Patent Description:
Large-scale quantum computers have the potential to provide fast solutions to certain classes of difficult problems. Multiple challenges in the design and implementation of quantum architecture to control, program and maintain quantum hardware impede the realization of large-scale quantum computing. Reference is made to <NPL>", which discloses an approach to measurement based on a microwave photon counter demonstrating raw single-shot measurement fidelity of <NUM>%. Further reference is made to <CIT>, which discloses a system and method for circuit quantum electrodynamics measurement.

The present disclosure describes technologies for implementing a readout scheme for transmon qubits.

In general, one innovative aspect of the subject matter of the present disclosure is embodied in a detector for reading out a state of a qubit, which includes a flux qubit and a flux bias generator, wherein the flux qubit includes an inductor, a SQUID loop comprising at least one Josephson junction and a capacitor, wherein the inductor, the at least one Josephson junction and the capacitor are connected to each other in parallel, wherein the flux qubit is arranged to exhibit a first flux state and a second flux state, wherein the flux bias generator is configured to generate a first flux bias through the inductor and a second flux bias through the SQUID loop, wherein the flux qubit is configured such that, in response to a first value of the first flux bias, the energies of the first and the second flux states are substantially identical and such that, in response to a second value of the first flux bias, the energies of the first and the second flux states are different, and wherein, in response to a first value of the second flux bias, the flux qubit is configured to be coupled to the qubit and, in response to a second value of the second flux bias, to be decoupled from the qubit and to suppress tunneling between the first and the second flux states; and a measurement unit, wherein the measurement unit is configured to determine whether the flux qubit is in the first flux state or the second flux state and to output a signal in dependence on whether the flux qubit is in the first flux state or in the second flux state.

The foregoing implementation can optionally include one or more of the following features, alone or in combination.

In some implementations, the flux bias generator is configured to, in the following order: generate the first value of the first flux bias, such that the energies of the first and the second flux states of the flux qubits are substantially identical; generate the first value of the second flux bias, such that a barrier between the first flux state and the second flux state is minimized and a resonance frequency of the flux qubit is tuned to a frequency of interaction such that the flux qubit is coupled to the data qubit and the state of the data qubit is mapped to an energy state of the flux qubit; generate the second value of the first flux bias, such that the energies of the first and the second flux states of the flux qubits are different; and generate the second value of the second flux bias, such that the flux qubit is decoupled from the qubit and the energy state of the flux qubit is mapped to a superposition of the first flux state or the second flux state.

In some implementations, in response to the first value of the second flux bias, the flux qubit is configured to be coupled to the qubit by tuning a resonance frequency of the flux qubit into resonance of a resonance frequency of the qubit.

In some implementations, in response to the second value of the second flux bias, the resonance frequency of the flux qubit differs from the resonance frequency of the qubit by more than <NUM>.

In some implementations, the measurement unit includes a signal generator, a transmission line and a power detector. The flux qubit is connected to the transmission line via a shunt line. The signal generator is configured to send travelling waves to the power detector via the flux qubit through the transmission line. The measurement unit is configured to determine whether the flux qubit is in the first flux state or in the second flux state based on an output of the power detector.

In some implementations, the measurement unit does not comprise a circulator, a parametric amplifier, and a high electron mobility transistor HEMT.

In some implementations, the measurement unit comprises a single flux quantum SFQ circuit arranged to measure a flux generated by the flux qubit and a discriminator. The discriminator is configured to determine whether the flux qubit is in the first flux state or in the second flux state based on the output of the single flux quantum SFQ circuit.

In some implementations, a capacitance of the capacitor is between 10fF to 100fF.

In some implementations, an area occupied by the SQUID loop is between <NUM><NUM> to <NUM><NUM>.

In some implementations, the flux qubit is arranged such that, in response to the first value of the second flux bias, a potential barrier is formed between the first flux state and the second flux state such that the tunneling between the first flux state and the second flux state is reduced.

In some implementations, the flux qubit is arranged such that, in response to the second value of the first flux bias, the difference in the energies of the first flux state and the second flux state is generated.

In some implementations, the flux bias generator includes a current source configured to generate a current and a transducer arranged to convert the current into a magnetic field. The transducer is arranged such that the first flux bias and the second flux bias are provided by the magnetic field.

In some implementations, the transducer includes a first coil to generate the first flux bias and a second coil to generate the second flux bias.

In some implementations, the inductor includes a first gradiometric coil and the first coil comprises a second gradiometric coil, and the first gradiometric coil and the second gradiometric coil are configured such that the first flux bias is mainly coupled to the inductor and a coupling of the second flux bias from the second coil to the inductor is reduced.

Another innovative aspect of the subject matter of the present disclosure is embodied in a method of reading out a state of a data qubit, including providing a flux qubit including an inductor, a SQUID loop comprising at least one Josephson junction and a capacitor. The inductor, the at least one Josephson junction and the capacitor are connected to each other in parallel, and the flux qubit is arranged to exhibit a first flux state and a second flux state. The method further includes applying a first value of a first flux bias through the flux qubit, such that the energies of the first and the second flux states of the flux qubits are substantially identical, applying a first value of a second flux bias through the SQUID loop, such that a barrier between the first flux state and the second flux state is minimized and a resonance frequency of the flux qubit is tuned to a frequency of interaction, tuning a resonance frequency of the data qubit to the frequency of interaction such that the flux qubit is coupled to the data qubit and the state of the data qubit is mapped to an energy state of the flux qubit, applying a second value of the first flux bias, such that the energies of the first and the second flux states of the flux qubits are different and applying a second value of the second flux bias, such that the flux qubit is decoupled from the qubit and the energy state of the flux qubit is mapped to a superposition of the first flux state or the second flux state; determining whether the flux qubit is in the first flux state or the second flux state; and outputting a signal in dependence on whether the flux qubit is in the first flux state or the second flux state.

In some implementations, a first time interval between generating the first value of the second flux bias and generating the second value of the second flux bias is determined based on a degree of interaction such that the state of the qubit is entirely mapped to the flux qubit.

In some implementations, the method further includes providing a data qubit and a measurement qubit for measuring a state of the data qubit, exciting the data qubit into an excited state, biasing the measurement qubit into a single well potential energy configuration, tuning the measurement qubit so that a photon from the excited state of the data qubit is transferred to the measurement qubit, biasing the measurement qubit containing the transferred photon into a double well potential energy configuration and raising a potential barrier between a first well and a second well of the double well potential energy configuration. Either the first well or the second well comprises the transferred photon. The raised potential well prevents leakage of the transferred photon into an adjacent well of the double well potential energy configuration.

In some implementations, tuning the measurement qubit so that the photon from the excited state of the data qubit is transferred to the measurement qubit includes tuning the measurement qubit to be in resonance with the data qubit in the excited state.

In some implementations, biasing the measurement qubit containing the transferred photon into the double well potential energy configuration includes tilting a potential energy curve of the measurement qubit so that energy states of the measurement qubit containing the transferred photon are mapped to the first well and the second well of the double well potential energy configuration.

In some implementations, the method further includes reading out energy states of the measurement qubit.

In some implementations, reading out the energy states of the measurement qubit includes applying microwave reflectometry to the measurement qubit.

In some implementations, reading out the energy states of the measurement qubit includes reading out a flux difference between a first energy state and a second energy state of the measurement qubit.

In some implementations, reading out the flux difference is performed using a single flux quantum (SFQ) to measure the flux difference.

In some implementations, the data qubit is a transmon qubit.

In some implementations, the measurement qubit is a flux qubit.

In some implementations, the data qubit is on a first substrate and the measurement qubit is on a second substrate that is bonded to the first substrate.

Another non-claimed aspect of the subject matter of the present disclosure may be embodied in a method including performing a quantum computing operation with a qubit to place the qubit into a first excited state of two energy states within a single well potential energy configuration, biasing the qubit so that the two energy states are mapped to two wells, respectively, of a double well potential energy configuration, and raising a potential barrier between a first well and a second well of the double well potential energy configuration. The first excited state is mapped to either of the first well or the second well, and the raised potential well prevents leakage of the excited state into an adjacent well of the double well potential energy configuration.

The foregoing and other implementations can each optionally include one or more of the following features, alone or in combination.

In some implementations, the method includes determining the excited state of the qubit using microwave reflectometry.

