[0001] The present application claims priority from United Kingdom (GB) patent application no. 1011855.2 filed 14 July 2010, the entire contents of which are incorporated by reference.

[0002] The present invention relates to quantum interference devices, and in particular to vector magnetometers and read-out devices based on quantum interference devices.

[0003] Superconducting Quantum Interference Devices (SQUIDs) are well known as extremely sensitive vector magnetometers and read-out devices for superconducting quantum systems. A basic form of a SQUID 10 is shown schematically in Fig. 1 of the accompanying drawings and consists of a superconducting loop 11 interrupted by quantum tunnelling barriers 12, known as Josephson junctions (JJs). Due to the Josephson effect and

superconducting quantum interference, the current between points 13 and 13 at the onset of superconductivity is sensitive to the magnetic flux, Φ, through the loop, making a SQUID a sensitive magnetic flux-meter. This is described in T. Ryhanen, H. Seppa, R. Ilmoniemi, and J. Knutila, J.Low Temp. Phys., 16, 287-386, (1989) and the references therein. SQUIDs work in two regimes: "underdamped" and "overdamped".

[0004] Underdamped SQUIDs can be used for read-out of superconducting quantum states e.g. in quantum bits. However they have a number of disadvantages. First, to produce a readout the SQUID is switched into a voltage state, a process that strongly disturbs both the measured quantum circuit and the SQUID itself and shows hysteresis. Bursts of non- equilibrium quasiparticles are created with energies exceeding the superconductor gap, thus "poisoning" the measured circuit. Second, due to the AC Josephson effect, the voltage across the SQUID produces a microwave voltage pulse that can drive neighbouring quantum circuits into their excited states. Finally, the values of the current that switches the SQUID to the normal (non-superconducting) state are random and high fidelity measurements require up to about 10 ⁵ switching events.

[0005] Overdamped SQUIDs contain small electrical resistors shunting the Josephson junctions. This helps to avoid hysteresis, however the shunting resistors create Johnson- Nyquist thermal noise that limits the sensitivity of the SQUID.

[0006] Alternative methods using dispersive read-out schemes have also been explored, but these require expensive Radio-Frequency equipment. [0007] An unavoidable contribution to the noise level of a SQUID-based magnetometer is due to electromagnetic coupling of the magnetometer superconducting loop to the measuring circuit which includes measuring leads, amplifiers and current/voltage sources via mutual segments (wires) and/or mutual inductance. The coupling is unavoidable as it is required by the measuring mechanism.

[0008] An alternative to a SQUID is a hybrid interferometer known as an Andreev probe. A hybrid interferometer 20 is shown schematically in Fig. 2 of the accompanying drawings and consists of a normal (N) (non-superconducting) nanoscale conductor connected to a superconductor loop 22. Such a device is described in V T Petrashov, V N Antonov, P Delsing, and T Claeson, Phys Rev Letters, 74, 52685271 (1995). The physics of the sensitivity of hybrid interferometers to magnetic flux is different from that of SQUIDs. The normal-superconducting interfaces at points 23 and 24 play the role of mirrors reflecting electrons via an unusual mechanism first described by Andreev in A.F. Andreev, Zh. Eksp. Teor. Fiz. 46 1823 (1964) [Sov. Phys. JETP 19 1228 (1964)].

[0009] Quantum interference of Andreev reflected electrons results in high sensitivity to the magnetic flux Φ of electrical resistance of hybrid interferometers that can be measured using a simple, inexpensive measurement setup. The operating voltages applied to contacts 25, 26 are smaller than the superconducting gap, hence the measurements do not create non- equilibrium quasiparticles, thus not "poisoning" the measured circuit. No microwave voltage pulses are produced. However, when measuring leads are connected to contacts 25, 26, fluctuations in the measuring circuit, which includes measuring leads, amplifiers and current/voltage sources, are transferred to the superconducting loop through parasitic inductances M thus limiting the sensitivity of the device.

[0010] As shown in Fig. 3 of the accompanying drawings, extra current leads can be placed so that the corresponding superconducting phase difference between points 23, 24 can be controlled by the current between contacts 27 and 28. This converts the hybrid interferometer to a transistor 20' with the current across the interferometer (between contacts 25) controlled by bias current in the superconducting wire. Other parts in Figure 3 are the same as like numbered parts in Figure 2.

