A trapped ion system

Abstract

A trapped ion system (100) for quantum computing configured to encode a first qubit in first and second metastable hyperfine states of a barium ion (105). 5

Description

[0001] A TRAPPED ION SYSTEM

[0002] Technical Field

[0003] The present disclosure relates to a trapped ion system for quantum computing.

[0004] Background

[0005] A trapped ion system may be used to encode a qubit. A qubit is the fundamental unit of information used in quantum computing.

[0006] The qubit comprises a pair of atomic states, a first state and a second state and the qubit can exist as a superposition of these two states. The qubit is encoded with the first state and the second state through the trapped ion system. Encoding, in this context, refers to the process of setting the first state and the second state of the qubit.

[0007] Summary

[0008] It is desirable to provide an improved trapped ion system for use in quantum computing.

[0009] In a first aspect of the disclosure, there is provided a trapped ion system for quantum computing configured to encode a first qubit in first and second metastable hyperfine states of a barium ion.

[0010] Optionally, the trapped ion system comprising an ion trap configured to trap the barium ion.

[0011] Optionally, the trapped ion system comprising a vacuum chamber, the ion trap being within the vacuum chamber. Optionally, the trapped ion system comprising a barium ion source configured to provide the barium ion to the ion trap.

[0012] Optionally, the barium ion source comprises: a neutral atom source configured to provide a barium atom; an ionization device configured to ionize the barium atom, thereby providing the barium ion.

[0013] Optionally, the trapped ion system comprising: a qubit manipulation system configured to encode the first qubit in the first and second metastable hyperfine states of the barium ion by applying a first signal at a first frequency to the barium ion; wherein: the first frequency is associated with a qubit frequency of the first and second metastable hyperfine states.

[0014] Optionally, the first signal is applied using a current carrying antenna or a pair of Raman lasers.

[0015] Optionally, the trapped ion system comprising a magnetic field source configured to apply a magnetic field at approximately a field insensitive point of the qubit.

[0016] Optionally, the barium ion is an odd numbered isotope.

[0017] Optionally, wherein the first and second metastable hyperfine states of the barium ion comprise a D3 / 2 state or a D5 / 2 state.

[0018] Optionally, the barium ion is133Ba+.

[0019] Optionally, the first and second metastable hyperfine states of the barium ion comprise a D5 / 2 state.

[0020] Optionally, the first metastable hyperfine state comprises F=2, mF=+l and the second metastable hyperfine state comprises F=3, mF=+l; or the first metastable hyperfine state comprises F=2, mF+2 and the second metastable hyperfine state comprises F=3, mF=+2.

[0021] Optionally, the barium ion is135Ba+.

[0022] Optionally, the first and second metastable hyperfine states of the barium ion comprise a D5 / 2 state.

[0023] Optionally, the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=2, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; or the first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=3, mF=0; or the first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=4, mF=+l; or the first metastable hyperfine state comprises F=2, mF=+l and the second metastable hyperfine state comprises F=4, mF=+2; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=4, mF=-3; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=4, mF=-2; or the first metastable hyperfine state comprises F=3, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=3, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=3, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; or the first metastable hyperfine state comprises F=3, mF=0 and the second metastable hyperfine state comprises F=4, mF=+l.

[0024] Optionally, the barium ion137Ba+.

[0025] Optionally, wherein the first and second metastable hyperfine states of the barium ion comprise a D5 / 2 state.

[0026] Optionally, the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=2, mF=-l; or the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-3; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; or the first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=3, mF=0; or the first metastable hyperfine state comprises F=2, mF=+l and the second metastable hyperfine state comprises F=3, mF=+l; or the first metastable hyperfine state comprises F=2, mF=+2 and the second metastable hyperfine state comprises F=3, mF=+2; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=3, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=3, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; or the first metastable hyperfine state comprises F=3, mF=0 and the second metastable hyperfine state comprises F=4, mF=+l.

[0027] According to a second aspect of the disclosure, there is provided a quantum computer comprising the trapped ion system according to the first aspect of the disclosure.

[0028] It will be appreciated that the quantum computer of the second aspect may including providing and / or using features set out in the first aspect and can incorporate other features as described herein.

