to perform any useful quantum computing, it is necessary to implement an architecture of at least two qubits coupled together. Thus, it is desirable to improve the tuning of coupled qubits, in order to improve the fidelity of qubit gates.

[0007] This invention aims to provide an improved method for tuning coupled qubits for quantum computing systems.

[0008] From a first aspect, the invention provides a method of tuning a circuit portion of a quantum information processing circuit, wherein the circuit portion comprises: a first qubit comprising a first Josephson junction and an inductive circuit element; a second qubit comprising a second Josephson junction; wherein the first qubit is coupled to the second qubit; the method comprising: i) measuring the anharmonicity of the first qubit and the anharmonicity of the second qubit; and ii) annealing the circuit portion to change the anharmonicity of the first qubit, such that the anharmonicity of the first qubit approaches substantially the same magnitude as, and opposite sign to, the anharmonicity of the second qubit.

[0009] From a second aspect, the invention provides a circuit portion of a quantum information processing circuit, comprising: a first qubit comprising a first Josephson junction and an inductive circuit element; a second qubit comprising a second Josephson junction; wherein the first qubit is coupled to the second qubit; and wherein the circuit portion is tuned using the method of the first aspect, such that the anharmonicity of the first qubit approaches substantially the same magnitude as and opposite sign to the anharmonicity as the second qubit.

[0010] Thus it will be seen that, in accordance with embodiments of the invention, the claimed method allows for the anharmonicity of a qubit to be changed after fabrication of the circuit portion.

[0011] When the circuit portion is fabricated, the first and second qubits may be fabricated and positioned next to one another, in order to couple the qubits together. For example, the first and second qubits may be arranged on the same substrate, e.g. in order to more easily facilitate coupling between them. The structure of the Josephson junction of each qubit upon fabrication of the circuit portion at least partially determines their respective resonant frequencies and anharmonicities.

[0012] The resonant frequency of a qubit is the frequency at which microwaves should be applied to the qubit to cause resonance, e.g. to excite the qubit between the two lowest energy levels, denoted as |0) and |1). This can put the qubit into a superposition of states to perform quantum computation.

[0013] Annealing a Josephson junction after fabrication can increase or decrease the resistance across the Josephson junction, and hence change the resonant frequency of the junction. Thus, annealing the circuit portion will change the resonant frequency of first and second qubits.

[0014] However, unlike the second qubit, the first qubit also comprises an inductive circuit element in addition to the Josephson junction. The Applicant has recognised that annealing the first qubit acts to change the inductance of the Josephson junction whilst the inductance of the inductive circuit element remains unchanged, such after annealing the anharmonicity of the first qubit is changed whilst the anharmonicity of the second qubit remains substantially unchanged.

[0015] Thus, after fabrication of the circuit portion, the anharmonicities of the first and second qubits are measured, in order to determine the difference in anharmonicities of the first and second qubits. This may inform how to anneal the circuit portion in order to change the anharmonicity of the first qubit to be equal in magnitude, and opposite in sign to the anharmonicity of the second qubit. The (e.g. entire) circuit portion may then be annealed in order to change the anharmonicity of the first qubit, without substantially changing the anharmonicity of the second qubit.

[0016] The anharmonicity of the qubit is the degree of deviation of the energy levels of the qubit from a harmonic oscillator. In a harmonic oscillator, the energy levels are evenly spaced. The two lowest energy levels |0) and |1) have an energy difference of E. In a harmonic oscillator, the next energy level |2) has an energy difference of E from 11 >. However, in an anharmonic qubit, the next energy level |2) has an energy difference of E ± a from 11 ).

[0017] When two qubits are coupled together to perform quantum computation, e.g. using a two qubit gate, the interaction of the lowest quantised energy levels (e.g. |0) and 11 > ) with non-computational higher energy levels (e.g. |2» can introduce errors such as the static cross-Kerr (“ZZ”) shift for two qubit gates. The ZZ shift is an energy shift experienced by one qubit depending on the state of the other qubit, and can cause coherent error in quantum computation. For example, the fidelity of entangling gates may be negatively affected by the ZZ shift.

[0018] Two coupled qubits can be modelled as two Duffing oscillators with small anharmonicities ai and 02 with a static exchange interaction of J. The ZZ shift can be approximated as ZZ where A is the qubit-qubit detuning. Thus, if the anharmonicities of the two qubits are equal in magnitude, and opposite in sign, the ZZ shift reduces to approximately zero.

[0019] Therefore, if the anharmonicity of the second qubit is measured as being -a, the anharmonicity of the first qubit is tuned using annealing towards being substantially +a. This can reduce the ZZ shift in quantum processing systems, especially low anharmonicity systems (e.g. wherein the circuit portion comprises a transmon).

[0020] The method according to the first aspect of the invention allows for the circuit portion to be annealed as a whole after fabrication, without needing to specifically target the first qubit in isolation from the second qubit. This may make creating a quantum information processing circuit with reduced error significantly easier, as the parameters of the qubits can be altered after fabrication. As the first qubit can be annealed (i.e. tuned by annealing) to have a particular anharmonicity, in-situ tuning of qubit anharmonicity, e.g. via magnetic flux biasing, may not be required.