In some implementations, the method includes determining the excited state of the qubit using a SFQ circuit.

In some implementations, an array for quantum computing with a quantum error correction algorithm is provided. The array includes a plurality of qubits, and a plurality of detectors according to aforementioned implementations of the detector for reading out a state of a qubit. The array is arranged such that each qubit has at least one detector as a nearest neighbor. The plurality of qubits act as data qubits and the plurality of detectors act as ancillary qubits according to a surface code quantum computing as the error correction. The flux qubit of each detector are ancillary qubits for the quantum error correction algorithm.

In some implementations, the plurality of qubits are disposed on a first substrate, and the plurality of the detectors are disposed on a second substrate. The flux qubits of the plurality of the detectors are coupled capacitively to the qubits via a vacuum gap formed between the first substrate and the second substrate.

In some implementations, the plurality of qubits are transmon qubits.

Another non-claimed aspect of the subject matter of the present disclosure may be embodied in a method including determining bias condition for a single well configuration and a double well configuration of a flux qubit such that the flux qubit is at an interaction frequency at the single well configuration. At the interaction frequency the flux qubit is resonant with a data qubit. The method further includes determining a first bias condition for the data qubit for the interaction frequency, determining a second bias condition for the data qubit for a frequency away from the interaction frequency, applying a microwave pulse to the data qubit to prepare a state and to tune into the interaction frequency and measuring the state of the flux qubit for reading out the state of the data qubit.

Quantum computing entails coherently processing quantum information stored in the quantum bits (qubits) of a quantum computer. Superconducting quantum computing is a promising implementation of solid-state quantum computing technology in which quantum information processing systems are formed, in part, from superconducting materials. To operate quantum information processing systems that employ solid-state quantum computing technology, such as superconducting qubits, the systems are maintained at extremely low temperatures, e.g., in the <NUM> of mK. The extreme cooling of the systems keeps superconducting materials below their critical temperature and helps avoid unwanted state transitions. To maintain such low temperatures, the quantum information processing systems may be operated within a cryostat, such as a dilution refrigerator.

In some cases, large-scale quantum computers may be implemented using transmon qubits or their variants. The transmon qubit includes a large capacitor shunting one or more Josephson junctions, which improves qubit insensitivity to charge noise and allows the qubit to exhibit a long coherence time. Furthermore, high accuracy single and two-logic gate operations have been demonstrated using transmon qubits. When the transmon qubits are used as data qubits for quantum computation operation, reading out the state of these qubits with high fidelity is an important part of the operation.

However, since the computational states of the transmon qubit cannot be distinguished through a single-shot flux or charge measurement, the states of the transmon qubit are measured based on the difference in energy and not based on a difference in flux or charge. Moreover, the energy difference between the two states of the transmon qubit is only one microwave photon. A microwave photon around <NUM> frequency, has only <NUM> meV of energy, and is too low to detect with conventional means. For this reason, a relatively complicated and indirect dispersive measurement scheme is typically employed: Travelling waves are sent into a resonator coupled to the qubit via a transmission line, and depending on the state of the transmon qubit, different degrees of phase shift or amplitude change are imparted on the travelling waves. This scheme requires special equipment with a relatively large volume within the cryostat and is known to cause non-idealities, which may compromise the fidelity of operations performed by the quantum computer, as will be discussed below.

An alternative strategy is to transfer the state of the transmon qubit into another qubit, a detector qubit, where flux or charge measurement is possible. This reduces the need for amplification of the small signal associated with trying to measure a change in the state and the need for sending in a relatively large amount of photons into the transmon qubit. The detector qubit can be dynamically tuned into and out of resonance with the transmon qubit such that the state of the transmon qubit is transferred on demand. This has been tested with a phase qubit as the detector qubit. However, a disadvantage of using a phase qubit as a detector qubit lies in its long dead time which precludes a fast operation, as will also be discussed in <FIG> below. Also, when the detection is performed with a phase qubit, the phase qubit state jumps from a shallow potential well to a deep potential well. This leads to emitting many tens of microwave photons, which can propagate to other parts of chip compromising the quantum coherence of the qubits. This will also be discussed in <FIG> below.

In order to address these issues, the present disclosure relates to using a flux qubit as a detector qubit and capacitively coupling the flux qubit to the transmon qubit, such that the state of the transmon qubit can be mapped to the flux qubit, and detected by the difference in a self-flux of the flux qubit. The level of self-flux of the flux qubit is large enough to be detected by a technology such as SFQ. Furthermore, the flux qubit does not emit any microwave photons.

<FIG> is a schematic that illustrates an exemplary embodiment of the dispersive measurement scheme for measuring the computational states of a transmon qubit <NUM>.

An input probe signal <NUM> is sent into a transmission line <NUM>. The input probe signal <NUM> is a travelling wave which may be one or more guided modes of the transmission line <NUM>. A frequency of the input probe signal <NUM> may be a microwave frequency at or near a resonance frequency of the transmon qubit <NUM> such that the transmon qubit <NUM> may be addressed by the input probe signal <NUM> either resonantly or dispersively.

The transmon qubit <NUM> may be coupled to the transmission line <NUM> via a readout resonator <NUM>. For example, the readout resonator <NUM> may be a quarter wave co-planar waveguide resonator within a superconducting layer on which the transmon qubit <NUM> and the transmission line <NUM> are fabricated. The input probe signal <NUM> sent into to the readout resonator <NUM> may acquire a phase shift and/or an amplitude change depending on the state of the transmon qubit <NUM>. The transmon qubit <NUM> is dispersively coupled to the readout resonator <NUM>. In other words, the resonance frequency of the transmon qubit <NUM> is detuned from the centre frequency of the readout resonator <NUM>. The transmon qubit <NUM> and the readout resonator <NUM> form so-called dressed cavity states in which the resonance frequency of the readout resonator <NUM> changes depending on the state of the transmon qubit <NUM>. Also the nonlinearity of the Josephson junction, therefore the impedance of the transmon qubit <NUM>, depends on the state of the transmon qubit <NUM>. Therefore, the transmission line <NUM> outputs a first output probe signal <NUM> if the transmon qubit <NUM> was in a first state <NUM>-<NUM> and the transmission line <NUM> outputs a second output probe signal <NUM> if the transmon qubit <NUM> was in a second state <NUM>-<NUM>. The state of the transmon qubit <NUM> may be inferred by whether the output signal is the first output probe signal <NUM> or the second output probe signal <NUM>.

Coupling to the environment via the readout resonator <NUM> leads to damping of the transmon qubit <NUM> or the reduction of radiative lifetime T1, which reduces the coherence of the transmon qubit <NUM>. This also places a limit on the measurement time of the transmon qubit <NUM> and presents a minimum required operation speed. Therefore, in addition to detuning the resonance of the readout resonator <NUM> from the resonance frequency of the transmon qubit <NUM>, a leakage rate, or a quality factor of the readout resonator <NUM> may be optimised such that it allows the necessary measurement speed while keeping the damping of the transmon qubit <NUM> at an acceptable rate.

To further isolate the transmon qubit <NUM> from the damping of the external circuit, a Purcell filter <NUM> may be also placed between the transmission line <NUM> and the transmon qubit <NUM>, for example, in series with the readout resonator <NUM>, on the output side of the readout resonator <NUM>. The Purcell filter <NUM> decouples the transmon qubit <NUM> from the external circuit over a frequency range including the resonance frequency of the transmon qubit <NUM> to suppress the damping of the transmon qubit <NUM>. The photons near the resonance frequency of the transmon qubit <NUM> can be prevented from being coupled to the external circuit. The Purcell filter may be implemented with, for example, a symmetric pair of quarter wave stubs connected to the ground.

Although a reasonably high accuracy, such as <NUM>% on a single transmon qubit <NUM>, was demonstrated with the dispersive measurement schemes as described in <FIG>, scaling such dispersive measurement scheme to a system with a large number of transmon qubits <NUM> may be complicated by several factors. For example, the dispersive measurement schemes as described in <FIG> may require a series of elements to amplify a weak signal, a quantum limited parametric amplifier, a low noise cryogenic amplifier such as a high electron mobility transistor (HEMT). The dispersive measurement schemes may further require a magnetically non-reciprocal element, such as a circulator, to isolate the transmon qubit <NUM> from the noise generated by these amplifiers. These elements may occupy a lot of the limited space of the milliKelvin stage of the cryostat and the heat generated by each element may add up to go beyond the cooling capacity of the cryostat. Moreover, if the output signals <NUM>, <NUM> are processed by demodulation electronics performing heterodyne detection and thresholding at room temperature, this may further require the implementation of low latency feedback conditioned on the measurement results.