[0029] According to a third aspect of the disclosure, there is provided a method of encoding the first qubit in the first and second metastable hyperfine states of the barium ion using the trapped ion system of the first aspect of the disclosure.

[0030] Optionally, the method comprising: applying a magnetic field at approximately a field insensitive point of the qubit.

[0031] Optionally, the method comprising trapping the barium ion using an ion trap. Optionally, the method comprising preparing the barium ion in an initial state.

[0032] Optionally, the method comprising: encoding the first qubit in the first and second metastable hyperfine states of the barium ion by applying a first signal at a first frequency to the barium ion; wherein: the first frequency is associated with a qubit frequency of the first and second metastable hyperfine states.

[0033] It will be appreciated that the method of the third aspect may including providing and / or using features set out in the first aspect and / or the second aspect and can incorporate other features as described herein.

[0034] Description of the drawings

[0035] The disclosure is described in further detail below by way of example only and with reference to the accompanying drawings, in which:

[0036] Figure 1(a) is a schematic of a trapped ion system for quantum computing that uses barium ions according to the present disclosure, Figure 1(b) is a schematic of a specific embodiment of the trapped ion system of Figure 1(a);

[0037] Figure 2 is a table showing the pairs of metastable hyperfine states for a 133Ba+ion;

[0038] Figure 3 is a table showing the pairs of metastable hyperfine states for 135Ba+ion;

[0039] Figure 4 is a table showing the pairs of metastable hyperfine states for 137Ba+ion;

[0040] Figure 5 is a schematic showing how the trapped ion system of Figure 1(b) can be used to encode a qubit with a pair of states from the table in Figure 4; Figure 6 is a plot showing the spectator transitions for two pairs of metastable hyperfine states of 137Ba+ion;

[0041] Figure 7 a graph showing how qubit frequency varies with magnetic field for a qubit encoded with a pair of metastable hyperfine states for 137Ba+in the D5 / 2 manifold;

[0042] Figure 8 is a table of matrix transition elements for transitions from the F=2, mF=l metastable hyperfine state for 137Ba+ion;

[0043] Figure 9 is a schematic of a quantum computer comprising the trapped ion system, in accordance with a second embodiment of the present disclosure; and

[0044] Figure 10(a) is a graph showing the splitting of energy states for the D5 / 2 manifold of a 137Ba+ion, Figure 10(b) is a graph showing the splitting of energy states for only the F=1 and F=2 metastable states for D5 / 2 manifold of a 137Ba+ion.

[0045] Description

[0046] Trapped ion systems for quantum computing purposes, in general, comprise of an ion trap in a vacuum chamber, a voltage source coupled to the ion trap, a source of neutral atoms, a source of static magnetic field, a plurality of lasers and a fluorescence detector. The plurality of lasers serve a number of purposes, including the excitation and photoionisation of the neutral atoms into ions and trapping the ions in the ion trap.

[0047] The qubits are often encoded into the ground states of the ionised atom being used, for example a Calcium ion, as ground states are the most stable energy states and have a long life-time. When selecting atoms to be used as qubits for use in quantum computing the field-sensitivity of the energy state should also be considered. Qubits that are field-sensitive are inferior for storing quantum information as the encoded energy states of the qubit will change in response to fluctuations in the magnetic field being applied. Quantum information can be stored into states other than the ground state, and recent work has moved towards encoding the qubits into the long-lived metastable states, for example the D5 / 2 states. A metastable state is an energy state of an atom or ion which is of higher energy than the ground state. A metastable state has a sufficiently long lifetime for quantum computing.

[0048] The lifetime of a metastable state is much longer than the timescale on which quantum gates and other quantum operations (such as readout) occur. For example, for trapped ions, single quantum operations typically take approximately 100 microseconds. Therefore a metastable state has a lifetime longer than approximately 10 milliseconds.

[0049] Ground state and metastable Zeeman qubits have been studied in the dissertation by Chris Crocker titled: 'High Purity Single Photons Entangled with Barium Ions for Quantum Computing’. However, these Zeeman qubits cannot be made field-insensitive and hence acquire error (decohere) quickly, making them less suitable for storing quantum information.