[0011] Further developments of these devices are described in V. T. Petrashov, K. G. Chua, K.M. Marshall, R. Sh. Shaikhaidarov, and J. T. Nicholls, Phys Rev Letters 95, 147001 (2005). As described therein, the interferometer structure is a symmetric structure to exclude parasitic potential differences, the critical current induced in the normal wires is zero and the length of the normal segment must be greater than the coherence length but less than the phase breaking length of electrons in the normal conductor. In this case the Johnson-Nyquist thermal noise in the normal conductor limits the sensitivity of the Andreev probe.

[0012] Francesco Giazotto, Joonas T. Peltonen, Matthias Mescke and Jukka P. Pekola, Nature Physics, Vol 6 April 2010 disclose a further development of this device, referred to as a SQUIPT (Superconducting Quantum Interference Proximity Transistor) and shown schematically in Figure 4 of the accompanying drawings. SQUIPT 30 comprises a superconducting loop 31 of aluminium interrupted by a normal metal (copper) section 32. Superconducting contacts 33, 34 are connected to the superconducting loop opposite the normal metal section. Superconducting electrodes 35, 36 are connected to the normal metal section 32 via a tunnelling barrier 37 of A10 _x . This device exhibits low flux noise and dissipation, but requires high voltages (i.e. higher than superdconducting gap) for readout which can cause quasi-particle poisoning. The device has an unavoidable contribution to the noise level resulting from electromagnetic coupling of the magnetometer superconducting loop via mutual segments (wires) and mutual inductance to the measuring circuit that includes measuring leads, amplifiers and current/voltage sources.

[0013] It is an aim of the invention to provide an improved quantum interference device, and in particular such a device that avoids quasi-particle poisoning and has low, preferably negligible back action and hence low, preferably negligible intrinsic noise level including 1/f (flicker) noise.

[0014] According to an embodiment of the present invention, there is provided a quantum interference device comprising:

a superconducting loop interrupted by a normal conducting segment; and

first and second normal conducting spurs connected to the normal conducting segment at the middle point to form a cross, wherein the first normal conducting spur is separated from the normal conducting segment by a tunnelling barrier.

[0015] The tunnelling barrier provided in an embodiment of the invention between one branch of the normal interferometer and the normal segment that interrupts the

superconducting loop has the effect of decoupling the normal part of the interferometer from the environment, leading to reductions of the Johnson-Nyquist thermal noise. The flux- sensitive superconducting loop is electromagnetically decoupled from the measuring circuit. Accordingly the invention can provide a device having negligible back action and noise level. [0016] According to a preferred embodiment of the invention, the quantum interference device further comprises a pair of superconducting leads connected to the second normal conducting spur at a second end thereof.

[0017] By using superconducting leads rather than normal leads to connect a branch of the interferometer to the environment, further reduction of the Johnson-Nyquist thermal noise is achieved.

[0018] According to a preferred embodiment of the invention, the normal conducting segment and the first normal conducting spur are formed in first and second layers and the tunnelling barrier is formed between the first and second layers.

[0019] According to a preferred embodiment of the invention the tunnelling barrier is formed by passivating a surface of the first normal conducting spur or the normal conducting segment. In other embodiments, the tunnelling barrier is formed by depositing a layer of another material on a surface of the first normal conducting spur or the normal conducting segment.

[0020] According to a preferred embodiment of the invention the interferometer branch and the second interferometer branch substantially overlap one another.

[0021] According to another aspect of the invention, there is provided a quantum

interference device comprising:

a superconducting loop interrupted by a normal conducting segment;

first and second normal conducting spurs connected to the normal conducting segment at the middle point to form a cross; and

a pair of superconducting leads connected to one of the normal conducting spurs at a second end thereof.

[0022] According to another aspect of the invention, there is provided a quantum

interference device comprising:

a superconducting loop interrupted by a normal conducting segment; and first and second normal conducting spurs connected to the normal conducting segment at the middle point to form a cross, wherein

the second normal conducting spur is folded back over the first normal conducting spur.

[0023] In an embodiment, an insulating spacer is provided between the first and second normal conducting spurs.