[0021] In addition to resulting in faster and higher fidelity entangling gates in a compact circuit architecture, by reducing error the circuit portion may be integrated into larger devices with improved scalability.

[0022] When the qubit pair is annealed such that the first qubit approaches substantially the same magnitude as, and opposite sign to, the anharmonicity of the second qubit, the ZZ error of the circuit portion is reduced. For example, the magnitude of the anharmonicity of the first qubit is tuned to be within 10% of the magnitude of the anharmonicity of the second qubit, e.g. within 5%, e.g. within 2%, e.g. within 1%, e.g. within 0.5%, e.g. within 0.2%, e.g. within 0.1%.

[0023] The relative anharmonicities of the qubit pair may also be tuned to a different, arbitrary value, e.g. to improve the fidelity of a particular two qubit gate or to remove other error sources. Whilst the ZZ error is reduced as the first qubit approaches substantially the same magnitude as, and opposite sign to, the anharmonicity of the second qubit, the fidelity of a two qubit gate may be improved at a higher magnitude of anharmonicity mismatch. Thus, the method may comprise tuning the anharmonicity of the first qubit to balance the improvement of the fidelity of the two qubit gate and the reduction of the ZZ error. For example, the ZZ error may be reduced by bringing the anharmonicity of the first qubit to within 10% of the anharmonicity of the transmon, rather than 1 %, when the fidelity is reduced for a 1% difference but improved for a 10% difference. This may be useful in instances where reducing the ZZ error might require a different value of the anharmonicity of the first qubit than improving the fidelity of a particular type of two qubit gate.

[0024] The anharmonicity of the first qubit may be measured without the presence of any external bias control (e.g. magnetic flux biasing). However, the anharmonicity (e.g. and resonant frequency) of the first qubit may vary depending on the magnetic flux applied.

[0025] Preferably, step i) comprises biasing the first qubit, and measuring the anharmonicity of the first qubit when the first qubit is biased. The biasing may comprise applying a magnetic flux to the first qubit. For example, during the steps of measuring, the first qubit may be biased towards its preferred operation point, e.g. by applying magnetic flux at or close to a half flux quantum, in order for quantum computations to be performed. At this operation point, the anharmonicity of the first qubit may be at a positive value, e.g. a local maximum, whilst also protecting the first qubit from flux noise.

[0026] Therefore, the anharmonicity may be tuned by annealing such that, during operation (e.g. when biased, e.g. with or close to a half flux quantum), the anharmonicity is substantially equal and opposite to the anharmonicity of the second qubit.

[0027] The anharmonicity of the second qubit may not be affected by biasing (e.g. magnetic flux control). Therefore, in some embodiments step i) comprises measuring the anharmonicity (and / or resonant frequency) of the second qubit when no external bias is applied to the second qubit.

[0028] In some embodiments, step i) comprises measuring the anharmonicity of the first qubit when no external bias is applied to the first qubit. For example the method may comprise using the relationship between the anharmonicity and the degree of biasing (e.g. the applied magnetic flux) for the first qubit to determine the anharmonicity of the first qubit when it is biased at its preferred operational point (e.g. at or close to a half flux quantum), based on its unbiased anharmonicity. This may be used to determine how to tune the first qubit such that its anharmonicity is substantially equal and opposite to the anharmonicity of the second qubit during operation. However, this may be less accurate than biasing the first qubit and measuring its anharmonicity when it is being biased.

[0029] In some embodiments, the method further comprises: iii) measuring the anharmonicity of the first qubit after annealing the circuit portion; iv) repeating steps ii) and iii) until the anharmonicity of the first qubit is substantially the same magnitude as and opposite sign to the anharmonicity to the second qubit.

[0030] This may allow for the anharmonicity of the first qubit to be tuned iteratively over successive anneals. After the first anneal, the anharmonicity of the first qubit may be measured in order to determine how close it is to the target anharmonicity (e.g. substantially equal in magnitude and opposite in sign to the second qubit). The parameters of the anneal (e.g. the length of time of the anneal) may then be adjusted, to accurately approach the target anharmonicity, e.g. an arbitrary number of times.

[0031] For example, step iv) may be repeated between 1 and 10 times, e.g. 5 times. The targeted change of anharmonicity may be reduced for each iteration, as this may prevent ‘overshooting’ the target anharmonicity, e.g. the length of time or temperature of the anneal may be changed for each iteration. In practice, this may involve a cryogenic measurement, e.g. cooling the circuit portion to cryogenic temperatures to measure the anharmonicity of the first qubit.

[0032] For example, steps ii) and iii) are repeated until the magnitude of the anharmonicity of the first qubit is within 10% of the magnitude of the anharmonicity of the second qubit, e.g. within 5%, e.g. within 2%, e.g. within 1%, e.g. within 0.5%, e.g. within 0.2%, e.g. within 0.1%.

[0033] Preferably step iii) comprises biasing the first qubit (e.g. by applying a magnetic flux) whilst measuring the anharmonicity of the first qubit. For example, the first qubit may be biased at its preferred operational point (e.g. at or close to a half flux quantum), such that the anharmonicity of the first qubit is at a positive value, e.g. a local maximum.