[0050] Optical qubits have also been studied in the work of Dietrich et al. (2010) 'Hyperfine and Optical Barion Qubits’. In this case the qubit is encoded between two long-lived states (the ground state and a metastable state).

[0051] However, to use these optical qubits in a trapped ion system would require more demanding narrow-linewidth lasers which can be difficult to scale making them less adequate for quantum computing purposes. The same work also looked at ground state qubits with hyperfine structure. Hyperfine structure refers to the detailed splitting of energy levels for an atom caused by the interactions of the magnetic moments of the nucleus and the electrons in the atom. However, in the work of Dietrich et al. (2010), the ground state hyperfine barium ions being used as qubits exhibited large frequency splitting and an inability to sympathetically cool via another barium ion making them less suitable for use in quantum computing. The theoretical paper by I.D. Moore et. al. entitled “Photon scattering errors during simulated Raman transitions in trapped-ion qubits” considers the effect of certain laser operation on qubits, with examples relating to barium chosen for calculations. There is no discussion of practical considerations or any indication that such systems are suitable for quantum computing.

[0052] Figure 1(a) is a schematic of a trapped ion system 100 for quantum computing configured in accordance with a first embodiment of the present disclosure. The trapped ion system 100 is configured to encode a first qubit in first and second metastable hyperfine states of a barium ion 105.

[0053] Figure 1(b) is a schematic of a specific embodiment of the trapped ion system 100. The trapped ion system 100 may comprise one or more of an ion trap 110; a vacuum chamber 120; a barium ion source 130; a qubit manipulation system 140; and a magnetic field source 150a, 150b. The trapped ion system 100 may further comprises a fluorescence detector 160, electrodes 170 and a voltage source 180. The qubit manipulation system 140 may comprise a pair of antennas, not shown in Figure 1(b).

[0054] The trapped ion system 100 may further comprise a control unit 190. In operation, the control unit 190 receives a signal from the fluorescence detector 160 that includes information on one or more characteristics of the barium ion 105 as acquired by the fluorescence detector 160. The control unit 190 then provides a control signal to the voltage source 180 and to the qubit manipulation system 140 which controls the output of the voltage source. This control, for example, might be based on the measured characteristic, or characteristics.

[0055] The ion trap 110 is configured to trap the barium ion 105 and is situated within the vacuum chamber 120. The ion trap 110 comprises electrodes 170, which couple the ion trap 110 to the voltage source 180. The electrodes 170 in the example trapped ion system 100 of the present disclosure comprise two types of electrodes: RF electrodes and DC electrodes. It will be appreciated that in further embodiments, alternative electrodes and electrode configurations may be used, in accordance with the understanding of the skilled person.

[0056] The ion trap 110 is also coupled with the barium ion source 130 which is configured to provide the barium ion 105 to the ion trap 110. The barium ion source 130 comprises a neutral atom source to provide the neutral barium atom and an ionisation device configured to ionize the barium atom and hence provide the barium ion 105. The neutral atom source and ionisation device are not shown in the Figure. The neutral atom source could be, for example, a resistively heated atomic oven or an ablation target. The ionisation device could be, for example, a network of lasers of various operational wavelengths.

[0057] The qubit manipulation system 140 is configured to encode the first qubit in the first and second metastable hyperfine states of the barium ion 105 by applying a first signal at a first frequency to the barium ion 105. The first frequency is associated with a qubit frequency of the first and second metastable hyperfine states. The qubit frequency is defined as the most likely frequency for a photon emitted during the decay of the qubit to have.

[0058] For example, for an ion with two atomic states |0> and | 1> with respective energies Eo and Ei where Eo is of greater value than Ei, the qubit will have an energy: E = Eo - Ei. Therefore, the qubit frequency will be fq= E / h where h is Planck’s constant. The first signal can be applied, for example, by using a current carrying antenna or a pair of Raman lasers. In the present embodiment the qubit manipulation system 140 comprises a plurality of lasers. In the context of the present disclosure, a qubit is a unit of information that comprises a pair of atomic states, a first state and a second state. The qubit can exist as a superposition of these two states. Encoding the qubit refers to the process of setting the first state and the second state. In the present disclosure, the qubit is encoded with metastable hyperfine states of a barium ion 105. A metastable state of the barium ion 105 has higher energy than the ground state and has a long life-time before it will transition towards a more stable energy state. An example of a metastable state is the D5 / 2 state which has a life time of approximately 30 seconds. It will be appreciated that the life time may be less than approximately 30 seconds as a result of leakage light. Another example of a metastable state is the D3 / 2 state which has a lifetime of approximately 80 seconds.

