Microwave-based reset of persistent current qubits

Abstract

A system and method are provided for resetting a qubit including a superconducting loop and a compound Josephson junction. A first bias magnetic flux is supplied to the superconducting loop. A second bias magnetic flux is supplied to the compound Josephson junction. Each of the first bias magnetic flux and the second bias magnetic flux is supplied such that a given excited state of the qubit is near the top of a potential barrier associated with the potential of the qubit. A continuous microwave signal having a frequency equal to the transition frequency between the other excited state of the qubit and the given excited state is generated.

Description

Technical Field

[0001] The present invention relates to quantum systems, and more particularly, to microwave-based reset of persistent current qubits. (Government Interest) The present invention was made under a government contract. Accordingly, the United States government has certain rights in the invention as specified in that contract.

Background Art

[0002] Preparing a qubit in a well-defined initial state is one of the important requirements for quantum computing algorithms. In particular, for most quantum algorithms, it is assumed that a large number of high-fidelity ground state qubits are available to function as ancilla qubits in various operations. Current methods for preparing ground state persistent current qubits involve applying a large direct current (DC) magnetic flux shift to destabilize the excited state and waiting for it to decay to the ground state. Unfortunately, this requires a relatively high bandwidth magnetic flux bias line to apply the destabilizing pulse to the persistent current qubit. The addition of this high bandwidth control line to the circuit introduces broadband noise that causes decoherence.

Summary of the Invention

[0003] According to one example, an assembly includes a qubit that includes a superconducting loop interrupted by a composite Josephson junction. A first bias source supplies a first bias to the superconducting loop, and a second bias source supplies a second bias to the composite Josephson junction. Each of the first bias source and the second bias source is responsive to system control to select a first value for the first bias and a second value for the second bias such that each of the first value and the second value is selected such that a given excited state of the qubit is near the top of a potential barrier associated with the potential of the qubit. A microwave source generates a continuous microwave signal having a frequency equal to the transition frequency between another excited state of the qubit and the given excited state.

[0004] According to another example, a method for resetting a qubit that includes a superconducting loop and a composite Josephson junction is provided. A first bias magnetic flux is supplied to the superconducting loop. A second bias magnetic flux is supplied to the composite Josephson junction. Each of the first bias magnetic flux and the second bias magnetic flux is supplied such that a given excited state of the qubit is near the top of a potential barrier associated with the potential of the qubit. A continuous microwave signal having a frequency equal to the transition frequency between another excited state of the qubit and the given excited state is generated.

[0005] According to a further example, a method for resetting a flux qubit that includes a superconducting loop and a composite Josephson junction is provided. A first bias magnetic flux is supplied to the superconducting loop. A second bias magnetic flux is supplied to the composite Josephson junction. Each of the first bias magnetic flux and the second bias magnetic flux is supplied such that a second excited state of the flux qubit is near the top of a potential barrier associated with the potential of the qubit. A continuous microwave signal having a frequency equal to the transition frequency between a first excited state and the second excited state of the qubit is generated. BRIEF DESCRIPTION OF THE DRAWINGS

[0006]

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[0007] As used herein, the term "includes" means including but not limited to, and the term "including" means including but not limited to. The term "based on" means based at least in part on. Additionally, when the present disclosure or claims enumerate "a," "an," "a first," or "another" component, or equivalents thereof, it should be construed to include one or more such components, and does not necessarily require or exclude more than one such component. Ordinal terms such as "first" or "second" are generally arbitrary and do not imply a particular order, except when used to describe an excited state of a qubit or other quantum system. For example, the first excited state is the state of a qubit immediately above the ground state.

[0008] The systems and methods described herein provide microwave-based reset or initialization of persistent current qubits. The systems and methods shown herein use microwave tones that transition a persistent current qubit from an excited state through an intermediate state to a ground state. This microwave-based reset enables the use of only a DC flux bias line that is low-pass filtered for device tuning, and includes a narrowband microwave drive for reset, resulting in reduced noise and less decoherence.

