Quantum methods for hyperpolarization

Abstract

The present disclosure relates to a method, quantum circuit, and computer-readable memory for hyperpolarization. Illustratively, the method for the system, which system includes a target system, an auxiliary system, and a reset system each with their own energy levels, includes applying one or more operations to increase the probability of the target system energy levels in lower energy state, and to reduce the probability of the target system energy levels that have the target element in the higher energy state.

Description

QUANTUM METHODS FOR HYPERPOLARIZATIONTECHNICAL FIELD

[0001] The present disclosure relates to a method of hyperpolarization of spins.BACKGROUND

[0002] Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are powerful techniques for studying the structure and dynamics of molecules and materials, as well as the function and metabolism of living systems.

[0003] The sensitivity and resolution of NMR and MRI are limited by the low polarization of the nuclear spins used by the respective processes. The polarization is proportional to the magnetic field strength and the Boltzmann factor at thermal equilibrium.

[0004] Various methods have been developed to increase the polarization of the nuclear spins, such as dynamic nuclear polarization (DNP), parahydrogen induced polarization (PHIP), and optical pumping. These methods rely on transferring the polarization from an external source, such as electrons, hydrogen molecules, or photons, to the nuclear spins, and can achieve signal enhancements of several orders of magnitude.

[0005] These aforementioned methods can be deficient in that they either have limited achievable polarization or can require undesirable amounts of time, operations or energy to achieve polarizations beyond the polarization source. Accordingly, there is a need for new methods leveraging quantum operations to overcome the limitations of existing methods.SUMMARY

[0006] The present disclosure provides methods to increase polarization of target elements for use in, for example, imaging in NMR and MRI systems. The disclosure includes a quantum operation which, in at least some example embodiments, is realized in, for example, a quantum circuit, or a pulse sequence, or via optimal control theory, for a system with three elements (alternatively referred to as a three (3) spin system). The disclosed method involves, for example, applying a series of electromagnetic pulses to a sample containing several spins, in a magnetic field, and using a quantum circuit to manipulate the spin states.

[0007] The disclosed method may enhance the NMR and MRI signals by several orders of magnitude and enable the detection and characterization of various molecular and biological processes.

[0008] The disclosed method can improve trade off profiles in existing techniques. For example, the disclose method can result in quicker implementations and yet achieve high polarization (compared to a polarization source) or can reduce the amount of energy or the number of operations required to achieve comparable or slightly lower amounts of polarization. The disclosed method can also lead to so called “hyperpolarization,” in the sense that it can generate greater polarization as compared to certain existing techniques for increasing polarization in the systems (e.g., DNP).BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Embodiments of the present disclosure will now be described, by way of example only, with reference to the attached figures.

[0010] FIGS. 1A, 1 B, and 1C are diagrams of states of a spin (FIG. 1A), an example notation for different states of a spin (FIG. 1 B), and an example notation for states of three spin systems (FIG. 1C), according to embodiments described herein;

[0011] FIGS. 2A, 2B, and 2C are diagrams each showing different representations of quantum operations. FIG. 2A shows a single spin operation and notation associated therewith. FIG. 2B shows two spin operations and notation associated therein. FIG. 2C shows the Pauli-spin matrices associated with the notation in FIGS. 2A and 2B;

[0012] FIGS. 3A and 3B are schematic diagrams illustrating examples of a quantum circuit acting on three spins, according to various embodiments described herein;

[0013] FIG. 4 is a diagram illustrating an example quantum circuit of FIG. 3 implemented in an NMR system;

[0014] FIG. 5 illustrates an example of how two-spin gates may be implemented in an NMR pulse sequence;

[0015] FIG. 6 is a diagram showing how the pulse sequence illustrated in FIG. 4 may be applied when spins Si and S2 are on the same channel, such as when they are spins of the same species; and

[0016] FIG. 7 is a diagram showing how the pulse sequence illustrated in FIG. 4 may be applied when spins S2 and S3 are on the same channel, such as when they are spins of the same species.DETAILED DESCRIPTION

[0017] The disclosed quantum operations can illustratively be realized via a quantum circuit that consists of a sequence of quantum gates. The disclosed system can be adapted and directly implemented for, for example, NMR or MRI based systems. These include singlespin rotations around any axis in the X-Y plane of the Bloch sphere (NMR pulses) that can be realized via electromagnetic pulses. The disclosed quantum circuit also includes two-spin or multi-spin rotations that are enabled by the spin couplings in the system of interest.