Therefore, the dispersive measurement schemes as described in <FIG> may not be suitable in scaling the operation to a large number of transmon qubits <NUM>. Furthermore, although the signal-to-noise ratio of the dispersive measurements may improve with the intensity of the input probe signal <NUM>, it has been observed that too many photons sent into the readout resonator <NUM> lead to spurious qubit state transitions, which compromise the fidelity of operations.

As an alternative method, the dispersive measurement scheme as described in <FIG> may be somewhat simplified using a Josephson Photo-Multiplier (JPM) as a microwave photon counter at the output of the transmission line <NUM> to detect the output signals <NUM>, <NUM>. The Josephson Photo-Multiplier includes a single Josephson junction in an rf superconducting quantum interference device (SQUID) loop that is biased close to the critical flux where a phase slip occurs. The transmon qubit <NUM> may still be dispersively coupled to the readout resonator <NUM>. However, instead of using a circulator and multiple stages of amplifiers, a difference in the photon occupation of the readout resonator <NUM> may be detected by the Josephson Photo-Multiplier. The detection and discrimination of the states of the transmon qubit <NUM> may therefore be performed directly at the millikelvin stage of the cryostat by the Josephson photomultiplier. The single-shot measurement fidelity demonstrated to date using this scheme is <NUM>%.

These relatively complex dispersive measurement schemes have been used because a single photon detector in the microwave frequency range is difficult to implement. The states of the transmon qubit <NUM> have no difference in the first moment of their charge or flux wave functions and only differ in energy by a single microwave photon. There are differences in the higher moments of charge and flux, but those are known to be hard to measure to be feasible as a measurement scheme of the transmon qubit <NUM>.

<FIG> is a schematic that illustrates an exemplary measurement scheme in which a detector qubit <NUM> is used as a state detector of a data qubit <NUM>.

The data qubit <NUM> may be a superconducting qubit that is arranged to take part in the quantum computation with other data qubits <NUM>. The data qubit <NUM> may therefore be arranged to exhibit a level of nonlinearity required to perform the quantum computation and arranged to receive excitation microwave pulses and flux biases, as required for the quantum computation. For example, the data qubit <NUM> may be the transmon qubit <NUM>.

The data qubit <NUM> may be arranged to be coupled to the detector qubit <NUM> via a coupling element <NUM>.

The detector qubit <NUM> may be any one type of a superconducting qubit, which includes one or more Josephson junctions. For example, the detector qubit <NUM> may be a phase qubit or a flux qubit. The techniques for reading out a phase qubit or a flux qubit will be described later in <FIG> and <FIG>. Alternatively, the detector qubit <NUM> may comprise any other type of qubits, such as a microwave transition of a quantum dot, a diamond N-V centre, or a Rydberg atom, which can be resonant with the transition frequency of the data qubit <NUM>. Depending on the type of detector qubit <NUM>, any suitable technique may be used to read out the state of the detector qubit <NUM>. The detector qubit <NUM> may allow measurement of the energy states of the data qubit <NUM> based on the quantities such as flux, charge, or UV/visible/near IR photons.

The detector qubit <NUM> may be capable of being dynamically tuned into and out of resonance with the data qubit <NUM>. When the detector qubit <NUM> is tuned into or near the resonance of the data qubit <NUM>, the state of the data qubit <NUM>, or the photon of the data qubit <NUM>, may be able to be swapped with the state of the detector qubit <NUM>. In other words, the data qubit <NUM> and the detector qubit <NUM> may be coupled such that the interaction between the data qubit <NUM> and the detector qubit <NUM> may be in the form of a virtual photon or an exciton, which is a quantum of the excitation shared by the data qubit <NUM> or the detector qubit <NUM>. This is because the state of data qubit <NUM>, which may be the superposition of the ground state and the first excited state of the data qubit <NUM>, may exhibit quantum coherent oscillation between the data qubit <NUM> and the detector qubit <NUM>. For the rest of the specification, the word "photon being swapped" between the data qubit <NUM> and the detector qubit <NUM> will be understood in this context, namely that the photon may refer to any intermediary quanta of the interaction between the data qubit <NUM> and the detector qubit <NUM> and not be limited to an isolated quanta of propagating light. For example, the "photon being swapped" may also refer to the exciton or the virtual photon delocalized between the data qubit <NUM> and the detector qubit <NUM>. In this sense, the detector qubit <NUM> may act as a single photon detector of the data qubit <NUM>.

The coupling element <NUM> may comprise a capacitive coupling in which the data qubit <NUM> and the detector qubit <NUM> are coupled to each other capacitively. For example, the metallic parts of the data qubit <NUM> and the detector qubit <NUM> may be placed in close proximity to allow capacitive coupling. For another example, a capacitor may be placed in between the data qubit <NUM> and the detector qubit <NUM>. Alternatively, the coupling element <NUM> may comprise an inductive coupling in which the data qubit <NUM> and the detector qubit <NUM> are coupled to each other inductively. For example, the inductive parts of the data qubit <NUM>, such as loops or elongated parts, of the data qubit <NUM> and the detector qubit <NUM> may be positioned such that a magnetic flux generated by the data qubit <NUM> may generate a current in the detector qubit <NUM>, and vice versa. Alternatively, the coupling element <NUM> may comprise a combination of the inductive coupling and the capacitive coupling. Alternatively, the coupling element <NUM> may comprise a transmission line, such as a co-planar waveguide. Alternatively, the coupling element <NUM> may comprise a superconducting coupler qubit disposed between the data qubit <NUM> and the detector qubit <NUM>. In this case, the resonance frequencies of the data qubit <NUM> and the detector qubit <NUM> need not be tuned to come in and out of resonance with each other and only the superconducting qubit being used as the coupling element 210may be controlled to adjust the coupling between the data qubit <NUM> and the detector qubit <NUM>. Alternatively, the coupling measure <NUM> may comprise a Josephson junction parametric amplifier or Josephson junction parametric converter.

In order for the state of the transmon qubit <NUM> to be transferred to the detector qubit <NUM>, either the resonance frequency of the transmon qubit <NUM> or the resonance frequency of the detector qubit <NUM> may be tuned dynamically. In case the coupling measure <NUM> is another superconducting qubit, the coupling measure <NUM> may be tuned dynamically. The quantum states occupied in the data qubit <NUM> and the detector qubit <NUM> may be time-dependent and may exhibit quantum coherent oscillations. The time-dependence of the states may be determined by the degree of interaction between the data qubit <NUM> and the detector qubit <NUM>. By dynamically tuning in and out of mutual resonance, the state of the transmon qubit <NUM> may be mapped or transferred to the detector qubit <NUM>. The swapping of the photon may be performed either partially or wholly, depending on the duration of the interaction. The swapping of the state between the data qubit <NUM> and the detector qubit <NUM> may be performed within the coherence time of the data qubit <NUM> and the detector qubit <NUM>.

The concept of using another qubit as the detector qubit <NUM> has been tested with a phase qubit <NUM> as the detector qubit <NUM>.

<FIG> is a schematic that illustrates an exemplary measurement scheme in which the phase qubit <NUM> is used as the detector qubit <NUM> to detect the state of a transmon qubit <NUM> as the data qubit <NUM>, with references to <FIG>.

The transmon qubit <NUM>, used as the data qubit <NUM> in this example, may comprise a capacitor <NUM> and a SQUID loop <NUM> which contains a first Josephson junction <NUM>-<NUM> and a second Josephson junction <NUM>-<NUM>. <FIG> shows a schematic drawing of a potential curve <NUM> of the transmon qubit <NUM>, which specifies a ground state <NUM>-<NUM> and a first excited state <NUM>-<NUM> of the transmon qubit <NUM>. Due to the anharmonicity of the potential curve <NUM> or the nonlinearity of the transmon qubit <NUM>, the energy levels of the states are not equally spaced, and a microwave excitation resonant with the transition from the ground state <NUM>-<NUM> to the first excited state <NUM>-<NUM> may be largely off-resonant to the other transitions. Therefore, although there exists higher excited states, these two states <NUM>-<NUM>, <NUM>-<NUM> may be considered as a computational space of the transmon qubit <NUM>. The larger the nonlinearity of the transmon qubit <NUM> is, the larger the difference is between the frequency of the transition from the ground state <NUM>-<NUM> to the first excited state <NUM>-<NUM> and the frequency of the transition from the first excited state <NUM>-<NUM> to a second excited state, which is not shown in the potential curve <NUM>.