[0034] In some embodiments, step iii) comprises measuring the anharmonicity of the second qubit. Whilst the anharmonicity of the second qubit may be substantially unchanged by the annealing process, it may change by a small amount (e.g. less than 1%).

[0035] Therefore, the method may comprise measuring the anharmonicity of the second qubit after any annealing step, in order to more accurately tune the anharmonicity of the first qubit to be substantially equal and opposite to the second qubit. For example, whether the anharmonicity of the second qubit is measured after an annealing step may depend on the required accuracy of the anharmonicity matching between the first and second qubit, e.g. a 5% mismatch may not require the anharmonicity of the second qubit to be measured after annealing.

[0036] In some embodiments, the measuring the anharmonicity comprises measuring one or more circuit parameters of the first and / or second qubits (e.g. at room temperatures) and determining the anharmonicity based on the circuit parameter(s). This may allow for the anharmonicity of the first and / or second qubit to be measured indirectly. For example, the circuit parameters may be measured at room temperature, e.g. the resistance of the first and / or second Josephson junction at room temperature. This may avoid cooling the circuit portion to cryogenic temperatures between anneals, and may therefore speed up the method of tuning the first qubit’s anharmonicity.

[0037] In some embodiments, the inductive circuit element comprises a linear inductor in parallel with the first Josephson junction, e.g. a linear geometric inductor. The inductance of the inductive circuit element may not change upon annealing. However, upon annealing, the resistance of the first Josephson junction increases, corresponding to an increase of the Josephson inductance of the first Josephson junction when in a superconducting state. For example, the linear geometric inductor (e.g. a meandering inductor) may be made out of the same metal as electrodes that may be used for controlling and reading out the first and / or second qubits.

[0038] The inductive circuit element may be made using materials with a high kinetic inductance, or an array of Josephson junctions. This may be useful when creating a more sensitive inductive element. However, an inductive element made using an array of Josephson junctions may be more sensitive to the annealing, e.g. the annealing method may undesirably change the inductance of the inductive element.

[0039] When the first Josephson junction of the first qubit is placed in parallel with a inductive circuit element (e.g. a linear inductor), and the circuit portion is annealed, the Josephson inductance Lj of the first Josephson junction is changed whilst the inductance L of the inductive circuit element (e.g. linear inductor) remains substantially the same. The ratio — of the two inductances is therefore changed by annealing the

[0040] Li circuit portion, which in turn changes the anharmonicity of the first qubit. Thus, the relative change of Josephson inductance compared to the fixed inductance L may act to change the anharmonicity of the first qubit.

[0041] This may enable the anharmonicity of the first qubit to be tuned relative to the second qubit, as the anharmonicity of the first qubit may be changed whilst the anharmonicity of the second qubit remains substantially the same.

[0042] In some embodiments second qubit comprises a second capacitor in parallel with the second Josephson junction. The second capacitor may enable the second qubit to reduce charge noise, in order to reduce the probability of the second qubit decohering, helping to allow calculations to be performed by the quantum information processing circuit.

[0043] For example, the second qubit may comprise a transmon. A transmon is a simple, well-defined qubit, and may thus be well-suited to be integrated into a circuit portion to be coupled with the first qubit. Furthermore, as the transmon comprises just a capacitor and a Josephson junction (i.e. it does not comprise an inductive circuit element), its anharmonicity is substantially unchanged during annealing, as there is no ‘ratio’ that changes, in spite of the inductance of the second Josephson junction changing upon annealing. This may allow the second qubit to maintain its anharmonicity whilst it is tuned by annealing.

[0044] The first qubit may comprise a positive anharmonicity qubit, e.g. an inductively- shunted transmon (1ST). A positive anharmonicity qubit may be a qubit that has an anharmonicity that comprises a positive value when it is unbiased, and / or when it is biased, e.g. when a magnetic flux is applied to the qubit. For example, the 1ST may comprise a negative anharmonicity when it is unbiased, but a positive anharmonicity when biased with a magnetic flux to a particular operation point, e.g. at or close to a half flux quantum.

[0045] As the 1ST has similar components and a similar geometry to the transmon, it may be easier to couple the two different types of qubits together, e.g. as only a simple static coupling is required, removing the complexity of other common gate schemes relying on tunable coupling elements. Furthermore, an 1ST may be compact and / or tileable, e.g. when coupled to a transmon. The entangling gate formed by a coupled transmon and an 1ST may be faster than an equivalent transmon-transmon system.

[0046] In some embodiments, the first qubit comprises a first capacitor in parallel with the first Josephson junction. Similar to the second capacitor, this may enable the first qubit to reduce charge noise to reduce the probability of qubit decoherence. However, in embodiments where the first qubit comprises an 1ST, the 1ST may be less affected by charge noise, and thus may not require a capacitor to reduce charge noise. For example, the second capacitor may be larger than the first capacitor.

[0047] Whilst helpful in reducing charge noise, using a capacitor to shunt the Josephson junction reduces the anharmonicity of the first and / or second qubits (e.g. the transmon and 1ST), meaning it is harder to address individual energy levels. This may make tuning the anharmonicities of the first qubit (e.g. the 1ST) relative to the second qubit (e.g. the transmon) even more useful in reducing the ZZ error of the coupled qubit pair.