[0018] The disclosed system consists of a set of target spins that are to be hyperpolarized (referred to hereinafter as “target spins”) and other spins in the system (referred to as hereinafter as “auxiliary spins”). In some cases, some of the auxiliary spins have short relaxation times or can be reset (e.g. by waiting a relaxation time or by optical pumping). Optionally, these spins can be used to extract entropy from the entire system and are referred to as “reset spins.”

[0019] In one aspect, the present disclosure provides a method for managing a system, the system comprising a target system having a target element (e.g.,1H,13C, or15N) with target system energy levels, the system comprising an auxiliary element with auxiliary system energy levels, the system comprising a reset system with reset system energy levels, the system having a set of system energy levels comprising combinations of the target system energy levels, the auxiliary energy levels and the reset system energy levels (denoted by target, auxiliary, reset, respectively). The method includes applying one or more operations to increase the probability of the target system energy levels that have the target element in a lower energy state and reduce the probability of the target system energy levels that have the target element in the higher energy state.

[0020] Each of the target system energy levels, the auxiliary energy levels and the reset system energy levels can be binary. The one or more operations can generate state permutations of the system energy levels such that a first system energy state of 011 is moved to any one of second system energy states 100, 101 , 110 and 111 , or the first system energy state 100 is moved to any one of second system energy states 000, 001 , 010 and 011. Herein, the term “moved” or an arrow (->) indicates a change in the likelihood of the denoted system state being found in the shown resulting state (also known as the state population). Alternatively, this change can be denoted by a “swap,” as the energy states do not per se move, but the probability of finding the system in that state changes.

[0021] The one or more operations can generate state permutations of the system energy levels such that the system energy states 000, 001 , 010 are moved to system energy states that have the target element in the lower energy state.

[0022] The one or more operations can generate state permutations of the system energy levels such that the system energy states 111 , 101 , 110 are moved to system energy states that have the target element in the higher energy state.

[0023] The one or more operations can generate state permutations of the system energy levels such that at least one of the below permutations occurs: the first system energy states of 001 and 011 are moved to any one of the following second system energy states: 100, 101 , 110 or 111 , or the first system energy states of 100 and 110 are moved to any one of the following second system energy states: 000, 001 , 010 or 011 .

[0024] The one or more operations can generate state permutations of the system energy levels such that at least one of the below permutations occurs: the first system energy states of 000 and 010 are moved or maintained in to any one of second system energy states: 000, 001 , 010 or 011 ; or the first system energy states of 111 and 101 are moved or maintained in to any one of second system energy states: 100, 101 , 110 or 111 .

[0025] The one or more operations can generate state permutations of the system energy levels such that the below permutations occurs:

[0026] a first system energy state of 000->a second system energy state of 000;

[0027] a first system energy state of 100-> a second system energy state of 001 ;

[0028] a first system energy state of 001 -> a second system energy state of 010;

[0029] a first system energy state of 010-> a second system energy state of 011 ;

[0030] a first system energy state of 111 — > a second system energy state of 100;

[0031] a first system energy state of 011 -> a second system energy state of 101 ;

[0032] a first system energy state of 101 -> a second system energy state of 110; and

[0033] a first system energy state of 110-> a second system energy state of 111 .

[0034] The method can include substitute operations, where one or more substitute operations affect the auxiliary and reset elements without affecting the polarization of the target element.

[0035] Each target element can be a spin (i.e. , a nucleus having a spin), and the one or more operations can comprise applying electromagnetic pulses.

[0036] Some or all of the target, auxiliary or reset elements can be completely or partially pre-polarized. The pre-polarization can be achieved by DNP, distortionless enhancement by polarization transfer (DEPT), insensitive nuclei enhancement by polarization transfer (INEPT), signal amplification by reversible exchange (SABRE), or other known magnetic resonance hyperpolarization techniques. This means that the current method can be combined with other hyperpolarization techniques to achieve higher polarization.

[0037] The target elements can be one of1H,13C, and15N.

[0038] The system can be a magnetic resonance imaging-based system or a nuclear magnetic resonance-based system.

[0039] In example embodiments, the one or more operations swap instances of the target system energy levels in lower energy state having low probability with instances of the target system energy levels that have the target element in the higher energy state having a high probability.

[0040] In another aspect, a quantum circuit comprising one or more gates is configured to perform any one of the above methods.