The phase qubit <NUM>, used as the detector qubit <NUM> in this example, may comprise a Josephson junction <NUM>, a capacitor <NUM>, and an inductor <NUM>. The inductor <NUM> may be inductively coupled to a line carrying a flux bias current. A potential curve <NUM>, <NUM>, <NUM> of the phase qubit <NUM> as a function of flux may comprise a double well structure. The wave functions may be narrowly confined in each well, as shown in the rightmost potential curve <NUM>. Since the bottom of each potential well can be approximated as a quadratic function, therefore a harmonic potential well, the energy spacing between the states near the bottom of the potential well may be largely equally spaced. Therefore, the anharmonic nature of the potential well is not pronounced and the phase qubit <NUM> may exhibit a substantially linear behavior. To recover the nonlinearity, a bias current or a flux bias may be applied to introduce asymmetry in the potential curve as shown in the leftmost potential curve <NUM> of the phase qubit <NUM>.

The leftmost potential curve <NUM> shows that a left potential well, circled and shown in detail in a potential curve <NUM>, is made shallow such that only a ground state <NUM>-<NUM> and a first excited state <NUM>-<NUM> can be confined within the left potential well. The computational space of the phase qubit <NUM> may be provided by the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> in the left potential well under this flux bias condition.

For the measurement of the state of the phase qubit <NUM>, a short bias pulse may be provided to momentarily lower the height of the barrier between the left well and the right well. As indicated by an arrow in the potential curve <NUM>, this may allow the first excited state <NUM>-<NUM> to tunnel out of the shallow left well and fall into the deep right well but mainly prevent the ground state <NUM>-<NUM> from exiting the left well. Consequently, the barrier between the left well and the right well may be heightened again and the potential curve <NUM> may be brought back into a symmetric shape. Then the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> may be separated and trapped in the left well and the right well, respectively. In other words, the barrier between the left well and the right well may largely suppress tunneling between the two wells. Then the two flux states, corresponding to the wave functions narrowly confined in the left well and the right well, respectively, may be detected and distinguished by magnetic flux. The amount of the flux generated by the phase qubit <NUM> on each flux state will be referred to as "self-flux" in this specification. The self-flux of the phase qubit can be measured using devices such as a SQUID or a SFQ (Single Flux Quantum) circuitry.

The transmon qubit <NUM> may be coupled to the phase qubit <NUM> by a coupling element <NUM>. As discussed in <FIG>, the coupling element <NUM> may be any one of capacitive coupling, inductive coupling or combination of the capacitive coupling and the inductive coupling, a transmission line, a coupler superconducting qubit, a Josephson parametric converter or Josephson parametric amplifier. The transmon qubit <NUM>, as a result of the quantum computation in cooperation with other transmon qubits <NUM>, may carry a quantum state, which is a superposition state between the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM>. In order to detect the quantum state currently existing in the transmon qubit <NUM>, the phase qubit <NUM> may be tuned into resonance with the transmon qubit <NUM>. Alternatively, in order to detect the quantum state currently existing in the transmon qubit <NUM>, the transmon qubit <NUM> may be tuned into resonance with the phase qubit <NUM>. By being dynamically tuned in and out of resonance with the transmon qubit <NUM>, the photon of the transmon qubit <NUM> may be swapped into the phase qubit <NUM>. In other words, the phase qubit <NUM> may receive the quantum state onto the computational space of the phase qubit <NUM>, which is the shallow left well as shown in the potential curve <NUM>. In still other words, the superposition state of the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> of the transmon qubit <NUM> may be mapped onto a superposition state of the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> of the phase qubit <NUM>. As discussed above, by applying a flux bias pulse to lower the barrier between the left well and the right well, the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> of the phase qubit <NUM> may be separated into two different flux states, as shown in the rightmost potential curve <NUM>. The flux may be measured using devices such as a SQUID or a SFQ circuitry. Therefore, the phase qubit <NUM> may be used as a single photon detector or the state detector of the transmon qubit <NUM>. The quantum state was distinguished with <NUM>% accuracy with a very short pulse, roughly 10ns, to lower the barrier.

However, there are several disadvantages in using the phase qubit <NUM> as the detector qubit <NUM>. Once a single photon is swapped into the phase qubit <NUM>, in order to separate the two flux states <NUM>-<NUM>, <NUM>-<NUM>, the phase qubit <NUM> is biased so that the first excited state <NUM>-<NUM> has a higher probability than the ground state <NUM>-<NUM> of tunnelling out of the metastable, shallow left well. However, the tunnelling rate difference between the ground state <NUM>-<NUM> and the first excited states <NUM>-<NUM> is large enough only to provide ~<NUM>% maximum theoretical contrast. Furthermore, the decay of the tunnelled first excited state <NUM>-<NUM> to the bottom of the right well of the potential curve <NUM>, <NUM>, <NUM> is a dissipative process. Emission of energy during this process has been observed to drive neighbouring qubits into excited states, causing measurement crosstalk errors. The process of tunnelling into the right hand well also renders the phase qubit <NUM> lose the phase coherence due to the dissipative evolution of the wave function. Therefore, to be used again as the detector qubit <NUM>, the phase qubit <NUM> need to be reset such that the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> are reset in the left shallow well of the potential curve <NUM>, <NUM>, <NUM>. Practical reset times for the phase qubit <NUM> are known to be in the tens to hundreds of microseconds, which may be long compared to the coherence times of currently available transmon qubits <NUM>.

To address the issues of the dispersive detection scheme described in <FIG> and the issues in using the phase qubit <NUM> as the detector qubit <NUM> described in <FIG>, the present specification discloses using a flux qubit <NUM> as the detector qubit <NUM>, such that the state of the transmon qubit <NUM> can be mapped to the flux qubit <NUM> coupled to the transmon qubit, and detected by the difference in the self-flux of the flux qubit <NUM>.

<FIG> is a schematic that illustrates an exemplary measurement scheme in which the flux qubit <NUM> is used as the detector qubit <NUM> to detect the state of a transmon qubit <NUM> as the data qubit <NUM>, with references to <FIG> and <FIG>.

The transmon qubit <NUM>, used as the data qubit <NUM> in this example, may comprise a capacitor <NUM> and a SQUID loop <NUM> which contains a first Josephson junction <NUM>-<NUM> and a second Josephson junction <NUM>-<NUM>. <FIG> shows a schematic of a potential curve <NUM> of the transmon qubit <NUM>, which specifies a ground state <NUM>-<NUM> and a first excited state <NUM>-<NUM> of the transmon qubit <NUM>. Although there exists higher excited states, only these two states may be considered as a computational space of the transmon qubit <NUM> for the reasons discussed above in <FIG>.

The flux qubit <NUM>, used as the detector qubit <NUM> in this example, may comprise a SQUID loop <NUM> including a first Josephson junction <NUM>-<NUM> and a second Josephson junction <NUM>-<NUM> and an inductor <NUM>. Importantly, the flux qubit <NUM> is shunted with a capacitor <NUM>. The capacitance of the capacitor <NUM> may be set to be large enough such that it may behave like a transmon qubit under a certain range of flux bias. Although a larger capacitance of the capacitor <NUM> may increase the phase coherence of the flux qubit <NUM>, it may reduce the nonlinearity. A higher coherence prolongs the time window of interaction between the transmon qubit <NUM> and the flux qubit <NUM>. Since the flux qubit <NUM> is used as the detector qubit <NUM>, the capacitance may be set to lengthen the coherence time rather than keeping the nonlinearity in the range to be used as the data qubit <NUM>. In this case, the capacitance of the capacitor <NUM> may range from 10fF to 100fF. Alternatively, the capacitance of the capacitor <NUM> may be determined such that the flux qubit <NUM> may be used interchangeably between the data qubit <NUM> and the detector qubit <NUM>. In this case, the capacitance of the capacitor <NUM> may range from 1fF to 50fF.