[0009] FIG. 1 shows an example of a system 100 for resetting a persistent current qubit 110 to a ground state. The persistent current qubit 110 can be implemented, for example, as a flux qubit. The persistent current qubit 110 includes a superconducting loop 112 interrupted by a composite Josephson junction 114. In one implementation, the composite Josephson junction 114 is implemented as a direct current superconducting quantum interference device (DC SQUID). A first bias source 116 supplies a first bias to the superconducting loop, and a second bias source 118 supplies a second bias to the composite Josephson junction. In one implementation, each of the first bias source 116 and the second bias source 118 can supply flux. In one example, the qubit 110 can be tuned via the first and second bias sources 116 and 118 to take on a double-well potential that includes states within two potential wells where the energy states of the device are separated by a potential barrier. In this example, the first bias source 116 controls the symmetry of the two wells, i.e., the depth of the wells relative to each other, and the second bias source 118 controls the height of the potential barrier between the two wells.

[0010] Each of the first bias source 116 and the second bias source 118 is made to select a first value for the first bias source and a second value for the second bias source in response to the system control 120. In one implementation, the values of the first bias and the second bias can be selected from a range between 0 flux quanta and 1 flux quantum. The microwave source 122 generates a microwave signal having a frequency equal to the transition frequency between the excited state just above the ground state and the selected excited state of the qubit assembly in response to the system control 120.

[0011] When qubit reset is desired, the system control 120 can instruct the first bias source 116 and the second bias source 118 to select the values of the first and second biases to provide a multi-level quantum system within the potential well. In one example, the value of the second bias is set between three-fifths and four-fifths of a flux quantum during the reset process. In particular, the height of the potential barrier and the asymmetry between the wells can be tuned such that the ground state in one well is near the bottom of the well and the excited state is near the top of the potential barrier. "Near the top of the potential barrier" means that the excited state has a significant probability amplitude in both wells of the potential. The microwave source 122 can then be instructed to generate a microwave signal at a frequency equal to the transition frequency between the excited state just above the ground state and the selected excited state. This has the effect of moving the population of the excited state just above the ground state to the selected excited state. From there, the population relaxes back to the excited state just above the ground state so as to transition back to the selected excited state by microwave excitation or relaxes to the ground state. By maintaining the excitation for a sufficient time, any level of population can be forced to the ground state, which varies depending on the desired fidelity of the reset to the ground state. In one example, the time is predetermined as a function of the relaxation time from the selected excited state to the ground state.

[0012] Generally, the selected excited state is an excited state near the top of the potential barrier, but it will be understood that a multi-step approach can be used in which a first microwave signal is applied to excite the occupancy state of the excited state just above the ground state to the first selected excited state, and a second microwave signal is used to excite the occupancy state of the first selected excited state to a second excited state. In this case, the first microwave signal can have a first frequency equal to the transition frequency between the excited state just above the ground state and the first selected excited state, and the second microwave signal can have a second frequency equal to the transition frequency between the first selected excited state and the second selected excited state. Further, the selected excited state need not necessarily be a state immediately higher than the excited state just above the ground state, and it will be understood that the microwave signals can be selected such that the occupancy state is excited to a state at a level two or more higher than the excited state just above the ground state.

[0013] FIG. 2 shows an example of a persistent current qubit 200, specifically a flux qubit, that can be reset using a microwave-based reset process. The qubit 200 includes a superconducting loop 202 interrupted by a first Josephson junction 204, a second Josephson junction 205, a first inductor 206, a second inductor 208, and a compound Josephson junction 210. A first flux source 212 that supplies flux to the compound Josephson junction 210 is provided with a first current source Φ α connected to a first inductor 214, and the flux generated in the inductor is a function of the magnitude of the current supplied to the first inductor. A second flux source 216 that supplies flux to the superconducting loop 202 is provided with a second current source Φ Δ connected to a second inductor 218, and the flux generated in the inductor is a function of the magnitude of the current supplied to the second inductor.