[0041] In another aspect a computer-readable medium (CRM) is provided. The CRM includes computer executable instructions that, when executed, cause a computing device to perform any one of the above methods.

[0042] The present disclosure describes a method for hyperpolarizing target spins in a spin system by reducing the entropy of a quantum system.

[0043] For simplicity and clarity of illustration, reference numerals may be repeated among the figures to indicate corresponding or analogous elements. Numerous details are set forth to provide an understanding of the embodiments described herein. The embodiments may be practiced without these details. In other instances, well-known methods, procedures, and components have not been described in detail to avoid obscuring the embodiments described.

[0044] Herein, the term “hyperpolarization” refers to an increase in polarization of elements within the quantum system (as described herein), compared to existing systems. As used in this disclosure, hyperpolarization can mean that the polarization achieved is greater than that in existing systems. It should be noted that that the term “hyperpolarization” is not intended to be limiting.

[0045] “Spin system” or “Quantum system,” (also referred to herein simply as the “system”), as used in this disclosure means a physical system having discrete energy levels, referred to as the system energy levels. Quantum systems include systems that may be considered classical systems or quasi-classical systems, such as NMR samples.

[0046] The system includes target spins, auxiliary spins and reset spins. The target system includes one or more target elements, the auxiliary system includes one or more auxiliary elements, and the reset system includes one or more reset elements. The target elements and the reset elements may be any size, for example, spin ! particles, or a multilevel quantum system. Multilevel quantum systems include elements that have morethan two states or energy levels. Multilevel quantum systems may include, for example, spin 1 particles, and nitrogen vacancy (NV) centers.

[0047] The target system has a number of target system energy levels, the auxiliary system has a number of auxiliary system energy levels, and the reset system includes a number of reset system energy levels. For example, when the target elements and reset elements comprise non-zero spin particles, placing the system in a magnetic field will cause the different states of the target system and the reset system to split into target system energy levels and reset system energy levels, respectively. Each state of the system has an associated system energy level. Similarly, each target system state, auxiliary system state and reset system state has, respectively, an associated target system energy level, an associated auxiliary system energy level and an associated reset system energy level. In this disclosure, “state” and “energy level” are used interchangeably.

[0048] Referring now to the Figures, FIGS. 1A, 1 B, and 10 are diagrams illustrating notations used in this disclosure. The notations relate to quantum systems. FIG. 1A defines the notations for the spin states of a single element (e.g., a target element, as discussed herein). The up arrow 10 indicates the spin being aligned with the external magnetic field (first energy level or the ground state) and the down arrow 12 indicates being aligned in the opposite direction of the external magnetic field (second energy level or the excited state). In this notation the ground state is denoted as |0>, and the excited state is denoted as |1 >. FIG. 1 B shows the notation used to represent a three-spin system (as described herein), and the constituent target spin 102, the auxiliary spin 104 and the reset spin 106. The ket notation from quantum physics is used, i.e. |si , S2, S3> where si refers to a first spin state (the target spin 102 in this case), S2 refers to the second spin state (the auxiliary spin 104 in this case) and S3 refers to a third spin state (the reset spin 106 in this case). FIG. 1C shows notations for all combinations / energy states of the target, auxiliary and reset system energy levels within a 3-spin quantum system.

[0049] FIGS. 2A, 2B, and 2C each show additional notation used within the present disclosure. In FIG. 2A, the notation for a single spin operation 202, on spin, sn, is shown. The single spin operation consists of three Euler rotations, denoted a, f>, and y in FIG. 2A, describing the sequence of active rotations, / ?z(y) / ?y(cr) / ?z( ?) about the y- and z-axes, where _i0 . / ?j(0) = e These angles may be translated to x-rotations and y-rotations that can be implemented directly by electromagnetic pulses in an NMR device.

[0050] FIG. 2B shows the notation for a two-spin operation 204, acting on spins n andThe two-spin operation 204, alternatively referred to as Rzz gates, are periodsof evolution under a scalar coupling between two spins of interest for a duration determined by the provided evolution angle, labelled 9 in FIG. 2B. This can be implemented in a liquidstate NMR experiment via the scalar J coupling between nuclei. The full evolution time, T, ofQ an Rzz gate in experiment is related to the evolution angle by the equation T = —, where J is TTJ the coupling strength between the two nuclei of interest, given in the unit of Hz.

[0051] FIG. 2C shows the Pauli spin matrices which form part of FIGS. 2A and 2B.