The inductance of the inductor <NUM> may be determined to be as large as possible to minimize the effects of magnetic flux noise. However, there are practical constraints including the fact that a coil-wound inductor has self-resonances when the size of the inductor <NUM> is too large. Typically, this can be overcome by using additional Josephson junctions <NUM>-<NUM>, <NUM>-<NUM> to increase inductance without adding coil length.

A potential energy curve <NUM>, <NUM>, <NUM> of the flux qubit <NUM> as a function of flux may comprise a double well structure, which includes two wells separated by a potential barrier, in which each of the wells corresponds to a different discrete flux states, a left flux state <NUM>-<NUM> and a right flux state <NUM>-<NUM>. When the barrier between the two wells is high enough, the wave functions are narrowly confined in each well, as shown in the rightmost potential curve <NUM>. In other words, the barrier between the left well and the right well may be high enough to largely suppress tunneling of the left flux state <NUM>-<NUM> and the right flux state <NUM>-<NUM> between the two wells. For example, for a flux qubit <NUM> where the self-resonance of the inductor <NUM> and the capacitor <NUM> is around <NUM>, a barrier of 2meV may suppress the tunneling rate to <NUM>.

The two flux states <NUM>-<NUM>, <NUM>-<NUM> may be detected and distinguished by the magnetic flux generated by the flux qubit <NUM> depending on the flux state. As in the phase qubit <NUM>, the amount of the flux generated by the flux qubit <NUM> on each flux state <NUM>-<NUM>, <NUM>-<NUM> will be referred to also as "self-flux" in this specification. The difference in the self-flux between the left flux state <NUM>-<NUM> and the right flux state <NUM>-<NUM> may be as large as a single flux quantum. The self-flux of the flux qubit <NUM> can be measured using devices such as a SQUID or a SFQ circuitry or other equivalent devices capable of measuring the self-flux. The difference in the self-flux between the left flux state <NUM>-<NUM> and the right flux state <NUM>-<NUM> may slightly deviate from a single flux quantum or Φ<NUM>. This is because the parabolic potential of the inductor <NUM> may cause the double well to deviate from the ideal periodicity of the junction potential, which corresponds to a single flux quantum. In case superinductance is used for the inductor <NUM> or the SQUID <NUM> for the Josephson junctions <NUM>-<NUM>, <NUM>-<NUM>, these nonidealities may render the difference in the self-flux further deviate from the single flux quantum.

The shape of the potential energy curve can be controlled with a first flux bias threading through the whole circuit of the flux qubit <NUM> and a second flux bias threading through the SQUID loop <NUM> of the flux qubit <NUM>. By controlling these two flux biases separately and dynamically, mapping the state of the transmon qubit <NUM> to the flux qubit <NUM> and the subsequent measurement of the flux state of the flux qubit can be performed, as explained in more detail later.

By applying the first flux bias threading through the whole circuit of the flux qubit <NUM>, or mostly through the inductor <NUM> of the flux qubit <NUM>, the potential energy curve <NUM>, <NUM> of the flux qubit <NUM> can be "tilted," in other words, an asymmetry in energy is introduced between the two discrete flux states <NUM>-<NUM>, <NUM>-<NUM>. In the example shown in the potential energy curves <NUM>, <NUM>, the energy of the left flux state <NUM>-<NUM> is lower than the energy of the right flux state <NUM>-<NUM>.

Tilting of the potential energy curve <NUM>, <NUM> localizes the hybridized energy states <NUM>-<NUM>, <NUM>-<NUM> of the flux qubit <NUM> into the two flux states <NUM>-<NUM>, <NUM>-<NUM> of the flux qubit <NUM> corresponding to the states confined within the two wells. When the potential curve is not tilted, the two flux states of the flux qubit <NUM> both occupy a ground state of each well with a substantially identical energy. When the barrier height is finite, these two flux states <NUM>-<NUM>, <NUM>-<NUM> form two hybridized states <NUM>-<NUM>, <NUM>-<NUM> delocalized over the two wells, as shown in the potential curve <NUM>. The potential curve <NUM> corresponds to a case where the barrier between the two wells is minimized. Even if there is a finite barrier between the two wells, the hybridized states <NUM>-<NUM>, <NUM>-<NUM> will be also delocalized over the two wells via tunneling through the barrier. These two hybridized states form two different energy levels, a ground state <NUM>-<NUM> and a first excited state <NUM>-<NUM> as indicated in the potential curve <NUM>.

Without tilting, each of the energy state <NUM>-<NUM>, <NUM>-<NUM> will map into either the left flux state <NUM>-<NUM> or the right flux state <NUM>-<NUM> with an equal probability when the barrier is heightened. Therefore, the energy states <NUM>-<NUM>, <NUM>-<NUM> may not be distinguished based on the self-flux.

By applying the second flux bias threading through the SQUID loop <NUM> of the flux qubit <NUM>, the critical current of the Josephson junctions <NUM>-<NUM>, <NUM>-<NUM> can be controlled. This consequently changes the height of the potential barrier between the two flux states <NUM>-<NUM>, <NUM>-<NUM> and also changes the resonance frequency of the flux qubit <NUM>.

Due to tilting the potential energy curve <NUM>, <NUM>, <NUM> such that the left well has a lower energy than the right well, as the barrier height is adiabatically heightened, the ground state <NUM>-<NUM> will be guided into the left flux state <NUM>-<NUM> and the first excited state <NUM>-<NUM> will be guided into the right flux state <NUM>-<NUM>.

In particular, the area of the SQUID loop <NUM> of the flux qubit <NUM> may be arranged to be large enough such that the second flux bias, through the SQUID loop <NUM>, may be applied largely independent of the first flux bias. The area may be, for example, <NUM><NUM> to <NUM><NUM>. In some implementations, the area of the SQUID loop <NUM> may be around <NUM><NUM>. Although such a large area of the SQUID loop <NUM> may render the flux qubit <NUM> more sensitive to the flux noise or the stray capacitance, the capability of controlling the barrier height and the resonance frequency largely independent of the tilt of the potential may be important in using the flux qubit <NUM> as the detector qubit <NUM>, as will be explained below.

<FIG> shows a flow chart that illustrates a method of reading out a state of the transmon qubit <NUM> using the flux qubit <NUM> with references to <FIG>, <FIG> and <FIG>.

In step <NUM>, a first value of the first flux bias may be applied to the flux qubit <NUM> such that the potential energy curve <NUM>, <NUM>, <NUM> of the flux qubit <NUM> is largely symmetrical. At this state, the resonance frequency of the transmon qubit <NUM> may be far detuned from the resonance frequency of the flux qubit <NUM> such that the interaction between the transmon qubit <NUM> and the flux qubit <NUM> is not significant. For example, the resonance frequency of the transmon qubit <NUM> may be detuned from the resonance frequency of the flux qubit <NUM> by <NUM> or more.

In some cases, a second value of the second flux bias may be applied for this detuning condition, as will be explained in more detail in step <NUM>.

In step <NUM>, the transmon qubit <NUM> may be excited such that the state of the transmon qubit <NUM> is prepared.

In step <NUM>, a first value of the second flux bias may be applied to the flux qubit <NUM>. At the first value of the second flux bias, the barrier height is minimized as shown in the potential energy curve <NUM> and the flux qubit <NUM> is brought into an interaction frequency at which it will interact with the transmon qubit <NUM> and the state of the transmon qubit <NUM> will be mapped to the flux qubit <NUM>. At the first value of the second flux bias, the flux qubit <NUM> may be arranged to receive the photon from the transmon qubit <NUM> such that the quantum state can oscillate between the transmon qubit <NUM> and the flux qubit <NUM>. As discussed above, the second flux bias, applied through the SQUID loop <NUM>, controls the barrier height between the two wells and the resonance frequency of the flux qubit <NUM>. The phase coherence of the flux qubit <NUM> is maximized under this condition, which provides a time window for coherent interaction with the transmon qubit <NUM>. The T1 time of the flux qubit <NUM> may be around <NUM>. In step <NUM>, the first value of the first flux bias applied in step <NUM> may be maintained such that the potential energy curve <NUM>, <NUM>, <NUM> of the flux qubit <NUM> remains symmetrical.