[0024] The present invention thereby provides a device where the superconducting loop interrupted by a normal conducting segment has only a single common point and no mutual segments and mutual inductance with the measuring circuit that includes measuring leads, amplifiers and current/voltage sources.

[0025] In preferred embodiments of all aspects of the invention, the normal conducting segment and spurs are formed of a normal material that can be passivated such as Magnesium or Antimony. Other normal materials that can be used include Bismuth, Antimony, alloys thereof, carbon nanotubes and Graphene.

[0026] Embodiments of the invention may further comprise a pair of superconducting current leads connected to the superconducting loop either side of the normal conducting segment so that the electrical conductance of the normal conducting spurs is controlled by a bias current between the pair of superconducting current leads.

[0027] In such an embodiment, the superconducting quantum interference device can be used as a superconducting quantum interference proximity transistor.

[0028] The present invention also provides a vector magnetometer including a quantum interference device as described above.

[0029] The present invention also provides a computer system including at least one qubit and a quantum interference device as described above acting as a readout device for the qubit.

[0030] In a quantum computing application, the device of the invention may be referred to as a non-demolition device, meaning that it does not destroy or contaminate the quantum state of the device being read out.

[0031] The present invention will be described further below with reference to exemplary embodiments and the accompanying drawings, in which:

[0032] Figures 1 to 4 are schematic diagrams of prior art quantum interference devices;

[0033] Figure 5 is a schematic diagram of a quantum interference device according to an embodiment of the invention;

[0034] Figure 6 is a schematic diagram of a quantum interference proximity transistor according to an embodiment of the invention;

[0035] Figure 7 is a schematic diagram of a quantum interference device according to an embodiment of the invention with an alternative arrangement of the branches of the interferometer;

[0036] Figure 8 is a schematic diagram of a qubit according to an embodiment of the invention;

[0037] Figure 9 is a schematic diagram of another quantum interference device according to an embodiment of the invention; [0038] Figure 10 is a schematic diagram of another quantum interference device according to an embodiment of the invention; and

[0039] Figure 11 is a graph of Power Spectral Density vs. frequency measured on an embodiment of the invention.

[0040] In the drawings, like parts are depicted by like reference numerals.

[0041] A quantum interference device (QID) 50 according to an embodiment of the invention is described below with reference to Figure 5, which is a schematic plan view of the device. QID 50 comprises a superconducting loop 51 interrupted by a normal segment 52 which connects to the superconducting loop 51 at junctions 53, 54. A two branch

interferometer 55 is connected to the normal segment 52. The two branches 55a, 55b are connected to the midpoint of the normal segment 52 to form a cross.

[0042] A first branch 55a of the interferometer includes a tunnelling barrier 56 separating the normal leads 57, 58 from the normal segment 52. A second branch 55b of the

interferometer comprises a normal spur 59 connecting to the normal segment 52 and superconducting leads 60, 61. When a current is passed across the interferometer 55, electrons are reflected from the normal superconducting interfaces 53, 54 (Andreev reflection). The flux through the superconducting loop 51 affects the phase difference between 53 and 54 and hence causes quantum interference between the electrons reflected by the two boundaries. Therefore the current I across the interferometer 55 is sensitive to the flux Φ.

[0043] QID 50 has an increased sensitivity to magnetic flux due to the introduction of the tunnelling barrier. The barrier sharpens V-flux dependence and decouples the normal part of interferometer from the environment. The latter leads to further reductions of the Johnson- Nyquist thermal noise. 1/f (flicker) noise is also reduced.

[0044] One of the branches 55a of the normal interferometer is decoupled from the environment by the tunnelling barrier 56. The other branch 55b is decoupled by the replacement of the current-potential leads connecting it to the environment with

superconducting material 60, 61. The superconducting leads 60, 61 act as reservoirs for the interferometer. This arrangement provides for a magnetic flux-dependent superconducting gap (tunnelling barrier 56) in the normal part of interferometer. As a result the Johnson- Nyquist thermal noise is strongly suppressed and the dependence of current through the interferometer on magnetic flux is much steeper than in the absence of the barrier.