[0052] Each of the Rzz gates described in FIG. 2B have some free parameter. The free parameters are set to give specific permutations, including the permutations described below.

[0053] The quantum operation can be expressed as a pre-determined set of permutation operations on the system energy states. The set of permutation operations may be performed in the system by applying a set of electromagnetic (EM) pulses to the system.

[0054] For simplicity, the methods for elements referred to herein are discussed as comprising two energy states, such as a target element, an auxiliary element, and a reset element comprising two energy states. This could, for instance, include spin ! particles or qubits for the target system or the reset system.

[0055] Achieving hyperpolarization of the target spin(s), as disclosed herein, includes increasing the probability of the system being in a state with the target element in the 0 (ground) state. Quantum operations that increase the probability of the states that have the target element in the ground state 0 (e.g. 000, 001 , 010, 011) and reduce the probability of the states that have the target element in the excited state 1 (e.g. 100, 101 , 110, 111) can beneficially be performed to increase hyperpolarization.

[0056] Generating the conditions of (1) increasing the probability of states that have the target element in the ground state 0, or (2) reducing the probability of states that have the target element in the excited state 1 , can include swapping (a) the states with the target spin in the 0 state and having a low probability with (b) states that have the target spin in the 1 state and higher probability.

[0057] Various quantum operations are contemplated to achieve the above contemplated operations. For example, U.S. Patent No. 10,560,096 describes example quantum operations that can be arranged to generate at least some of the above noted conditions.

[0058] Certain quantum operations comprise permutations that are challenging to implement. These challenging operations can require undesirably longer quantum circuits, longer operation times, etc. Efficient permutations are desirable.

[0059] In at least some example embodiments, this disclosure provides quantum operations that can in part optimize both the single-iteration (with only one iteration) achievable polarization (hyperpolarization) and the operation time. For example, in at least some example embodiments, the quantum operations can be applied between the populations of the states of the system according to:

[0060] a first system energy state of 000-> a second system energy state of 000;

[0061] a first system energy state of 100-> a second system energy state of 001 ;

[0062] a first system energy state of 001 -> a second system energy state of 010;

[0063] a first system energy state of 010-> a second system energy state of 011 ;

[0064] a first system energy state of 111 — > a second system energy state of 100;

[0065] a first system energy state of 011 -> a second system energy state of 101 ;

[0066] a first system energy state of 101 -> a second system energy state of 110; and

[0067] a first system energy state of 110-> a second system energy state of 111 .

[0068] Hereinafter, the above permutation is generally referred to as the optimized permutation.

[0069] This optimized permutation can also be expressed as:

[0070] (P000, P100, P001 , P010, P111 , P011 , P101 , P110).

[0071] For further clarity, if Psi,S2,S3 gives the population or probability of state |si, S2, S3>, the population of the states of the system initially can be expressed as

[0072] (P000, P001 , P010, P011 , P100, P101 , P110, P111)

[0073] The optimized quantum operation (i.e., the optimized permutation above) would change the sequence to

[0074] (P000, P100, P001 , P010, P111 , P011 , P101 , P110).

[0075] The optimized quantum operation may also be expressed as the following matrix.

[0077] Variations of the optimized quantum operation are contemplated. For example, operation or variations of the optimized permutation that include additional elements that operate on elements other than the target element, or that remove certain operations, or include a rearrangement (e.g., using inverse elements), and rearrangement or reordering to this sequence are contemplated.

[0078] The optimized quantum operation can be realized via electromagnetic pulses driving transitions in a spin system.

[0079] FIG. 3A is a schematic diagram illustrating an example quantum circuit 302 acting on a three-spin system according to the described optimized quantum operation. In FIG. 3A, the circuit 302 corresponds to a process with a single iteration (quantum operation), with horizontal lines indicating a spin state or quantum bit, wherein the top line is the target spin or quantum bit, si , and the middle and bottom horizontal lines indicate the auxiliary spin, S2, and the reset spin, S3, respectively. The quantum circuit of FIG. 3A, includes single spin rotations, and two-spin free evolutions (Rzz) gates. The single spin rotations operate on a single spin (one of the three spins, si , S2 or S3) and the Rzz gate operates on two spins (e.g., si & S2, si & S3 or S2 & S3).

[0080] The shown circuit 302 is for hyperpolarizing the first spin, shown as Si. As shown in FIGS. 3A and 3B, various operations can be performed on each of the three spins, where unconnected, horizontally aligned operations may occur simultaneously or sequentially. Further, according to various embodiments, operations may be moved earlier or later if they directly follow or precede an empty space on their spin channel or channels.