In step <NUM>, the transmon qubit <NUM> may be tuned into resonance with the flux qubit <NUM>, to the interaction frequency, such that if the transmon qubit <NUM> is excited, the photon is swapped into the flux qubit <NUM>. A superposition state of the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> may be mapped into a superposition state of the ground state <NUM>-<NUM> and the first excited state <NUM>-<NUM> of the hybridized energy states of the flux qubit <NUM>.

In some implementations, steps <NUM> and <NUM> may be performed simultaneously.

In some implementations, if the transmon qubit <NUM> and the flux qubit <NUM> are tuned into resonance in step <NUM> by application of the first value of the second flux, step <NUM> may be omitted.

In case the transmon qubit <NUM> is excited in step <NUM> to have a state prepared within the transmon qubit <NUM>, steps <NUM> and <NUM> may be performed immediately following the excitation of the transmon qubit <NUM>.

In step <NUM>, a second value of the first flux bias may be applied to the flux qubit <NUM> such that the potential energy curves <NUM>, <NUM>, <NUM> are tilted. Then the energies of the first flux state <NUM>-<NUM> and the second flux state <NUM>-<NUM> may become different. As explained in <FIG>, this is such that the energy states <NUM>-<NUM>, <NUM>-<NUM> can be mapped into the left flux state <NUM>-<NUM> and the right flux state <NUM>-<NUM> as the barrier is adiabatically heightened in step <NUM>.

The first value of the second flux bias applied in step <NUM> may be maintained such that the height of the barrier remains minimized at this stage. In some implementations, steps <NUM> and <NUM> may be performed simultaneously. In some implementations, the second value of the first flux bias may be applied to the flux qubit <NUM> throughout the procedure such that the potential energy curve <NUM>, <NUM>, <NUM> of the flux qubit <NUM> is always tilted. This is on the condition that swapping of the state in steps <NUM> and <NUM> is not affected by the tilt of the potential energy curve <NUM>, <NUM>, <NUM> of the flux qubit <NUM>.

In step <NUM>, the second value of the second flux bias may be applied to the flux qubit <NUM> such that the barrier between the two wells are heightened to "lock in" the flux states <NUM>-<NUM>, <NUM>-<NUM> such that the tunneling between the left flux state <NUM>-<NUM> and the right flux state <NUM>-<NUM> may be substantially suppressed. As discussed above, in some implementations, the height of the barrier may be around 2meV. The transition from the first value to the second value of the second flux bias may be adiabatic, in other words, gradual to minimize the probability of the flux qubit changing state. The flux states <NUM>-<NUM>, <NUM>-<NUM> can be preserved in the wells for sufficient amount of time before measurements. By having a large barrier, the qubits will stay in their respective wells much longer without tunneling, removing the need to immediately measure like in some of the current systems.

The second value of the second flux bias may also bring the flux qubit <NUM> out of resonance with the transmon qubit <NUM> by tuning away from the interaction frequency. The measurements of the state of the flux qubit <NUM> may be made when the flux qubit <NUM> is far detuned from the transmon qubit <NUM>. The detuning may be, for example, by <NUM> or more.

When the microwave reflectometry is employed for state detection, the second value of the first flux bias applied in step <NUM> may be maintained to keep the potential energy curves <NUM>, <NUM>, <NUM> asymmetric, as will be discussed in more detail later.

The resonance frequency of the transmon qubit <NUM> may also be tuned away from the interaction frequency such that the interaction between the transmon qubit <NUM> and the flux qubit <NUM> is not significant.

A time interval between steps <NUM>, <NUM> for bringing the transmon qubit <NUM> and the flux qubit <NUM> into resonance and steps <NUM>, <NUM> for measuring the state from the flux qubit <NUM> may be determined in view of the quantum coherent oscillations between the transmon qubit <NUM> and the flux qubit <NUM> such that the flux qubit <NUM> is decoupled from the transmon qubit <NUM> at the moment when the mapping of the state of the transmon qubit <NUM> is complete. For example, in order to determine the time interval for maximum transfer efficiency between the transmon qubit <NUM> and the flux qubit <NUM>, the transmon qubit <NUM> may be excited to have a predetermined quantum state at step <NUM>. After the transmon qubit <NUM> and the flux qubit <NUM> are brought into resonance by performing steps <NUM> and <NUM>, a first time interval T may be introduced before steps <NUM> and <NUM> may be performed to measure the state transferred to the flux qubit <NUM>. These steps <NUM>, <NUM>, <NUM>, <NUM>, <NUM> can be repeated while varying the first time interval T. The duration of the first time interval T for maximizing the transfer efficiency between the transmon qubit <NUM> and the flux qubit <NUM> can be determined, which gives maximum detection probability at the flux qubit <NUM>. <FIG> shows a flow chart that illustrates a method of calibrating the flux qubit <NUM> for reading out a quantum state of the transmon qubit <NUM>, with references to <FIG> and <FIG>.

At step <NUM>, the first value of the second flux bias, a condition for a single well configuration, and the second value of the second flux bias, a condition for a double well configuration for locking up the flux states <NUM>-<NUM>, <NUM>-<NUM>, of the flux qubit <NUM> may be determined. The first value of the second flux bias may be determined such that the resonance frequency of the flux qubit is at the interaction frequency.

At step <NUM>, the bias condition of the transmon qubit <NUM> to bring the resonance frequency of the transmon qubit <NUM> to the interaction frequency may be determined.

At step <NUM>, the resonance frequency of the transmon qubit <NUM> may be tuned away from the interaction frequency and the resonance frequency away from the interaction frequency may be probed spectroscopically by sending in microwave pulses while sweeping the frequency of the pulses. The first value of the second flux bias is applied to the flux qubit <NUM> to lower the potential barrier such that once the transmon qubit <NUM> is brought into the interaction frequency, the photon can be swapped from the transmon qubit <NUM> into the flux qubit <NUM>.

The rest of the procedure relates to determining the time interval for maximum transfer efficiency between the transmon qubit <NUM> and the flux qubit <NUM>, which was discussed above.

At step <NUM>, microwave pulses may be sent into the transmon qubit <NUM> to prepare a quantum state within the transmon qubit <NUM>. This step may be performed at step <NUM> described above.

Shortly after sending in each pulse to prepare a quantum state in the transmon qubit <NUM>, in other words within a time scale much shorter than the coherence time of the transmon qubit <NUM>, the resonance frequency of the transmon qubit <NUM> may be tuned into the interaction frequency. This may be achieved by following steps <NUM> and <NUM> described above.

After the transmon qubit <NUM> and the flux qubit <NUM> are brought in to resonance, a first time interval T may be introduced.

During the first time interval T, the prepared quantum state of the transmon qubit <NUM> may be transferred, to the flux qubit <NUM>.

At step <NUM>, the state of the transmon qubit <NUM> may be read out by measuring the state of the flux qubit <NUM> by following steps <NUM> and <NUM> described above.

By repeating steps <NUM> and <NUM> while varying the first time interval T, the duration of the first time interval T for maximizing the transfer efficiency between the transmon qubit <NUM> and the flux qubit <NUM> can be determined. Therefore, the readout condition of the transmon qubit <NUM> may be established.

The step <NUM> and <NUM> may be performed within the coherence time of the transmon qubit <NUM> from the moment of the microwave pulse to prepare the quantum state. In other words, the first time interval T may be varied within the coherence time of the transmon qubit <NUM>.

In relation to measuring the state of the flux qubit <NUM>, there may be at least two ways, as explained below.

A microwave reflectometry may be used to discern the left flux state <NUM>-<NUM> and the right flux state <NUM>-<NUM>. The flux qubit <NUM> may be biased such that the left well and the right well behave like classical harmonic oscillators with different spacing of levels. For example, this may be achieved by adjusting the second flux bias such that each well becomes deep and the bottom of each well can be approximated as a harmonic potential and adjusting the first flux bias such that the asymmetry between the two wells are large enough to be detected by the difference in the spacings between the ground state and the first excited state of each well. Such frequency difference may be detected with microwave reflectometry, analogous to the dispersive scheme described in <FIG>. However, since a relatively large intensity of input probe signal <NUM> may be used to detect the frequency difference, amplifiers and circulators may not be necessary to detect ouput signals <NUM>, <NUM> may be necessary.