[0014] When resetting to the ground state of the flux qubit is desired, the two flux sources 212 and 216 can be adjusted to tune the qubit to generate a three-level quantum system. Specifically, the parameters of the critical current of the Josephson junctions in the composite Josephson junction 210 and the superconducting loop 202 are selected in the correct region, and when the second bias is set to have a value or magnitude of about seven-tenths of one flux quantum, the potential energy of the device has a double-well characteristic as seen in FIG. 3. In this bias configuration, the first flux source 212 tunes the height of the barrier between the two potential wells of the flux qubit 200, and the second flux source 216 tunes the asymmetry of the two potential wells of the flux qubit 200, effectively tilting the potential to one side so that one well is deeper than the other.

[0015] FIG. 3 is a chart 300 representing the potential 302 of the flux qubit 200, where energy is represented on the vertical axis 304 in gigahertz or, more precisely, in units of the product of h and the frequency represented in gigahertz, h being Planck's constant, and the phase of the qubit at the second Josephson junction 205 is represented on the horizontal axis 306. The chart shows the ground state, i.e., the lowest energy state |0>, the first excited state |1>, and the second excited state |2>. In reset, it is desirable to force the flux qubit to occupy only the lowest energy state |0>, so all occupancy states in the excited state |1> must be forced to transition between the wells. As can be seen from FIG. 3, there is a large potential barrier 308 between the two wells, which makes thermal transitions over the barrier very unlikely and the speed of quantum mechanical tunneling to the other well very low for the first excited state. However, when the flux sources 212 and 216 are properly tuned, the potential barrier separating the wave functions of the second excited state is significantly reduced, and thus the second excited state spreads between the two potential wells.

[0016] To complete the reset, the flux qubit 200 is given a transition frequency f from |1> to |2>12 A microwave signal resonating with 12 is provided from a microwave drive (not shown) to excite the occupancy state of |1> to |2>. From there, it can undergo Rabi oscillations and return to |1>, or decay to |0> through dissipation to the environment. While the drive is applied, all occupancy states that oscillate back to |1> are continuously driven to return to |2>, giving them a chance to decay to |0>. Since the transition frequency between the first excited state and the second excited state is different from the transition frequency f between the ground state and the second excited state 02 the microwave signal does not shift the occupancy state from |0> to |2>, and hf 02 ≫ k B T (where T is the temperature and k B is the Boltzmann constant), no re-occupation of |2> occurs due to thermal processes. After the microwave drive is applied over a sufficient interval, essentially all occupancy states in |1> transition to |0> through decay from |2>, and the qubit is reset to the ground state. It will be understood that the sufficient interval can be based on the known or estimated relaxation time for the second excited state.

[0017] Considering the above-described structural and functional features, the exemplary method will be better understood with reference to FIGS. 4 and 5. For the sake of simplicity, the exemplary methods of FIGS. 4 and 5 are shown and described as being executed sequentially, but in other examples, some operations may be performed multiple times and / or simultaneously in a different order than shown and described herein, so it should be understood and recognized that the present embodiment is not limited by the order shown. Further, not all of the described operations need to be performed to implement the method.

[0018] Figure 4 shows a method 400 for resetting a qubit that includes a superconducting loop and a composite Josephson junction. At 402, a first bias magnetic flux is supplied to the superconducting loop. At 404, a second bias magnetic flux is supplied to the composite Josephson junction. Each of the first bias magnetic flux and the second bias magnetic flux is supplied such that a given excited state of the qubit is near the top of a potential barrier associated with the qubit potential. In various implementations of flux qubits, it should be understood that there are practical limitations on the height of the barrier, and thus limitations on the range of excited states that can be selected as a given excited state. In one example, the first bias magnetic flux and the second bias magnetic flux are supplied such that other excited states below a given excited state have a probability amplitude split between a first well of the qubit potential and a second well of the qubit potential. The magnitude of the first bias magnetic flux can be selected such that the first well is deeper than the second well and other excited states are farther from the bottom of the first well than from the bottom of the second well. The magnitude of the second bias magnetic flux can be selected to tune the height of the barrier near a given excited state. In one example, the second bias magnetic flux is supplied with a magnitude between three-fifths and four-fifths of one flux quantum.