[0081] Variations of the quantum circuit in FIG. 3A that would correspond with the optimized quantum operations, or provide similar performance, are contemplated. For example, the quantum circuit 303 in FIGS. 3B involves additional single spin rotations 304 on the second spin and the third spin would achieve the same amount of hyperpolarization for the target spin after a single iteration. In another example (not shown), the angles of the rotations in FIG. 3A can be adjusted while keeping the rotation the same (e.g. (Rx(0) = R_x(2n - 9 ), or evolution angles may be adjusted that change the evolution itself, but resultin an equivalent evolution when combined with other operations (e.g. Rzz(&) = i Rzz(9 - n)R (n)R (n) , where Rz (n) represents a n rotation about the z axis for spin n), etc.

[0082] The rotations and operations in the quantum circuits 302, 303 can be translated to an NMR / MRI pulse sequence. For example, these pulse sequences can be programmed into the NMR / MRI machines and be implemented using the firmware of the NMR / MRI machines.

[0083] FIG. 4 is a schematic diagram illustrating an example of how the quantum circuit depicted in FIG. 3 may be implemented in an NMR system. In FIG. 4 each row represents a spin (i.e., si, S2 and S3), and horizontally aligned pulses may be applied simultaneously or sequentially. Two-spin operations (e.g., exemplary two-spin operation 403) are implemented using free evolution periods of the two spins of interest, labelled by sections listing the two spins and the associated evolution angle.

[0084] The single spin operations (e.g., single-spin rotation 402) are shown translated into XYX Euler angles from ZYZ Euler angles to allow for implementation on a spectrometer. This can be accomplished with one, two, or three pulses depending on the precise angles. Additionally, depending on the initial magnetization of a spin, it may be possible to achieve the same effect of a ZYZ rotation via a single pulse with some phase in the xy plane even if the precise operator representation of the two rotations are not equal (i.e., the ZYZ rotation of a single vector can always be reproduced by a single rotation of angle 9 about an axis of rotation, <p, in the xy plane, but this is not the case for the rotation of a set of vectors).

[0085] The frequencies of the EM pulses that affect the permutation operations may be determined based on the difference in energy between the system energy levels between the states corresponding to the swap. The difference in energy associated with each pair of system energy levels may be determined by, for example, spectroscopy measurements performed on the system. Each swap operation may be associated with one EM pulse of the set of pulses or may be associated with multiple EM pulses. For example, multiple EM pulses may be applied such that the permutation operation is affected via intermediary system energy levels. Further, because the EM pulses are determined based on an energy difference between the states corresponding to the specific transition, it is possible that a single EM pulse may be associated with multiple pairs of system energy levels if the multiple pairs of system energy levels are separated by the same energy difference. The EM pulses may be 7r-pulses.

[0086] The set of EM pulses applied in FIG. 4 for different spins may be applied simultaneously or may be applied sequentially, or a portion may be applied simultaneously while another portion is applied sequentially.

[0087] For the Rzz gates / quantum operations 403, the spins of interest are preferably together decoupled from other spins and the environment to allow for evolution under the J coupling, which has the form JnmS'lS'nbetween two spins, n and m. Periods where other spins and the environment are decoupled from these spins therefore allow for evolution via the operator e~iTJnmSzs™, where T is the duration of the evolution period. Interactions with other spins and the environment are decoupled via the application of n pulses during the evolution time. Simultaneous application of n pulses at the halfway point of the evolution period on both spins n and m can cause all other interactions to have no effect on the state of these spins at the end of the evolution period.

[0088] The effect of the n pulse itself can be removed by application of a second, identical n pulse at the end of the evolution period.

[0089] When more than two spins are considered, it is preferable to also decouple the third spin from the environment, while ensuring that it remains uncoupled from the two spins meant to evolve under their J coupling. This can be accomplished by also applying two n pulses on the third spin but placing these pulses at a time such that the first two spins remain unaffected by the third at the end of the evolution period. In a simplifiedT 3T example, n pulses are added on the third spin at the - and — points of the evolution period.More complicated decoupling schemes are possible and may be necessary if the spins are coupled to an environment where magnetization quickly relaxes.

[0090] FIG. 5 shows one example of the above, implemented in an NMR pulse sequence, where four n pulses are used to help maintain signal by reducing the intermittent transfer of magnetization to the environment, which may then quickly relax and lead to signal loss. Additionally, this type of scheme, generally known in the literature as dynamical decoupling, makes use of variable phases of the pulses, which can help to reduce the effects of errors in pulse power.