Introduction of tunnelling barriers in both branches as well as replacement of both normal leads with superconductors is not advantageous since it leads to an increase in operating voltages thus strongly increasing back-action of the device. Threshold tunnelling voltage in a device with superconducting current leads is larger than in a device with normal current leads by the value of the superconducting gap in the lead. The superconducting gap is the gap between the ground state which allows for superconduction and the first excited state. It depends on the material. For Al the superconducting gap is about 0.1 meV meaning that a potential difference of at least 0.1 mV is required to excite electrons (charge - e) to the first excited state. For Nb, the superconducting gap is about 1 meV.

[0045] According to another embodiment of the invention, as shown in Figure 6, extra current leads 62, 63 are provided to convert the interferometer to a transistor. The electrical conductance across the interferometer is controlled by the bias current ¾ in the

superconducting wire. Other parts in this embodiment are the same as like-numbered parts in the embodiment of Figure 5 and are not described in detail.

[0046] In an embodiment of the invention, the parts of the device can be formed by known thin film deposition techniques, using masking layers patterned by lithographic techniques, e.g. e-beam lithography. The tunnelling barrier can be formed by the natural passivation of the material used for the normal conducting parts of the device. Alternatively, an additional layer of another material can be deposited. For example a normal part made of a semi-metal can be coated with a thin Al layer that oxides to form an insulating layer.

[0047] In an embodiment, the superconducting parts of an embodiment of the invention are formed of aluminium for operation at temperatures below 1 Kelvin. For operation at higher temperature, the superconducting part of an embodiment of the invention is formed of a superconductor with higher critical temperature, e.g. Niobium. Normal parts can be formed of passivating normal materials such as Magnesium or Antimony or a semimetal with low carrier concentration, such as Bismuth, Antimony, alloys thereof, Carbon nanotubes and Graphene. The use of a semi-metal has the effect that Johnson-Nyquist thermal noise is strongly reduced. The tunnelling junction between one branch of the interferometer and the normal segment can be formed by passivating the layer forming either the normal segment or the interferometer branch.

[0048] An alternative geometry of a quantum interference device according to an

embodiment of the invention is shown in Figure 7, which is a schematic perspective view. As can be seen, in the embodiment of Figure 7 the two branches 55a and 55b of interferometer 55' are stacked on top of each other so as to overlap, rather than being on opposite sides of the normal segment 52. An insulating spacer 64 separates the two branches of the

intereferometer. The insulating spacer is thicker than the tunnelling barrier. Superconducting leads 60, 61 similar to those of the embodiment of Fig. 5 are provided in the second interferometer branch.

[0049] Functionally, quantum interference device 50" is the same as the embodiment of Figure 5. Again, additional current leads can be provided to create a quantum interference proximity transistor as in the embodiment of Figure 6.

[0050] The folded geometry of the embodiment of Figure 7 minimises the mutual inductance between the measuring and superconducting circuits and so minimises the influence of fluctuations in the measurement device on the superconducting loop. In some embodiments, the mutual inductance can be eliminated entirely. Parasitic fluxes are avoided.

[0051] Figure 8, which is a schematic plan view, shows a flux qubit device 70 according to an embodiment of the invention. The qubit device is formed as a superconducting loop 71 interrupted by a number of Josephson junctions 72. Although four are shown in the Figure, more or fewer Josephson junctions 72 can be provided. Superconducting loop 51 interrupted by normal segment 52 and non-demolition interferometer 55 form the readout device.

Readout can be taken by measuring current or voltage between the ends of the two branches 55a, 55b of the interferometer 55.

[0052] Figure 9 is a schematic perspective view of a quantum interference device (QID) 80 according to another embodiment of the invention. QID 80 comprises a superconducting loop 81 interrupted by a normal segment 82 in electrical contact with the loop. Normal spurs 83, 84 contact the normal segment 82 at the middle point to form a cross. The cross-like geometry means that currents in orthogonal branches of the cross are independent: changes in one current do not lead to changes in the other. The two currents are orthogonal electric variables.

[0053] The other end of normal spur 84 is in electrical contact with normal measuring leads 85. Normal segment 82, normal spurs 83, 84 and normal measuring leads 85 can be made of a semimetal - such as Bismuth, Antimony, alloys thereof, or Graphene - with low carrier concentration. Carbon Nanotubes can also be used. The use of a semimetal strongly reduces the Johnson-Nyquist thermal noise.