[0019] At 406, a continuous microwave signal having a frequency equal to the transition frequency between another excited state of the qubit and a given excited state is generated. This causes the occupancy state to transition from another excited state to the given excited state, from which it can relax to the ground state. For this purpose, the continuous microwave signal can be generated over a predetermined time, which is a function of the relaxation time of the qubit from a given excited state to the ground state. In one example, there is an intermediate excited state between the given excited state and another excited state, and the occupancy state is excited by two or more states. In another example, a second continuous microwave signal having a second frequency equal to the transition frequency between the excited state just above the ground state of the qubit and another excited state of the qubit is used to transition the occupancy state from another excited state to the given excited state before and / or during the use of the first microwave signal, the occupancy state can be transitioned from the excited state just above the ground state of the qubit to another excited state.

[0020] FIG. 5 shows another method 500 for resetting a flux qubit including a superconducting loop and a composite Josephson junction. At 502, a first bias flux is supplied to the superconducting loop. At 504, a second bias flux is supplied to the composite Josephson junction. Each of the first bias flux and the second bias flux is supplied such that the second excited state of the flux qubit is near the top of the potential barrier associated with the potential of the flux qubit. In particular, the magnitude of each flux is selected to provide two asymmetric well potentials, and the occupancy state of the second excited state can move relatively freely between the two wells, while the occupancy state of the first excited state is split between the two wells. In one implementation, the second magnetic flux bias is supplied at a magnitude between three-fifths and four-fifths of one magnetic flux quantum.

[0021] At 506, a continuous microwave signal having a frequency equal to the transition frequency between the first excited state and the second excited state of the qubit is generated. This has the effect of transferring the occupancy state of the first excited state to the second excited state. From there, the occupancy state can relax back to the first excited state, from which it can be transferred back to the second excited state, or relax back to the ground state, and will remain in the ground state unless there is a thermal process. In one example, the continuous microwave signal is provided for a predetermined time that is a function of the relaxation time of the qubit from the second excited state to the ground state of the flux qubit.

[0022] In the foregoing description, specific details have been set forth in order to provide a thorough understanding of the exemplary implementations of the invention described in this disclosure. However, it will be apparent that various implementations may be practiced without these specific details. For example, circuits, systems, networks, processes, and other components may be shown as components in block diagram form in order not to obscure the exemplary implementations with unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the examples. The description of the exemplary implementations is provided to enable those skilled in the art to practice the examples of the invention, but it should be understood that various changes may be made in the function and configuration of the elements without departing from the spirit and scope of the invention. Accordingly, the invention is intended to embrace all such changes, modifications, and variations that fall within the scope of the appended claims.

Claims

Claim 1 An assembly comprising: a qubit including a superconducting loop interrupted by a compound Josephson junction; a first bias source for supplying a first bias to the superconducting loop; a second bias source for providing a second bias to the compound Josephson junction, wherein each of the first bias source and the second bias source is responsive to system control to select a first value for the first bias and a second value for the second bias, and each of the first value and the second value is selected such that a given excited state of the qubit is near the top of a potential barrier related to the potential of the qubit, the second bias source; a microwave source for generating a continuous microwave signal having a frequency equal to the transition frequency between the other excited state of the qubit and the given excited state. Claim 2 The assembly of claim 1, wherein the first value and the second value are selected such that the other excited state has an occupancy state divided between a first well of the potential of the qubit and a second well of the potential of the qubit. Claim 3 The assembly of claim 2, wherein the first value is selected such that the first well is deeper than the second well and the other excited state is farther from the bottom of the first well than from the bottom of the second well. Claim 4 The assembly of claim 1, wherein the first bias and the second bias are each supplied as magnetic flux, and the second value is selected to be between three fifths and four fifths of one magnetic flux quantum. Claim 5 The assembly of claim 1, wherein the microwave source provides the continuous microwave signal for a predetermined time responsive to the system control, and the predetermined time is a function of the relaxation time of the qubit from the given excited state to the ground state. Claim 6 The microwave source is a first microwave source, the frequency is a first frequency, the continuous microwave signal is a first continuous microwave signal, and the assembly further includes a second microwave source that generates a second continuous microwave signal having a second frequency equal to the transition frequency between the excited state immediately above the ground state of the qubit and the other excited state of the qubit. The assembly according to claim 1.