[0059] A hyperfine state refers to an energy state with detailed splitting of the energy levels due to the interaction of the magnetic moments of the nucleus and the electrons in the barium ion 105. Details of the metastable hyperfine states for barium ions that can be used in the trapped ion system 100 are discussed further below.

[0060] The magnetic field source 150a, 150b may be positioned within the vacuum chamber 120 or outside the vacuum chamber 120, and is configured to apply a magnetic field to the ion trap 110.

[0061] The strength of the magnetic field applied is at approximately a field insensitive point for the chosen metastable hyperfine states of the barium ion 105 that is trapped within the ion trap 110.

[0062] The trapped ion system 100 encodes qubits with the metastable hyperfine states in barium ions for quantum computing uses. These states were chosen as they provided a number of properties which are required for an improved quantum computer. They have long atomic state lifetimes, low qubit frequencies, low magnetic field insensitivity, large matrix elements, low frequency crowding and low off-resonant shifts from spectator transitions.

[0063] In the trapped ion system 100, the barium ions that are preferred are odd numbered isotopes, such as 133Ba+, 135Ba+and 137Ba+. The qubits are encoded into one of the two metastable states in odd-isotope Ba+, D5 / 2 manifold. However, the qubits could also be encoded into the D3 / 2 metastable manifold. The notation used is the standard atomic physics Lj notation, where L represents the electron orbital angular momentum quantum number and J is the electron total angular momentum quantum number. For each electron orbital, a letter is assigned to represent that orbital. For example, L=0 is assigned the letter S. Therefore, D5 / 2 means L = 2 and J = 5 / 2 and D3 / 2 means L = 2 and J=3 / 2.

[0064] Figure 2 shows a table 200 listing the pairs of atomic states for 133Ba+barium ion, wherein the first state and the second state are the metastable hyperfine states of the ion of the D5 / 2 manifold. The qubits may be encoded inside metastable D5 / 2 manifold in 133Ba+Barium isotopes and therefore naturally have long atomic lifetimes and low qubit frequencies.

[0065] We use the notation where each state is described by its low-field good quantum numbers F, mF (F is the number for total angular momentum, and mF is the projection on the quantisation axis). In this table, “f2_pl” means “F=2, mF = +1”, while “fl_ml” means “F=l, mF= - 1” etc.

[0066] The states in table 200 are ones where the encoded qubits have first-order magnetic field sensitivity of df(B) / dB = 0, where f(B) is the qubit frequency which is field insensitive at B=B0 and B is the magnetic field. In other words, these are the metastable hyperfine states of 133Ba+that are field-insensitive to first order.

[0067] Table 200 only shows states where the microwave matrix element it at least 10% of the Bohr magneton. Encoding the qubit with any of the states from 200 will provide a qubit for quantum computing with improved information storage and performance.

[0068] Figure 3 shows a table 300 listing the pairs of atomic states for 135Ba+barium ion, wherein the first state and the second state are the metastable hyperfine states of the ion of the D5 / 2 manifold. The qubits are encoded inside metastable D5 / 2 manifold in 135Ba+Barium isotopes and therefore naturally have long atomic lifetimes and low qubit frequencies. The states in table 300 are ones where the encoded qubits have first-order magnetic field sensitivity of df / dB = 0. In other words, these are the metastable hyperfine states of 135Ba+that are field-insensitive to first order. Table 300 only shows states where the microwave matrix element it at least 10% of the Bohr magneton. Encoding the qubit with any of the states from 300 will provide a qubit for quantum computing with improved information storage and performance.