[0048] The first qubit is coupled to the second qubit, in order for the circuit portion to perform two qubit gate operations for quantum computation. In some embodiments, the first qubit is coupled to the second qubit via a static coupling element. As the first and second qubits each comprise a (e.g. single) Josephson junction, they have similar architectures (e.g. wherein the first qubit comprises an inductively-shunted transmon and the second qubit comprises a transmon). This is a simple coupling scheme. For example, the first qubit may be coupled to the second qubit via capacitive arms, e.g. in embodiments where the first qubit and second qubit are arranged on the same substrate. In some embodiments, the first and second qubits may be coupled via a tunable coupling element. In some embodiments, step ii) comprises annealing the circuit portion by baking. For example, the baking may comprise placing the circuit portion on a heating plate. This may help to uniformly anneal both the first qubit and the second qubit, e.g. to tune the resonant frequencies of the qubits in addition to the anharmonicity of the first qubit. The temperature of the baking (e.g. of the heating plate) may be between 50 °C and 300 °C, e.g. between 100 °C and 200 °C, e.g. approximately 150 °C. Baking may be used to change the resistance / inductance of the first and second Josephson junctions, without damaging other circuit components (e.g. the inductive circuit element) by using excessive heat. For example, higher temperatures than 300 °C may be used, but this may damage the circuit portion / processing circuit more generally.

[0049] The duration of the annealing at step ii) may depend on the temperature and / or power of the annealing technique chosen. For example, the circuit portion may be annealed for a short time at a high temperature, or vice versa. In embodiments where step ii) comprises annealing the circuit portion by baking, the duration of the annealing at step ii) may be between 1 minute and 1 hour, e.g. between 5 minutes and 30 minutes, e.g. approximately 10 minutes. However, at high temperatures and / or for very fine tuning, the anneal may be as short as 10 seconds.

[0050] In some embodiments, step ii) comprises annealing the circuit portion using laser annealing. Laser annealing may comprise using a high-powered laser beam to heat the circuit portion. The laser beam may be focused onto the first qubit and / or the second qubit , e.g. in sequence, for example to tune the resonant frequencies of the qubits in addition to the anharmonicity of the first qubit. In some embodiments, the laser beam may be focused onto just the first qubit, e.g. where it is undesirable to change the resonant frequency of the second qubit by annealing the second Josephson junction. For example, the laser beam may be focused onto the first Josephson junction, to avoid heating the rest of the circuit portion, e.g. to avoid damaging the inductive circuit element in embodiments where the inductive circuit element may be adversely affected by the annealing process.

[0051] In some embodiments, step ii) comprises annealing the circuit portion using electron beam (e-beam) annealing. E-beam annealing may comprise using an e-beam lithography system to heat the circuit portion. For example, the e-beam may be used to individually anneal the first Josephson junction to tune the anharmonicity of the first qubit, or it may be focused on both the first qubit and the second qubit, e.g. in sequence. For example, the e-beam may be focused onto the first Josephson junction, to avoid heating the rest of the circuit portion, e.g. to avoid damaging the inductive circuit element in embodiments where the inductive circuit element may be adversely affected by the annealing process.

[0052] In some embodiments, step ii) comprises annealing the circuit portion using alternating bias assisted annealing. Alternating bias assisted annealing may comprise applying a changing magnetic or electric field during the annealing process to induce changes in the structure of the Josephson junction. This may be used to individually anneal Josephson junctions, e.g. to tune only the anharmonicity of the first qubit without affecting the resonant frequency of the second qubit.

[0053] Thus, in some embodiments, step ii) comprises annealing (e.g. only) the first qubit of the circuit portion, e.g. thus not annealing the second qubit (e.g. by isolating the second qubit from the annealing of the first qubit).

[0054] The first and second Josephson junctions may be approximately spatially isolated, e.g. from one another, or from other Josephson junctions that may be present within the first or second qubits. Spatially isolating the Josephson junction may allow the first and / or second Josephson junction of the first qubit and second qubits to be targeted alone in the annealing process. This may prevent the inductive circuit element, or other circuit elements from being affected by the anneal, which could change their properties and thus affect the anharmonicity and / or frequency of the first and / or qubit in an undesired way, or impact the functionality of the other circuit elements.

[0055] For example, the first and second Josephson junctions may be spaced by at least 30- 50 pm from other circuit elements (e.g. from other Josephson junctions). Common superconducting qubits typically comprise many Josephson junctions in close (e.g. sub 1 pm spacing) proximity. Thus, it may be difficult to individually anneal Josephson junctions in such qubits if they are not sufficiently spaced from one another.

[0056] In some embodiments, the circuit portion is part of an array of circuit portions. For example, the two qubit pair (of the first qubit and the second qubit) may be part of a wider array of qubits. This may allow computation to be performed across many (e.g. the array of) qubits. In some embodiments, the qubits in the array of circuit portions are globally tuned during step ii). For example, baking may be a useful technique to tune all circuit portions in the array. This may be useful where all first qubits in the array need to be tuned by substantially the same degree to achieve an anharmonicity that is equal in magnitude and opposite in sign to their respective second qubit.