Alternatively, the self-flux of the flux qubit <NUM> may be directly measured. The magnetic flux of the left flux state <NUM>-<NUM> and the right flux state <NUM>-<NUM> may differ by a magnetic flux quantum, which may be detectable by SFQ (single flux quantum) circuitry or SQUID magnetometer. For example a QFP (quantum flux parametron) may be coupled to the flux qubit <NUM> and the SFQ pulse trains may be sent to the QFT to readout the QFP state, which provides the state readout of the flux qubit <NUM>.

<FIG> is a schematic that illustrates an exemplary embodiment of a flux bias generator <NUM>. The flux bias generator <NUM> comprises a current source <NUM> configured to generate a current and a transducer <NUM> arranged to convert the current into a magnetic field. The transducer <NUM> may be arranged to generate the first flux bias and the second flux bias within the range necessary to perform the methods described above in <FIG> and <FIG>.

<FIG> is a schematic that illustrates an exemplary embodiment of the transducer <NUM> in use with the flux qubit <NUM> with references to <FIG>.

As discussed in <FIG> above, the flux qubit <NUM> comprises an inductor <NUM>, a capacitor <NUM> and a SQUID loop <NUM> including a first Josephson junction <NUM>-<NUM> and a second Josephson junction <NUM>-<NUM>. As discussed above, since the flux qubit <NUM> includes a large shunt capacitance, in some implementations, the capacitor <NUM> is in the form of a paddle, which comprises a first capacitor pad <NUM>-<NUM> and a second capacitor pad <NUM>-<NUM> on each side of the SQUID loop <NUM>. When the capacitor <NUM>, <NUM>-<NUM>, <NUM>-<NUM> is in the form of a paddle, the capacitor may be increased by increasing the area of the paddle. The first capacitor pad <NUM>-<NUM> and the second capacitor pad <NUM>-<NUM> are respectively electrically connected to two terminals formed between the first Josephson junction <NUM>-<NUM> and the second Josephson junction <NUM>-<NUM> along the SQUID loop <NUM>. The first capacitor pad <NUM>-<NUM> and the second capacitor pad <NUM>-<NUM> are connected to the inductor <NUM> via a first wire <NUM>-<NUM> and a second wire <NUM>-<NUM>, respectively. A first end of the first wire <NUM>-<NUM> and the second wire <NUM>-<NUM> may stem from the SQUID loop on each side of the first Josephson junction <NUM>-<NUM>, the first wire <NUM>-<NUM> directly connected to the first capacitor pad <NUM>-<NUM> and the second wire <NUM> directly connected to the second capacitor pad <NUM>-<NUM>, respectively, via the SQUID loop <NUM>. A second end of the first wire <NUM>-<NUM> and the second wire <NUM>-<NUM> are electrically connected to the two terminals of the inductor <NUM>.

In some implementations, the inductor <NUM> may comprise a gradiometric coil. As shown in <FIG>, starting from the two terminals connected to the first wire <NUM>-<NUM> and the second wire <NUM>-<NUM>, the inductor <NUM> forms two loops next to each other such that when a current is flown into the inductor <NUM>, the magnetic fields generated at the two loops are in opposite directions to each other. Therefore, when a magnetic field is applied threading through the overall area of the inductor <NUM>, for example, for the second flux bias, the effect of the magnetic field through the two loops formed within the inductor <NUM> largely cancel each other. When magnetic fields of opposite directions are coupled into the two loops formed within the inductor <NUM>, the generation of inductive current may be efficient.

The transducer <NUM> includes a first coil <NUM>-<NUM> and a second coil <NUM>-<NUM>. As discussed above in <FIG>, the shape of the potential energy curve can be controlled with a first flux bias threading through the whole circuit of the flux qubit <NUM>, <NUM>, or mostly through the inductor <NUM>, <NUM> of the flux qubit <NUM>, <NUM> and a second flux bias threading through the SQUID loop <NUM>, <NUM> of the flux qubit <NUM>, <NUM>. By controlling these two flux biases separately and dynamically, mapping the state of the transmon qubit <NUM> to the flux qubit <NUM>, <NUM> and the subsequent measurement of the flux state of the flux qubit can be performed.

The first coil <NUM>-<NUM> is used for applying the first flux bias threading through the inductor <NUM> of the flux qubit <NUM>, such that the potential energy curve <NUM>, <NUM> of the flux qubit <NUM>, <NUM> can be "tilted," in other words, an asymmetry in energy is introduced between the two discrete flux states <NUM>-<NUM>, <NUM>-<NUM>.

When the inductor <NUM> of the flux qubit <NUM> is configured as a gradiometric coil as discussed above, the first coil <NUM>-<NUM> may be also configured as a gradiometric coil such that the magnetic flux from the first coil <NUM>-<NUM> is only efficiently coupled to the inductor <NUM> and less efficiently to the other parts of the flux qubit <NUM>, such as the SQUID loop <NUM>.

In some implementations, the first wire <NUM>-<NUM> and the second wire <NUM>-<NUM> may be arranged to cross, in other words, to be on top of each other at at least one position without being electrically connected to each other, such that parasitic coupling of the second flux bias from the second coil <NUM>-<NUM> into the inductor <NUM> is reduced. For example, <FIG> shows that the first wire <NUM>-<NUM> and the second wire <NUM>-<NUM> are arranged cross once between the SQUID loop <NUM> and the inductor <NUM>. However, the number of crossing between the first wire <NUM>-<NUM> and the second wire <NUM>-<NUM> is not limited to once.

The second coil <NUM>-<NUM> is used for applying the second flux bias threading through the SQUID loop <NUM>, <NUM> of the flux qubit <NUM>, <NUM>, by controlling the critical current of the Josephson junction <NUM>-<NUM>, <NUM>-<NUM>. This consequently changes the height of the potential barrier between the two flux states <NUM>-<NUM>, <NUM>-<NUM> and also changes the resonance frequency of the flux qubit <NUM>, <NUM>.

When the first flux bias is applied via the inductor in the form of a gradiometric coil, the second flux bias generated from the second coil <NUM>-<NUM> may not be coupled efficiently to the inductor <NUM> of the flux qubit <NUM>. Therefore, a high degree of independent control of the first flux bias and the second flux bias may be achieved.

Therefore, the magnetic fluxes through the whole circuit of the flux qubit <NUM> and the SQUID loop <NUM> may be controlled independently using the first coil <NUM>-<NUM> and the second coil <NUM>-<NUM>.

The example given in <FIG> is only one embodiment of the transducer <NUM>. Other designs of the transducer <NUM> may be used to generate the first flux bias and the second flux bias. In some implementations, the transducer <NUM> may be disposed on a substrate separate from the substrate containing the flux qubit <NUM>. For example, the transducer <NUM> may be disposed on a face of a substrate which can be approached to a face of the substrate containing the flux qubit <NUM>. The arrangement of the first coil <NUM>-<NUM> and the second coil <NUM>-<NUM> may be such that when the two substrates are laterally aligned, the first coil <NUM>-<NUM> and the second coil <NUM>-<NUM> can be brought to a close proximity to the inductor <NUM> and the SQUID loop <NUM>, respectively, such that the first flux bias and the second flux bias can be provided.

The flux qubit <NUM>, <NUM> shunted with a relatively large capacitor may be used as a single photon detector of the transmon qubit <NUM>. The flux qubit <NUM>, <NUM> may be used as a single photon detector of any other qubit if it can brought into the resonance with a potential energy curve defining energy levels comparable to that of the flux qubit <NUM> when the barrier height is minimized.

Since the flux qubit <NUM>, <NUM> allows a negligible error rate in detecting the two flux states <NUM>-<NUM>, <NUM>-<NUM>, measurement accuracy may be improved, which will provide a high fidelity of operation. The reset time or cycle time of the flux qubit <NUM>, <NUM> may be determined by the speed at which the barrier height is heightened in step <NUM>. The speed should be low enough to ensure adiabaticity of the process but high enough to allow a reasonable detection and operation speed.