[0054] A thin insulating spacer 86 overlaps normal segment 82, normal spurs 83, 84 and normal leads 85. Overlapping the insulating spacer 86 is a superconducting spur 87, which contacts normal spur 83 at one end and superconducting measuring leads 88 at the other. Spacer 86 has two functions. Firstly, it insulates superconducting spur 87 from normal spurs 83, 84 and normal segment 82. Secondly, it minimises the magnetic flux produced by measuring currents. Superconducting spur 87 has the function of decoupling of the normal segment and making the superconducting gap in the normal segment 82, induced by the proximity effect, to have a finite value when the superconducting phase difference between the ends 89 of the normal segment 82 is equal to π (180 ). These ends, which contact the superconducting loop 81 , function as superconducting mirrors for the interferometer.

[0055] In an embodiment it is desirable that the critical current induced in the normal wires is high. To ensure this, the length of the normal segment can be made less than the coherence length of the normal segment, ξκ. This is the opposite approach to the prior art.

[0056] Preliminary results show that this device has very promising figures of merit in a benchmark test for a flux measuring device: measurements with a superconducting flux quantum bit (qubit), which is known as an efficient noise spectrum analyser as described by R. J. Schoelkopf, A. A. Clerk, S. M. Girvin, K. W. Lehnert, M. H. Devoret in arXivxond- mat/0210247vl . The figure of merit of the device is the relaxation rate introduced by measuring device during the measurement process:

T ^_1 _r ~ 2 _TC M ² (I _p ) ² f/hZ, ((:1) where M is the mutual inductance between the qubit and the measuring device, I _p is the persistent current circulating in the qubit loop, f is the measuring frequency, h is Plank's constant and Z is the line impedance of the measuring device seen by the qubit. State-of-the- art measuring devices based on SQUIDs [A. Lupascu, S. Saito, T. Picot, P. C. de Groot, C. J. P. M. Harmans and J. E. Mooij, Nature Physics 3, 119-125 (2007)] have M>~10pH, so induce relaxation rates corresponding to qubit relaxation times up to τ _Γ =10 μβ. To satisfy criteria enumerated in the DiVincenzo check-list for quantum computing ( D.P. DiVincenzo,

Fortschr. Phys. 48 771 (2000)) the relaxation time must be improved at least by two orders of magnitude.

[0057] Measurements with the device of Figure 9 showed relaxation times larger than requested by the DiVincenzo criteria. This means that much faster magnetic measurements can be realised with much less time for averaging to achieve required signal-to-noise ratio. For example, the measuring time required to achieve high sensitivity of superconducting gyroscopes used in space applications can be reduced from about 1 week to less than 1 hour. Another figure of merit, namely the noise equivalent flux (NEF) or "flux sensitivity" defined

2 1 /2 1 /2

as NEF=< V _N '> ^J, V\dV/dG>\ 8V' where V _N is the voltage noise within the frequency band δν , Φ is the magnetic flux. In our preliminary measurements the NEF was limited by the preamplifier noise and was found to be better than 10 ^"5 Φο Hz ^{1 2} and should be substantially higher than the QID intrinsic NEF, Φο is the flux quantum. The measurement technique used with the device of Figure 9 can be much simpler than that of a SQUID. This means that these devices have potential to replace SQUIDs in most applications.

[0058] A variation of the device of Figure 9 is shown in Figure 10. This device 80 is essentially the same as device 80 of Figure 9 save for the addition of extra current leads 90 to convert the hybrid interferometer to a transistor. The electrical conductance across the interferometer is controlled by the bias current ¾ in the superconducting loop.

[0059] Figure 11 shows the results of real time dynamic measurements with an embodiment of the invention according to Figure 9 attached to a four junction qubit. The results demonstrate the absence of 1/f noise. Figure 11 plots power spectral density (PSD) in V ₂ /Hz v.s. frequency (F) in Hz. Both axes are logarithmic. Crosses denote measurement results. The dashed line shows the Lorentzian curve:

Using parameters for the measurements: A, average voltage = 0.43 x 10 ^"5 , Tup, average time in UP qubit metastable state = 2.20s, Tdn, average time in DOWN qubit metastable state = 16.13s. As can be seen, the noise becomes substantially independent of frequency at about 0.05 Hz.

[0060] Having described embodiments of the invention, it will be appreciated that the scope of the present invention is not limited by the above described embodiments but only by the terms of the appended claims.