[0057] In some embodiments, each circuit portion is tuned locally during step ii), to selectively tune the first and second qubits of each circuit portion. For example, laser or e-beam annealing may be a useful technique to target particular circuit portions. This may be useful where many qubits are fabricated (e.g. on the same substrate) to form the quantum information processing circuit, but the first qubit of some (e.g. each) circuit portion may need to be annealed to a different degree to the other circuit portions, e.g. due to differences in the anharmonicities of first-second qubit pairs in different circuit portions. These differences may arise due to imperfections of the fabrication process.

[0058] In some embodiments, the array of circuit portions are first tuned globally, and then tuned locally. For example, array of circuit portions may be tuned globally (e.g. by baking of the array) to bring the anharmonicities of the first qubits in the array within a particular range of the desired anharmonicity. One or more of the first qubits may then be tuned locally (e.g. by laser beam, e-beam, or alternating bias assisted annealing) to more precisely tune the anharmonicity of the first qubit to be equal in magnitude and opposite in sign to its respective second qubit. This method may allow the array to be annealed quickly, whilst also ensuring the qubit anharmonicities are more precisely tuned to help prevent mismatched anharmonicities and thus low gate fidelities.

[0059] In some embodiments, the first and / or second qubit each comprise part of a coaxmon. A coaxmon is a control and read-out architecture for a superconducting qubit, including a control line for charge and / or flux control coupled to the qubit arranged to control the state of the qubit (e.g. using microwave or flux control), and a readout element coupled to the qubit arranged to measure the state of the qubit. Within the coaxmon, the Josephson junction of the qubit may be connected between two superconducting electrodes, wherein the two superconducting electrodes are coaxial and coplanar. The control line and the readout element are arranged in a plane that has a component that is perpendicular to the plane comprising the two superconducting electrodes, e.g. the control line and the readout element may be perpendicular or oblique to the two superconducting electrodes. Preferably the control line and the readout element are coaxial. Preferably the control line and / or the readout element are coaxial with (e.g. the two superconducting electrodes of) the qubit.

[0060] The coaxmon may help to isolate the qubit from the electromagnetic environment, to help further increase the coherence time of the qubit whilst it is being controlled to perform quantum computations.

[0061] The inductively-shunted transmon may also be used as a tunable coupling element between two transmon qubits. Thus, when viewed from another aspect, the invention comprises a method of tuning a coupling element between two qubits, wherein the coupling element comprises a first Josephson junction and an inductive circuit element; the method comprising: i) measuring the anharmonicity of the coupling element; and ii) annealing the coupling element to change the anharmonicity of the coupling element.

[0062] The Applicant has also appreciated that tuning the anharmonicity of a qubit comprising a Josephson junction and an inductive circuit element may also be useful when tuning a qubit lattice.

[0063] This is novel and inventive in its own right, and thus when viewed from another aspect, the invention comprises a method of tuning a qubit lattice, wherein the qubit lattice comprises: a plurality of qubits each comprising a first Josephson junction and an inductive circuit element; wherein the plurality of qubits are arranged in a two-dimensional lattice and each of the plurality of qubits is coupled to at least one adjacent qubit of the plurality of qubits; the method comprising: i) measuring the anharmonicity of each qubit of the plurality of qubits; and ii) annealing the qubit lattice to change the anharmonicity of each qubit of the plurality of qubits. Features of any aspect or embodiment described herein may, wherever appropriate, be applied to any other aspect or embodiment described herein. Where reference is made to different embodiments or sets of embodiments, it should be understood that these are not necessarily distinct but may overlap.

[0064] Certain embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0065] Figure 1a is a circuit diagram of a transmon qubit;

[0066] Figure 1b is a circuit diagram of an inductively shunted transmon qubit;

[0067] Figure 2 is a schematic diagram of a transmon coupled to an inductively shunted transmon;

[0068] Figure 3 is a flow diagram of a method of tuning the anharmonicity of a qubit;

[0069] Figure 4 is a schematic diagram of the energy levels of an inductively shunted transmon and a transmon after annealing;

[0070] Figure 5 is a graph of the change in resonant frequency of a transmon and an inductively shunted transmon over successive anneals;

[0071] Figure 6 is a graph of the change in anharmonicity of a transmon and an inductively shunted transmon over successive anneals.

[0072] Figure 7 is a schematic diagram of control architecture for a pair of qubits.

[0073] Embodiments of the present invention will now be described, with reference to the process of tuning a transmon and inductively-shunted transmon via annealing.

[0074] Figure 1a is a circuit diagram of a transmon 100, which is made up of a transmon Josephson junction 104 and a transmon capacitor 102 in parallel with the transmon Josephson junction 104. The transmon 100 uses the transmon capacitor 102 to shunt the transmon Josephson junction to realise a non-linear oscillator with eigenstates insensitive to charge noise. The resistance of the transmon Josephson junction 104 can be changed by annealing the transmon 100 after fabrication, thus changing the resonant frequency of the transmon 100.