[0069] Figure 4 shows a table 400 listing the pairs of atomic states for 137Ba+barium ion, wherein the first state and the second state are the metastable hyperfine states of the ion of the D5 / 2 manifold. The qubits are encoded inside metastable D5 / 2 manifold in 137Ba+Barium isotopes and therefore naturally have long atomic lifetimes and low qubit frequencies. The states in table 400 are ones where the encoded qubits have first-order magnetic field sensitivity of df / dB = 0. In other words, these are the metastable hyperfine states of 137Ba+that are field-insensitive to first order. Table 400 only shows states where the microwave matrix element it at least 10% of the Bohr magneton. Encoding the qubit with any of the states from 400 will provide a qubit for quantum computing with improved information storage and performance.

[0070] The meaning of the data in table 400 is explained below (this applies to the tables 200 and 300). The states column lists a short-hand name for the different pairs of metastable hyperfine states. The way the state names should be read is that “f3_m3” stands for a D5 / 2 manifold state with F=3, mF=- 3, while “f2_pl” stands for D 5 / 2 manifold state F-l, mF - +1, using the standard atomic physics notation and low-field good quantum numbers F, mF. F represents the total angular momentum and mF is the projection of the angular momentum onto the quantisation axis.

[0071] The field-insensitive point column lists the magnetic field strength at which the qubit encoded with that pair of states should be operated at. It is desirable to operate at the field-insensitive point as this is the point where errors from time-varying magnetic fields are minimised.

[0072] It is desirable to select states having a larger matrix element than a smaller matrix element. The transition matrix element can also be referred to as the magnetic dipole matrix element or the Ml matrix element. This value represents the strength of the of the coupling between the qubit and the external electromagnetic field. If the matrix element has a large value, then the coupling is strong and the quantum gates are much faster. The matrix elements, Rij, are defined so that:

[0073] - R[ j] == C-ir*Cq+l)<i|u_q|j>

[0074] - q := Mi - Mj = (-1, 0, 1)

[0075] - u_q is the qth component of the magnetic dipole operator in spherical coordinates.

[0076] This method can be applied more broadly. For example, for optical qubits with quadrapole transitions, this calculation would involve calculating the quadrapole matrix elements.

[0077] It is desirable to select states having a smaller second-order sensitivity than a larger second order sensitivity.

[0078] The BSB pi, BSB sigma, RSB pi, RSB sigma columns give a measure of off- resonant shifts from spectator transitions - it is desirable to select states having smaller values, rather than larger values for these parameters. For example, assuming a sideband frequency of 3MHz, a value of BSB pi = x Hz / uTA2 means that applying a pi-polarised magnetic field detuned by +3 MHz from the qubit transition of magnitude y uT, the resultant off-resonant qubit frequency shift is given by x*y*y Hz.

[0079] Figure 5 is an alternative schematic of the trapped ion system 100 of Figure 1(b), illustrating how the system 100 can be used to encode a barium ion qubit. The same labels have been used for the same components of previous Figures for consistency. To aid in the clarity of the drawing, some components of the system 100 have been omitted from Figure 5.