[0091] In the embodiment shown, the two-spin gate occurs between spins Si and S3 and follows a dynamical decoupling scheme to decouple the two spins from S2 and the environment, allowing for the intended evolution during one Rzz gate. The phases of this scheme can reduce the effect of experimental errors. The delay time, t, is determined based on the evolution angle of the gate, the coupling strength between spins Si and S3, and the length of the pulses. Refocusing pulses are also applied to the uncoupled spin, S2, to ensure that it is decoupled from the environment.

[0092] Inversion pulses may also be required on other spins in the system to ensure those are also decoupled from the environment.

[0093] Various implementations of dynamical decoupling have been studied previously.

[0094] In systems where one of the three sets of two-spin evolution periods requires a significantly longer evolution time than the other two, it may be possible to reduce the required time using a composite gate, depending on the precise J-coupling values. Specifically, performing an Rzz gate between spins / and j is equivalent to performing the sequentially following three operations: a SWAP gate between spins / and k, followed by an Rzz gate between spins k and j, then another SWAP gate between spins / and k, where spins / , j and k represent any permutation of spins 1 , 2 and 3.

[0095] The disclosed method of swapping target states and optimized permutation operations can be used once (single iteration) or can be iterated. An iterative implementation can achieve higher polarization. The number of times, or iterations, that the set of EM pulses are applied in order to reach convergence may be determined by, for example, the desired accuracy and precision of the operations. The number of iterations may be a predetermined number of iterations which relates to the number of iterations that are predicted for the system to reach a desired fidelity or for the system to vary from the ideal state by an amount that is less than or equal to a predetermined amount. Alternatively, or additionally, the system may be monitored such that the set of EM pulses are applied until the system is determined to have reached the desired fidelity or to vary from the ideal state by an amount less than or equal to a predetermined amount. The ideal state may be the maximally mixed state (MMS).

[0096] In the iterative implementation, after each step, the reset elements may need to be reset. This may involve waiting for the relaxation time of the reset element to facilitate at least some of the reset elements resetting from the higher reset system energy level to a lower reset system energy level. This would partially reset the state of the reset element to its initial (equilibrium) state. The time period that elapses may be on the order of the relaxation time of the reset system.

[0097] In some embodiments, the relaxation time of the reset system may be an effective relaxation time that is shorter than an intrinsic relaxation of the reset system. The effective relaxation time may be the result of manipulating the reset system to reduce the relaxation time from the intrinsic relaxation time to the effective relaxation time. For example, manipulating the reset system may include performing, optical polarization, optical pumping, or dynamic nuclear polarization during the time period that elapses.

[0098] The disclosed method of swapping target states and optimized permutation operations could involve steps of pre-polarization. Pre-polarization can involve usingtechniques to first polarize the target system (and / or the auxiliary system) and then applying operation as described herein.

[0099] For instance, in an implementation with nuclear spins one of which is a13C and one of which is a1H (as discussed in greater detail below), a technique such as refocused INEPT can be used to polarize the13C nuclear spins first and then apply the quantum operation described above. Similarly, in an implementation that involves an electron spin, a technique such as dynamic nuclear polarization (DNP) may be used to increase the polarization of all the nuclear spins in the system first and then followed by the hyperpolarization using one of the quantum circuits 302, 303 in FIGS. 3A, 3B.

[0100] Below are described example embodiments. It is understood that the example embodiments are not intended to limit the scope of the disclosure to the embodiments described therein. Alterations, modifications, and variations can be affected to the embodiments by those of skill in the art without departing from the scope, which is defined solely by the claims appended hereto.Example Embodiment I: Hyperpolarization of Metronidazole-15N3

[0101] The disclosed approaches can be used to assist in imaging of metronidazole, having the spin-active nitrogen nucleus,15N.15N is significantly less sensitive to a magnetic field than protons and is therefore much more difficult to observe in experiments.

[0102] In the disclosed embodiment in FIGS. 6A, 6B, hyperpolarization of a15N nucleus at the N1 site of metronidazole is considered, making use of another15N nucleus at the N3 site, as well as the proton at the H4 site.