[0075] Figure 1b is a circuit diagram of an inductively-shunted transmon (1ST) 110, which is made up of an 1ST Josephson junction 114 in parallel with an 1ST capacitor 112, in parallel with a linear inductor 116. The 1ST Josephson junction 114 has a Josephson inductance Lj, and the linear inductor 116 has an inductance L. The 1ST 110 is a particular realisation of an RF-SQUID (radio-frequency superconducting quantum interference device).

[0076] Furthermore, as the linear inductor 116 is in parallel with the 1ST Josephson junction 114, changing the inductance of the 1ST Josephson junction will change the inductance ratio between the Josephson inductance and the linear inductance and therefore the anharmonicity of the overall 1ST 110. Thus, the 1ST 110 can be annealed to change its anharmonicity by changing the resistance of the 1ST Josephson junction after fabrication of the 1ST circuit 110. Similarly to the transmon 100 shown in Figure 1a, the resonant frequency of the 1ST 110 shown in Figure 1b is also changed upon annealing.

[0077] Figure 2 is a schematic diagram of a transmon 200 (e.g. as shown in Figure 1a) coupled to an inductively shunted transmon (1ST) 210 (e.g. as shown in Figure 1b) via capacitive arms 208, forming a circuit portion of a quantum information processing circuit. The capacitive arms 208 are used as a static coupling method, however a tunable coupling method may be used instead. The transmon 200 and 1ST 210 are each surrounded by transmon and 1ST rings 201 , 203 respectively, where the first and second rings 201 , 203 are connected to the capacitive arms 208.

[0078] Figure 3 is a flow diagram of a method for tuning the anharmonicity of an 1ST. The transmon and 1ST (e.g. as shown in Figure 2) are fabricated as a circuit portion for a quantum information processing circuit in advance of the method shown in Figure 3, with methods of doing so being known to the skilled person.

[0079] At a first step 301 , the anharmonicity of the 1ST is measured whilst the 1ST is biased at a half-flux quantum (i.e. at a positive value, e.g. a local maximum), and at a second step 303, the anharmonicity of the transmon is measured. This allows for both the transmon and the 1ST to be characterised (e.g. their physical properties including resonant frequency and anharmonicity measured) after they have initially been fabricated, at their operational biases. By characterising the transmon and 1ST, the difference between their respective anharmonicities can be characterised. Thus, the degree of annealing required to bring the anharmonicity of the 1ST to be equal and opposite to the anharmonicity of the transmon can be estimated. At a third step 305, the circuit portion is annealed, e.g. by baking, laser annealing, e- beam annealing or alternating bias annealing. For example, where the circuit portion is annealed by baking, the circuit portion may be placed on a heating plate at a temperature of approximately 150 °C for between 10 and 60 seconds. The length of time and temperature of the anneal depends on the degree of annealing required, as determined at the second step 303. For example, data from previous anneals may be used to predict how the circuit portion should be annealed to reach the target anharmonicity of the 1ST, e.g. ‘calibration’ data.

[0080] Using a heating plate helps to heat the entire circuit portion uniformly, to predictably tune the resonant frequencies of the 1ST and transmon, and tune the anharmonicity of the 1ST.

[0081] At a fourth step 307, the anharmonicity of the 1ST is measured. If the anharmonicity is substantially the same magnitude as, and opposite in sign to, the anharmonicity of the transmon, the annealing does not need to be repeated. However, if the anharmonicity of the 1ST is not substantially the same magnitude as, and opposite in sign to, the anharmonicity of the transmon, the third step 305 and fourth step 307 are repeated, until the anharmonicity of the 1ST is substantially equal in magnitude, and opposite in sign to the anharmonicity of the transmon, e.g. the magnitude of the anharmonicity of the 1ST is within 1-10% of the magnitude of the anharmonicity of the transmon. The degree of ‘matching’ of the anharmonicities of the 1ST and transmon may depend on the particular application of the circuit portion.

[0082] For example, the magnitude of the anharmonicity of the 1ST may reach the threshold anharmonicity value (e.g. within 10% of the magnitude of the anharmonicity of the transmon) after a particular number of anneals, e.g. five anneals. The threshold anharmonicity value may be the difference in the magnitude of the anharmonicity of the transmon and 1ST where the ZZ error, and / or other errors that may arise from a discrepancy in anharmonicity, is reduced to a negligible level.

[0083] Once the anharmonicity of the 1ST is measured to be substantially equal and opposite to the anharmonicity of the transmon, the 1ST and transmon qubit pair is tuned, and the method is stopped. For example, the method may be stopped when the magnitude of the anharmonicity of the 1ST is within between 1 and 10%, e.g. 5% of the magnitude of anharmonicity of the transmon. The degree of anharmonicity required may depend on the ultimate application of the circuit portion.

[0084] After the method steps shown in Figure 3 are carried out, the circuit portion may then be used to operate high-fidelity entangling gates for use in quantum computation.

[0085] It will be appreciated by the skilled person that the method described with reference to Figure 3 can also be used for tuning a coupling element between two transmon qubits, wherein the coupling element is an inductively-shunted transmon. For example, at the second step 303, the anharmonicity of both transmons may be measured, to determine the degree of tuning of the inductively shunted transmon required, e.g. the coupling element is annealed until it has an anharmonicity at a desired level (which may or may not be the same magnitude as and opposite sign to the anharmonicity of the transmons).