7. The assembly according to claim 1, wherein an intermediate excited state is between the given excited state and the other excited state.

8. The assembly according to claim 1, wherein the qubit is a flux qubit.

9. The assembly according to claim 1, wherein the given excited state is the second excited state of the qubit and the other excited state is the first excited state of the qubit.

10. A method for resetting a qubit including a superconducting loop and a composite Josephson junction, comprising: supplying a first bias magnetic flux to the superconducting loop; supplying a second bias magnetic flux to the composite Josephson junction, wherein each of the first bias magnetic flux and the second bias magnetic flux is supplied such that a given excited state of the qubit is near the top of a potential barrier related to the potential of the qubit. The step of supplying the second bias magnetic flux; generating a continuous microwave signal having a frequency equal to the transition frequency between the other excited state and the given excited state of the qubit. A method comprising.

11. The method according to claim 10, wherein the first bias magnetic flux and the second bias magnetic flux are supplied such that the other excited state has a probability amplitude split between a first well of the potential of the qubit and a second well of the potential of the qubit.

12. The method according to claim 11, wherein the magnitude of the first bias magnetic flux is selected such that the first well is deeper than the second well and the other excited state is farther from the bottom of the first well than from the bottom of the second well.

13. The method according to claim 10, wherein an intermediate excited state is between the given excited state and the other excited state.

14. The frequency is a first frequency, the continuous microwave signal is a first continuous microwave signal, and the method further includes generating a second continuous microwave signal having a second frequency equal to a transition frequency between an excited state immediately above the ground state of the qubit and the other excited state of the qubit. The method according to claim 10.

15. The method according to claim 10, wherein the second bias magnetic flux is supplied with a magnitude between three-fifths and four-fifths of one magnetic flux quantum.

16. The step of generating the continuous microwave signal having a frequency equal to a transition frequency between the other excited state of the qubit and the given excited state includes generating the continuous microwave signal over a predetermined time, and the predetermined time is a function of a relaxation time of the qubit from the given excited state to the ground state. The method according to claim 10.

17. The method according to claim 10, wherein the given excited state is a second excited state of the qubit, and the other excited state is a first excited state of the qubit.

18. A method for resetting a flux qubit including a superconducting loop and a composite Josephson junction, supplying a first bias magnetic flux to the superconducting loop; supplying a second bias magnetic flux to the composite Josephson junction, wherein each of the first bias magnetic flux and the second bias magnetic flux is supplied such that a second excited state of the flux qubit is near a top of a potential barrier related to a potential of the flux qubit. The step of supplying the second bias magnetic flux; generating a continuous microwave signal having a frequency equal to a transition frequency between a first excited state and a second excited state of the flux qubit. A method including.

19. The method according to claim 18, wherein the second bias magnetic flux is supplied with a magnitude between three-fifths and four-fifths of one magnetic flux quantum.

20. The step of generating the continuous microwave signal having a frequency equal to the transition frequency between the first excited state and the second excited state includes generating the continuous microwave signal over a predetermined time, the predetermined time being a function of the relaxation time of the flux qubit from the second excited state to the ground state of the flux qubit, the method of claim 18.

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