[0080] The general steps are as follows. First, the magnetic field needs to be set to or near the field-insensitive point for the first metastable hyperfine state and the second metastable hyperfine state of choice for a given barium ion. This involves tuning the current 1_B on the magnetic field source 150a and 150b and measuring the magnetic field with the barium ion 105 acting as a sensor until it senses the correct magnetic field. The magnetic field source 150a and 150b could be, for example, a pair of coils. Then, the barium ion is encoded to the desired first metastable hyperfine state and the second metastable hyperfine state. Then the barium ion 105 is manipulated. One way to manipulate the barium ion is with current-carrying antenna 510, which can be integrated into the ion trap 110 or external to it. Specifically, gates can be performed by driving current oscillating near (within 10 MHz or so) the qubit frequency. Alternatively, a pair of Raman lasers 520a and 520b can be used. The Raman lasers can be delivered free-space to the ion, or via trap- integrated optics. Either way, quantum gates can be performed by using a pair of lasers offset by a frequency near (within 10 MHz or so) the qubit frequency. Quantum gates are the computational primitives of a quantum circuit. In other words, quantum computation is achieved by applying quantum gates on qubits and then reading them out. Quantum gates can be considered analogous to logic gates in classical computing, except quantum gates can act on qubits in superposition states and not just on classical bits with well-defined values. After the computation, the barium ion 105 can be read out to the fluorescence readout. As an example, consider using the trapped ion system 100 to encode a qubit with a first metastable hyperfine state comprising F=2, mF=-2 and a second metastable hyperfine state comprising F=3, mF=-2 of a 137Ba+ion in a D5 / 2 manifold. The data corresponding to this pair of states can be found on row 410 of table 400. First, the magnetic field source 150a and 150b is configured to set the magnetic field to the target value from the table, i.e. 20.048 Gauss. Afterwards, a 137Ba+ion is trapped and prepared in a well-defined initial state. This can be achieved through, for example, optical pumping. The initial state is usually the ground state, for example the S1 / 2 manifold comprising a state of F =2, mF=0. Afterwards, the qubit 530 can be initialised using a resonant quadrupole laser operating at 1762 nm, which transfers the population from the S1 / 2 manifold state comprising F=2, mF=0 to the D5 / 2 manifold comprising F=2, mF=2. Once the qubit 530 is initialised it is then encoded to the desired states F=2, mF=-2 and F=3, mF=-2. In this context, encoding the qubit refers to initialising the ion in a given state. For example, if a qubit is encoded as states A and B then the ion is initialised into either state A or state B. The ion is then manipulated throughout the quantum computation, such that it always remains in a subspace dictated by states A and B. In other words, the ion always remains either in state A, state B or a superposition of the two states. Therefore when qubit 530 is encoded to the states F=2, mF=-2 and F=3, mF=-2, the ion is being initialised into either the F=2, mF=-2 or the F=3, mF=-2 state before the quantum computation begins. Afterwards, the qubit 530 is manipulated. This can be achieved either by using near-resonant microwave radiation around 42 MHz, or using a pair of Raman beams with a frequency difference of around 42 MHz. After the qubit manipulation, the qubit 530 can be read out by transferring one of the qubit states to the ground state, for example by using a 1762nm laser as above, followed by standard fluorescence readout.

[0081] Figure 6 is a pair of graphs from simulation results showing the locations and strengths of the spectator transitions for a qubit encoded with a pair of metastable hyperfine states for 137Ba+in the D5 / 2 manifold. A spectator transition is any transition out of either of the qubit states. If the qubit transition has a near-overlap with a lot of spectator transitions then it is difficult to avoid driving the spectator transitions whilst driving the qubit which will result in errors. The plot 610 shows these spectator transitions for row 410 of table 400 which is a qubit encoded with a first metastable hyperfine state of F=2, mF=-2 and a second metastable hyperfine state of F=3, mF=-2. The plot 620 shows these spectator transitions for row 420 of table 400 which is a qubit encoded with a first metastable hyperfine state of F=2, mF=0 and a second metastable hyperfine state of F=3, mF=0. The bars show the values of the matrix elements in units of Bohr magnetron for other transitions out of either of the qubit states which are not the qubit frequency. The qubit frequency transition is denoted as a vertical black line. A transition labelled ‘pi’ is one which occurs between two levels with the same mF whereas a transition labelled ‘sigma’ is a transition which occurs between two levels with a difference in mF of 1. For example, a transition between a level with mF = +2 to mF = +1 would be considered a ‘sigma’ transition. The plots show that for the pairs of metastable hyperfine states of 137Ba+displayed there are not many spectator transitions crossing the qubit frequency transition and therefore any errors will be manageable.

[0082] Figure 7 is a graph showing how qubit frequency varies with magnetic field for a qubit encoded with a pair of metastable hyperfine states for 137Ba+in the D5 / 2 manifold shown in row 410 of table 400. In this plot, the qubit is encoded with a first metastable hyperfine state with F=2, mF=-2 and a second metastable hyperfine state with F=3, mF=-2. This shows the first and second-order sensitivity of such an encoded qubit measured experimentally and compared to the theoretical prediction. The qubit is found to be first- order field-insensitive at a magnetic field strength of 20.048 Gauss. The points on the graph are the experimental results obtained by scanning the magnetic field and measuring the qubit frequency using Rabi spectroscopy with a pair of 532 nm Raman lasers. The scanning of the magnetic field is achieved by changing the current in the coils. The theoretical prediction is shown with the solid curved line. The data matches the theoretical predictions used in the simulations up to a 3.5kHz offset. This offset is consistent with the value expected from the differential light shifts induced by the probing Raman lasers.