[0086] It will also be appreciated that the method described with reference to Figure 3 can be used for tuning each qubit within an inductively-shunted transmon qubit lattice. For example, there may be no second step 303 without the presence of any transmons. Instead, the qubit lattice is annealed until the anharmonicity of the ISTs are at the desired level.

[0087] Figure 4 is a representative diagram of the energy levels of a transmon and 1ST after annealing. The |0) and |1) levels of the 1ST and transmon are the computational levels, which are used for performing quantum computations. The energy difference between the |0) and |1) levels of the 1ST and the transmon is equal to E, where each qubit can be excited from the |0) level to the |1) level by a frequency f. The 1ST is biased at a half-flux-quantum, to reach a preferred operation point of the 1ST, e.g. where it is at a local maximum value of anharmonicity, and where it is also approximately insensitive to flux noise.

[0088] The |2) levels of the 1ST and transmon are non-computational levels. The |2) level of the 1ST has an energy difference of E+a from its respective |1) level, whilst the |2) level of the transmon has an energy difference of E-a from its respective |1) level, a is the magnitude of the anharmonicity of the qubit. Thus, the anharmonicities a of the transmon and 1ST are equal in magnitude, and opposite in sign. This reduces the ZZ error for operations performed using the coupled transmon and 1ST.

[0089] Figure 4 is merely representative of the energy levels and relative anharmonicities, and generally the 1ST and transmon will not have exactly the same E, to avoid hybridization. Typically, neighbouring qubits in a circuit have different resonant frequencies.

[0090] Figure 5 is a graph of the change in resonant frequency of a transmon and an inductively shunted transmon over successive post-fabrication anneals. The annealing was achieved via baking using a hot plate, e.g. using the method described with reference to Figure 3. The annealing steps were performed at temperatures between 100 °C and 180 °C, each for a duration of between 1 minute and 10 minutes.

[0091] The resonant frequency is on the y-axis, and the relative change in the inductance of the Josephson junction is on the x-axis. The change in the resonant frequency of the 1ST is shown by the dashed line, and the change in resonant frequency of the transmon is shown by the solid line. A first device (Dev 1) is shown in solid symbols, from fabrication (square) to a first anneal (circle). A second device (Dev 2) is shown in open symbols, from fabrication (square), to successive first, second, third and fourth anneals (circle, diamond, star, hexagon).

[0092] Both devices show that over successive anneals, the resonant frequency of the transmon decreases, whilst the resonant frequency of the 1ST increases, showing how the respective resonant frequencies can be tuned and brought together over successive anneals.

[0093] Figure 6 is a graph of the change in anharmonicity of a transmon and an inductively shunted transmon over the successive post-fabrication anneals shown in Figure 5. The annealing was achieved via baking using a hot plate, e.g. using the method described with reference to Figure 3.

[0094] The magnitude of anharmonicity is on the y-axis, and the relative change in the inductance of the Josephson junction is on the x-axis. The change in the anharmonicity of the 1ST is shown by the dashed line, and the change in anharmonicity of the transmon is shown by the solid line. A first device (Dev 1) is shown in solid symbols, from fabrication (square) to a first anneal (circle). A second device (Dev 2) is shown in open symbols, from fabrication (square), to successive first, second, third and fourth anneals (circle, diamond, star, hexagon).

[0095] Over successive anneals, the anharmonicity of the 1ST decreases, whilst the anharmonicity of the transmon remains approximately the same. Thus, the anharmonicity of the 1ST can be tuned over successive anneals, independently of the transmon, to be brought towards substantially the same magnitude as the transmon anharmonicity. The anharmonicity of the transmon always has negative sign, while the anharmonicity of the 1ST is positive, and therefore Figure 6 also shows the anharmonicity of the 1ST being brought towards substantially the same magnitude and opposite sign as the transmon anharmonicity.

[0096] Figure 7 shows schematically two coaxmons 618, 619, where a coaxmon is a control architecture for use in a quantum information processing system according to an embodiment of the present invention.

[0097] The first coaxmon 618 includes a transmon 600 having two superconducting electrodes 622, 624 and a Josephson junction 602 between the two superconducting electrodes 622, 624. The two superconducting electrodes 622, 624 are arranged as a circular inner superconducting electrode 624 which is surrounded by a coaxial and coplanar circular outer superconducting electrode 622. The Josephson junction 602 is arranged to extend radially between the two superconducting electrodes 622, 624.

[0098] The second coaxmon 619 includes an inductively shunted transmon (1ST) 610 also having two superconducting electrodes 623, 625 and a Josephson junction 612 between the two superconducting electrodes 623, 625, which are arranged in the same way as for the first coaxmon 618. In order to control the quantum state of the transmon 600 and 1ST 610, each coaxmon 618, 619 includes a control line 620 provided coaxially with the transmon 600 and 1ST 610. The control line 620 is arranged to radiate the transmon 600 / IST 610 with microwaves in order to set the state of the transmon 600 / IST 610, and can also be used to apply a flux bias to the transmon 600 / IST 610 e.g. during operation of the qubits. On the other side of the transmon 600 / IST 610, each coaxmon 618, 619 includes a readout resonator 626 and a readout line 628, both of which are also arranged coaxially with the transmon 600 / IST 610. The readout resonator 626 is arranged to couple to the transmon 600 / IST 610 in such a way that its resonant frequency is dependent on the state of the transmon 600 / IST 610. The readout line 628 is arranged to radiate the resonator 626 and measure the frequency shift of the resonator 626 and thus the state of the transmon 600 / IST 610 via the reflected microwave signal.