[0103] FIG. 6 shows an example implementation of the pulse sequence from FIG. 4, when applied to a system with Si and S2 on the same channel, such as for the three spins listed above. To ensure that pulses affect only one of those spins at a time, band selective pulses such as Gaussian pulses are used, and the transmitter frequency is moved between the two resonance frequencies such that it is on resonance with the indicated spin when the pulse is applied. The transmitter frequency can be moved either by explicitly altering the transmitter frequency, or by adding a linearly varying phase to the pulses to create an effective frequency offset. pulses with a length of 2 ms were found to sufficiently excite the spin of interest, while leaving the other spins mostly unaffected.

[0104] The lengths of the evolution periods are determined by the J coupling constants within the molecule, which can be obtained by measuring the distance between split peaks within the spectra. For example, the values for the three spins of interest are / 12 = 1.65 Hz, / i3 = 2.01 Hz, and J23 = 9.15 Hz. Based on these values, the lengths of evolution periods shown in FIG. 6 are, from left to right, 54.6 ms, 248.8 ms, 404.0 ms, 72.9 ms, and 248.8 ms.

[0105] Simulations of the system have been performed in MATLAB® by time evolving the density matrix describing all the spins in the system according to the Hamiltonian featuring terms describing the Zeeman interaction, the J couplings, and the applied radio-frequency pulses. When the nitrogen nuclei are pre-polarized using the refocused INEPT pulse sequence, application of the pulse sequence described above results in a polarization on the N1 site that is 1.41x greater than that obtained from refocused INEPT alone.Example Embodiment II: Hyperpolarization of Metronidazole-13C2,15N2

[0106] As an alternative to example embodiment I, metronidazole is also available with two15N labelled sites and 213C labelled sites. In this embodiment, the target spin is the N3 nitrogen site, with the labelled carbons at the C2 and methyl sites acting as the auxiliary and refresh spins.

[0107] FIG. 7 shows an example implementation of the pulse sequence from FIG. 4, when applied to a system with S2 and S3 on the same channel, as for the spins listed above. Since the three spins considered are much more well separated than in the previous example, shorter band-selective Gaussian pulses may be used. A pulses length of 0.2 ms was found to sufficiently excite the spins of interest while leaving other spins mostly unaffected.

[0108] The lengths of the evolution periods are determined by the J coupling constants within the molecule, which can be obtained by measuring the distance between split peaks within the spectra. For example, estimated J-coupling values for the three spins of interestare / 12=15 Hz, 713= 2 Hz, and J23= 50 Hz. Based on these values, the lengths of evolution periods shown in FIG. 7 are, from left to right, 10 ms, 250 ms, 44.4 ms, 13.3 ms, and 250 ms.

[0109] Simulations of the system have been performed in MATLAB® by time evolving the density matrix describing all the spins in the system according to the Hamiltonian featuring terms describing the Zeeman interaction, the J couplings, and the applied radio-frequency pulses. When all three nuclei are pre-polarized using the refocused INEPT pulse sequence from a single proton, application of the pulse sequence described above results in a polarization on the N1 site that is 1.31x greater than that obtained from refocused INEPT alone.

[0110] In applications relying on alanine or lactic acid, the spin-active carbon nucleus,13C, is less sensitive to a magnetic field than protons and can therefore have increased signal in observation by transferring polarization from protons. Both alanine-13C3 and lactic acid-13C3 feature similar structures and coupling constants, and are therefore described together.

[0111] In one example embodiment, hyperpolarization of a13C nucleus at the C1 site of alanine or lactic acid is considered. Other example embodiments, for example, can include focusing on another13C nucleus at the C2 site, or the proton attached to the C2 site.

[0112] The pulse sequence shown in FIG. 6 may also be applied to this system as Si and S2 are again on the same channel. The length of the pulses used must be chosen carefully to ensure that other spins remain largely unaffected, while also ensuring that the pulses adequately excite the full range of frequencies of the spin of interest. The large J coupling between S2 and S3 suggests that short pulses are suited for this system, but the proximity of S3 to another proton resonance frequency requires longer pulses to selectively excite S3. 300 ps pulses were found to handle the requirements from the large J coupling and small resonance difference simultaneously.

[0113] In alanine, the values for the three spins of interest are J12= 54.0 Hz, / 13= 5.0 Hz, and J23= 145.1 Hz. Similar values are estimated for lactic acid. Based on these values, the lengths of evolution periods shown in FIG. 6 are, from left to right, 3.4 ms, 100.0 ms, 12.3 ms, 4.6 ms, and 100 ms.