The total footprint of the flux qubit <NUM>, <NUM> within a chip may be compatible with a two-dimensional grid of the transmon qubits <NUM>, <NUM>. The flux qubit <NUM>, <NUM> removes the need for parametric amplifier HEMT circulator and alleviates corresponding heat dissipation on chip. It may not suffer from the spurious transitions due to high photon number of the dispersive scheme described in <FIG>.

To implement a practical large-scale quantum computation involving a large number of qubits, the error rate of the qubits constituting the quantum computer should be below an acceptable threshold. A common scheme adopted for error correction is so-called a "surface code" quantum computer, which includes a two-dimensional array of data qubits and ancillary qubits, or measurement qubits, where nearest neighbors can be coupled to each other. The data qubits and ancillary qubits may form an interleaved grid of two sub-grids.

In the surface code, data qubits and ancillary qubits are entangled together using a sequence of physical qubit CNOT operations, with subsequent measurements of the entangled states providing a means for error correction and error detection. The ancillary qubits are not directly involved in the computation but are couplable to the data qubit for monitoring the state of the data qubit to detect, e.g., an error in the data qubit. In the surface code, a set of data qubits and ancillary qubits entangled in this way is used to define a logical qubit.

Also, a specific sequence of entangling operations, so-called a stabilizer, on pairs of a data qubit and an ancillary qubit may act as stabilizing the state of the data qubit in that it suppresses spurious flipping of the qubit state by a set of measurements. By repeatedly measuring the qubits within a logical qubit using a complete set of commuting stabilizers, the logical qubit collapses into a simultaneous and unique eigenstate of all the stabilizers. One can measure the stabilizers without perturbing the system of the logical qubit. A spurious flipping of the data qubit may be detected when the measurement outcomes change, this corresponds to one or more qubit errors, and the quantum state is projected by the measurements onto a different stabilizer eigenstate.

The number of physical qubits needed to define a logical qubit depends strongly on the error rate of the physical qubits and the arrangement of the ancillary qubits and the data qubits.

In some implementations, the transmon qubits <NUM>, <NUM> may be used as both data qubits and ancillary or measurement qubits in the surface code quantum computer. The flux qubit <NUM>, <NUM> described in this specification may be used to read out the state of the ancillary qubits after parity measurements done between the data qubits and the ancillary qubits.

In some implementations, the flux qubit <NUM>, <NUM> described herein may be used as ancillary qubits, or measurement qubits in the surface code quantum computer. While the ancillary qubits are measuring the parities of the data qubits, the ancillary qubits may be biased into "transmon mode" where the barrier height is minimized, for high coherence. After the parity measurement is done, the flux qubit can be biased into the "double well mode" so that their state can be easily read out using superconducting electronics. This implementation may be advantageous in that the scheme does not require any amplifiers or other microwave circuits to read out the ancillary qubits.

The two-dimensional array of the data qubits, the transmon qubits <NUM>, <NUM>, and the ancillary qubits, the flux qubits, <NUM>, <NUM>, may be implemented on the surface of a single substrate. Alternatively, the flux qubits and the transmon qubits may be disposed on two separate substrates <NUM>, <NUM>, and the faces of the two substrates can be brought into proximity such that the flux qubits can couple to the transmon qubits via, e.g., vacuum capacitance.

In some implementations, both the data qubits and the ancillary qubits can be flux qubits <NUM>, <NUM> described in this specification. During the coherent operations, all of the flux qubits <NUM>, <NUM> can be biased in to "transmon mode" where the barrier height is minimized. Then for state measurement of the ancillary qubits, the ancillary qubits can be biased in to "double well mode.

Implementations of the quantum subject matter and quantum operations described in this specification can be implemented in suitable quantum circuitry or, more generally, quantum computational systems, also referred to as quantum information processing systems, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. The terms "quantum computational systems" and "quantum information processing systems" may include, but are not limited to, quantum computers, quantum cryptography systems, topological quantum computers, or quantum simulators.

The terms quantum information and quantum data refer to information or data that is carried by, held or stored in quantum systems, where the smallest non-trivial system is a qubit, e.g., a system that defines the unit of quantum information. In some implementations the computational basis states are identified with the ground and first excited states, however it is understood that other setups where the computational states are identified with higher level excited states are possible. It is understood that quantum memories are devices that can store quantum data for a long time with high fidelity and efficiency, e.g., light-matter interfaces where light is used for transmission and matter for storing and preserving the quantum features of quantum data such as superposition or quantum coherence.

Quantum circuit elements (also referred to as quantum computing circuit elements) include circuit elements for performing quantum processing operations. That is, the quantum circuit elements are configured to make use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data in a non-deterministic manner. Certain quantum circuit elements, such as qubits, can be configured to represent and operate on information in more than one state simultaneously. Examples of superconducting quantum circuit elements include circuit elements such as quantum LC oscillators, qubits (e.g., flux qubits, phase qubits, or charge qubits), and superconducting quantum interference devices (SQUIDs) (e.g., RF-SQUID or DC-SQUID), among others.

In contrast, classical circuit elements generally process data in a deterministic manner. Classical circuit elements can be configured to collectively carry out instructions of a computer program by performing basic arithmetical, logical, and/or input/output operations on data, in which the data is represented in analog or digital form. In some implementations, classical circuit elements can be used to transmit data to and/or receive data from the quantum circuit elements through electrical or electromagnetic connections. Examples of classical circuit elements include circuit elements based on CMOS circuitry, rapid single flux quantum (RSFQ) devices, reciprocal quantum logic (RQL) devices and ERSFQ devices, which are an energy-efficient version of RSFQ that does not use bias resistors.

Fabrication of the quantum circuit elements and classical circuit elements described herein can entail the deposition of one or more materials, such as superconductors, dielectrics and/or metals. Depending on the selected material, these materials can be deposited using deposition processes such as chemical vapor deposition, physical vapor deposition (e.g., evaporation or sputtering), or epitaxial techniques, among other deposition processes. Processes for fabricating circuit elements described herein can entail the removal of one or more materials from a device during fabrication. Depending on the material to be removed, the removal process can include, e.g., wet etching techniques, dry etching techniques, or lift-off processes. The materials forming the circuit elements described herein can be patterned using known lithographic techniques (e.g., photolithography or e-beam lithography).

During operation of a quantum computational system that uses superconducting quantum circuit elements and/or superconducting classical circuit elements, such as the circuit elements described herein, the superconducting circuit elements are cooled down within a cryostat to temperatures that allow a superconductor material to exhibit superconducting properties. A superconductor (alternatively superconducting) material can be understood as material that exhibits superconducting properties at or below a superconducting critical temperature. Examples of superconducting material include aluminum (superconductive critical temperature of about <NUM> kelvin), indium (superconducting critical temperature of about <NUM> kelvin), NbTi (superconducting critical temperature of about <NUM> kelvin) and niobium (superconducting critical temperature of about <NUM> kelvin). Accordingly, superconducting structures, such as superconducting traces and superconducting ground planes, are formed from material that exhibits superconducting properties at or below a superconducting critical temperature.

Claim 1:
A detector (<NUM>) for reading out a state of a qubit (<NUM>), the detector comprising:
a flux qubit (<NUM>);
a flux bias generator (<NUM>),
wherein the flux qubit comprises:
an inductor (<NUM>);
a SQUID loop (<NUM>) comprising at least one Josephson junction (<NUM>-<NUM>); and
a capacitor (<NUM>),
wherein the inductor, the at least one Josephson junction and the capacitor are connected to each other in parallel,
wherein the flux qubit is arranged to exhibit a first flux state (<NUM>-<NUM>) and a second flux state (<NUM>-<NUM>),
wherein the flux bias generator is configured to generate a first flux bias through the inductor and a second flux bias through the SQUID loop,
wherein the flux qubit is configured such that, in response to a first value of the first flux bias, the energies of the first and the second flux states are substantially identical and such that, in response to a second value of the first flux bias, the energies of the first and the second flux states are different, and
wherein, in response to a first value of the second flux bias, the flux qubit is configured to be coupled to the qubit and, in response to a second value of the second flux bias, to be decoupled from the qubit and to suppress tunneling between the first and the second flux states; and
a measurement unit, wherein the measurement unit is configured to determine whether the flux qubit is in the first flux state or the second flux state and to output a signal in dependence on whether the flux qubit is in the first flux state or in the second flux state.