[0099] The transmon 600 and 1ST 610 are coupled via capacitive arms 608, e.g. the transmon 600 and 1ST 610 are arranged on the same substrate, with their respective coaxmons 618, 619 extending above and below the plane of the substrate.

[0100] Thus, once the circuit portion shown in Figure 2 has been tuned after fabrication using the method described with reference to Figure 3, it can be incorporated into a coaxmon architecture as shown in Figure 7 (e.g. with a coaxmon 618 for each of the transmons 200 and ISTs 210), to control the qubit gates and readout the results of computations.

[0101] It will be appreciated by those skilled in the art that the invention has been illustrated by describing one or more specific embodiments thereof, but is not limited to these embodiments; many variations and modifications are possible, within the scope of the accompanying claims.

Claims

CLAIMS1. A method of tuning a circuit portion of a quantum information processing circuit, wherein the circuit portion comprises: a first qubit comprising a first Josephson junction and an inductive circuit element; a second qubit comprising a second Josephson junction; wherein the first qubit is coupled to the second qubit; the method comprising: i) measuring the anharmonicity of the first qubit and the anharmonicity of the second qubit; and ii) annealing the circuit portion to change the anharmonicity of the first qubit, such that the anharmonicity of the first qubit approaches substantially the same magnitude as and opposite sign to the anharmonicity of the second qubit.

2. The method as claimed in claim 1, further comprising: iii) measuring the anharmonicity of the first qubit after annealing the circuit portion; iv) repeating steps ii) and iii) until the anharmonicity of the first qubit is substantially the same magnitude as and opposite sign to the anharmonicity of the second qubit.

3. The method as claimed in claim 2, wherein step iv) is repeated between 1 and 100 times.

4. The method as claimed in claim 1 or 2, wherein the method comprises biasing the first qubit during the measuring of the anharmonicity of the first qubit.

5. The method as claimed in claim 4, wherein the biasing comprises magnetic flux biasing.

6. The method as claimed in claim 4 or 5, wherein the biasing comprises biasing the first qubit at a half-flux quantum.

7. The method as claimed in any preceding claim, wherein the inductive circuit element comprises a linear geometric inductor in parallel with the first Josephson junction.

8. The method as claimed in any preceding claim, wherein first Josephson junction is spaced by at least 30 pm from any other circuit elements in the first qubit.

9. The method as claimed in any preceding claim, wherein the second qubit comprises a capacitor in parallel with the second Josephson junction.

10. The method as claimed in any preceding claim, wherein the first qubit comprises a qubit with substantially positive anharmonicity.

11. The method as claimed in any preceding claim, wherein the first qubit comprises an inductively-shunted transmon.

12. The method as claimed in any preceding claim, wherein the second qubit comprises a transmon.

13. The method as claimed in any preceding claim, wherein the first and second qubits are mounted on the same substrate.

14. The method as claimed in any preceding claim, wherein step ii) comprises annealing the circuit portion by baking.

15. The method as claimed in claim 14, wherein the baking comprises placing the circuit portion on a heating plate.

16. The method as claimed in claim 14 or 15, wherein the temperature of the baking is between 50 °C and 300 °C.

17. The method as claimed in any preceding claim, wherein the duration of the annealing at step ii) is between 10 s and 1 hour.

18. The method as claimed in any of claims 1-13, wherein step ii) comprises annealing the circuit portion using laser annealing.

19. The method as claimed in any of claims 1-13, wherein step ii) comprises annealing the circuit portion using electron beam annealing.

20. The method as claimed in any of claims 1-13, wherein step ii) comprises annealing the circuit portion using alternating bias assisted annealing.

21. The method as claimed in any preceding claim, wherein the circuit portion is part of an array of circuit portions.

22. The method as claimed in claim 21 , wherein the qubits in the array of circuit portions are tuned globally during step ii).

23. The method as claimed in claim 21 , wherein each circuit portion is tuned locally during step ii), to selectively tune the first and second qubits of each circuit portion.

24. The method as claimed in any preceding claim, wherein the first and / or second qubit each comprise part of a coaxmon.

25. The method as claimed in any preceding claim, wherein the first and second qubits are statically coupled.

26. The method as claimed in any preceding claim, wherein the first and second qubits are coupled with capacitive arms.

27. The method as claimed in any of claims 1-24, wherein the first and second qubits are coupled via a tunable coupling element.

28. A circuit portion of a quantum information processing circuit, comprising: a first qubit comprising a first Josephson junction and an inductive circuit element; a second qubit comprising a second Josephson junction; wherein the first qubit is coupled to the second qubit; andwherein the circuit portion is tuned using the method as claimed in claim1 , such that the anharmonicity of the first qubit approaches substantially the same magnitude as and opposite sign to the anharmonicity of the second qubit.

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