[0083] Figure 8 is a table 800 showing the transition matrix elements for a 137Ba+ion qubit for transitions from a state comprising F=2, mF=-l. These values were found by measuring the frequencies of the qubit transitions. The column labelled 'expected frequency’ represents the microwave matrix element from simulations. The 'measured frequency’ column represents the measured values from experimentation. To obtain the measured value, Rabi spectroscopy can be used. This is achieved by driving the qubit by passing oscillating signal through a free-standing coil outside the vacuum chamber. For the table 800 a free-standing coil with 5 turns, 35 mm diameter, 1 mm x 2 mm enameled Cu wire was used, there was no impedance matching, and the orientation of the field is assumed to be unknown.

[0084] The experiment sequence to get the measured values of table 800 is as follows:

[0085] 1. Prepare into F=2, mF=0 in Sl / 2 using pure n-polarised 493 light.

[0086] 2. 1762 pulse from F=2, mF=0 in Sl / 2 to F=2, mF=-l in D5 / 2.

[0087] 3. Microwave pulse to another state.

[0088] 4. 1762 pulse from F=2, mF=-l in D5 / 2 to F=2, mF=0 in Sl / 2.

[0089] 5. Readout.

[0090] The outcome of Rabi spectroscopy is the transition pi-time, which is inversely proportional to the matrix element. Thus, it is expected that for every transition with the same polarization, the product of the simulated matrix element and the measured pi-time to be identical. In practice there will be deviations because the polarisation and the strength of the microwave field will have a weak frequency dependence. From table 800, a comparison between the 'expected frequency’ and 'measured frequency’ shows that they are similar, and any deviations are consistent with known imperfections, such as AC Zeeman shifts. The last column is the product the simulated microwave matrix element and the measured pi time. So for example, the top three columns are all about pi-transitions, and for each of them, the product of the simulated matrix element and the measured pi time is about 30.

[0091] Figure 9 is a schematic of a quantum computer 900 comprising the trapped ion system 100, in accordance with a second embodiment of the present disclosure. It will be appreciated that the trapped ion system 100 may comprise any of the features as described herein in relation to the trapped ion system 100 in accordance with the understanding of the skilled person.

[0092] Figure 10(a) is a plot showing the splitting of the metastable hyperfine states for the D5 / 2 manifold of a Barium ion. Specifically, a 137Ba+ion. Each state is denoted with the low-field good quantum numbers F, where F represents the total angular momentum. For each F value there are multiple lines, representing the hyperfine splitting of the mF states where mF is the projection of the angular momentum on to the quantisation axis. Each line represents the transition frequencies and the solid points represent the clock points for 137Ba+.

[0093] Figure 10(b) is a plot showing the splitting of the metastable hyperfine F=1 and F=2 states for the D5 / 2 manifold of a 137Ba+ion. There is only one field insensitive qubit between the F=1 and F=2 states at approximately 15 Gauss. The qubit frequency for this field insensitive qubit is the difference in the value of frequencies of the two dots on the graph.

[0094] Various improvements and modifications may be made to the above without departing from the scope of the disclosure.

Claims

CLAIMS1. A trapped ion system for quantum computing configured to encode a first qubit in first and second metastable hyperfine states of a barium ion.

2. The trapped ion system of claim 1 comprising an ion trap configured to trap the barium ion.

3. The trapped ion system of claim 2 comprising a vacuum chamber, the ion trap being within the vacuum chamber.

4. The trapped ion system of any preceding claim comprising a barium ion source configured to provide the barium ion to the ion trap.

5. The trapped ion system of claim 4, wherein the barium ion source comprises: a neutral atom source configured to provide a barium atom; an ionization device configured to ionize the barium atom, thereby providing the barium ion.

6. The trapped ion system of any preceding claim comprising: a qubit manipulation system configured to encode the first qubit in the first and second metastable hyperfine states of the barium ion by applying a first signal at a first frequency to the barium ion; wherein: the first frequency is associated with a qubit frequency of the first and second metastable hyperfine states.

7. The trapped ion system of claim 6, wherein the first signal is applied using a current carrying antenna or a pair of Raman lasers.

8. The trapped ion system of any preceding claim comprising a magnetic field source configured to apply a magnetic field at approximately a field insensitive point of the qubit.

9. The trapped ion system of any preceding claim, wherein the barium ion is an odd numbered isotope.

10. The trapped ion system of any preceding claim, wherein the first and second metastable hyperfine states of the barium ion comprise a D3 / 2 state or a D5 / 2 state.

11. The trapped ion system of any of claims 1 to 8, wherein the barium ion is133Ba+.

12. The trapped ion system of claim 11, wherein the first and second metastable hyperfine states of the barium ion comprise a D5 / 2 state.

13. The trapped ion system of claim 12, wherein: the first metastable hyperfine state comprises F=2, mF=+l and the second metastable hyperfine state comprises F=3, mF=+l; or the first metastable hyperfine state comprises F=2, mF+2 and the second metastable hyperfine state comprises F=3, mF=+2.

14. The trapped ion system of any of claims 1 to 8, wherein the barium ion is135Ba+.

15. The trapped ion system of claim 14, wherein the first and second metastable hyperfine states of the barium ion comprise a D5 / 2 state.

16. The trapped ion system of claim 15, wherein: the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=2, mF=-l; orthe first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; or the first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=3, mF=0; or the first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=4, mF=+l; or the first metastable hyperfine state comprises F=2, mF=+l and the second metastable hyperfine state comprises F=4, mF=+2; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=4, mF=-3; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=4, mF=-2; or the first metastable hyperfine state comprises F=3, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=3, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=3, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; orthe first metastable hyperfine state comprises F=3, mF=0 and the second metastable hyperfine state comprises F=4, mF=+l.

17. The trapped ion system of any of claims 1 to 8, wherein the barium ion137Ba+.

18. The trapped ion system of claim 17, wherein the first and second metastable hyperfine states of the barium ion comprise a D5 / 2 state.

19. The trapped ion system of claim 18, wherein: the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=2, mF=-l; or the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=l, mF=-l and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-3; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-2 and the second metastable hyperfine state comprises F=4, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=2, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; or the first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=3, mF=-l; orthe first metastable hyperfine state comprises F=2, mF=0 and the second metastable hyperfine state comprises F=3, mF=0; or the first metastable hyperfine state comprises F=2, mF=+l and the second metastable hyperfine state comprises F=3, mF=+l; or the first metastable hyperfine state comprises F=2, mF=+2 and the second metastable hyperfine state comprises F=3, mF=+2; or the first metastable hyperfine state comprises F=3, mF=-3 and the second metastable hyperfine state comprises F=3, mF=-2; or the first metastable hyperfine state comprises F=3, mF=-2 and the second metastable hyperfine state comprises F=3, mF=-l; or the first metastable hyperfine state comprises F=3, mF=-l and the second metastable hyperfine state comprises F=4, mF=0; or the first metastable hyperfine state comprises F=3, mF=0 and the second metastable hyperfine state comprises F=4, mF=+l.

20. A quantum computer comprising the trapped ion system of any preceding claim.

21. A method of encoding the first qubit in the first and second metastable hyperfine states of the barium ion using the trapped ion system of any of claim 1.

22. The method of claim 21 comprising: applying a magnetic field at approximately a field insensitive point of the qubit.

23. The method of claim 22 comprising trapping the barium ion using an ion trap.

24. The method of claim 23 comprising preparing the barium ion in an initial state.

25. The method of claim 24 comprising: encoding the first qubit in the first and second metastable hyperfine states of the barium ion by applying a first signal at a first frequency to the barium ion; wherein: the first frequency is associated with a qubit frequency of the first and second metastable hyperfine states.

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