[0114] Simulations of the system have been performed in MATLAB® by time evolving the density matrix describing all the spins in the system according to the Hamiltonian featuring terms describing the Zeeman interaction, the J couplings, and the applied radio-frequency pulses. When the carbon nuclei are pre-polarized using the refocused INEPT pulse sequence, application of the pulse sequence described above results in a polarization on the C1 site that is 1.31x greater than that obtained from refocused INEPT alone.

[0115] The length of the total pulse sequence may be shortened by replacing the final Rzz gate with a composite Rzz gate, as described above. In this specific case, the 100 ms Rzz gate between Si and S3 at the end of the sequence may be replaced by a SWAP gate between S2 and S3 followed by an Rzz gate between Si and S2. The trailing SWAP gate between S2 and S3 is omitted here since it does not affect the final state of Si. This reduces the required evolution time from 100 ms to 19.6 ms without affecting the final polarization of Si. Additionally, this reduces the amount of relaxation that occurs during the sequence (not considered here), and therefore is expected to lead to an overall improvement of the performance.

[0116] Embodiments of the present disclosure provide methods for managing a system for hyperpolarizing spins. The method utilizes a set of EM pulses that affect permutation operations between pairs of system states that implement a quantum circuit.

[0117] The disclosed methods can be executed through software. Coding of software for carrying out such a method is within the scope of a person of ordinary skill in the art given the present description. The method may contain additional or fewer processes than shown and / or described and may be performed in a different order. Computer-readable code executable by at least one processor of an electronic device to perform the method may be stored in a computer-readable storage medium, such as a non-transitory computer-readable medium. The device may also be configured to apply or to initiate the application of EM pulses as herein described, e.g., via an EM pulse generator.

[0118] Embodiments of the disclosure can be represented as a computer program product stored in a machine-readable medium (also referred to as a computer-readable medium, a processor-readable medium, or a computer usable medium having a computer- readable program code embodied therein). The machine-readable medium can be any suitable tangible, non-transitory medium, including magnetic, optical, or electrical storage medium including a diskette, compact disk read only memory (CD-ROM), memory device (volatile or non-volatile), or similar storage mechanism. The machine-readable medium can contain various sets of instructions, code sequences, configuration information, or other data, which, when executed, cause a processor to perform steps in a method according to an embodiment of the disclosure. Those of ordinary skill in the art will appreciate that other instructions and operations necessary to implement the described implementations can also be stored on the machine-readable medium. The instructions stored on the machine-readable medium can be executed by a processor or other suitable processing device and can interface with circuitry to perform the described tasks.

[0119] While the above description provides examples of one or more apparatus, methods, or systems, it will be appreciated that other apparatus, methods, or systems may be within the scope of the claims as interpreted by one of skill in the art.

Claims

WHAT IS CLAIMED IS:

1. A method for managing a system, the system comprising a target system having a target element with target system energy levels, the system comprising an auxiliary system having an auxiliary element with auxiliary system energy levels, the system comprising a reset system having a reset element with reset system energy levels, the system having a set of system energy levels comprising combinations of the target system energy levels, the auxiliary energy levels and the reset system energy levels, the method comprising: applying one or more operations to: increase the probability of the target system energy levels that have the target element in a lower energy state; and reduce the probability of the target system energy levels that have the target element in a higher energy state.

2. The method of claim 1 , wherein each of the target system energy levels, the auxiliary energy levels and the reset system energy levels are binary.

3. The method of claim 2, wherein the one or more operations generate state permutations of the system energy levels such that: a first system energy state of 011 is moved to any one of second system energy states of: 100, 101 , 110 and 111 ; or a first system energy state of 100 is moved to any one of second system energy states of: 000, 001 , 010 and 011.

4. The method of claim 3, wherein the one or more operations generate the state permutations of the system energy levels such that first system energy states of 000, 001 , 010 are moved to second system energy states that have the target element in the lower energy state.

5. The method of claim 3, wherein the one or more operations generate the state permutations of the system energy levels such that first system energy states of 111 , 101 and 110 are moved to second system energy states that have the target element in the higher energy state.

6. The method of claim 3, wherein the one or more operations generate the state permutations of the system energy levels such that at least one of: first system energy states of 001 and 011 are moved to any one of the second system energy states of: 100, 101 , 110 and 111 ; and first system energy states of 100 and 110 are moved to any one of the second system energy states of: 000, 001 , 010 and 011.

7. The method of any one of claims 4 or 5, wherein the one or more operations generate state permutations of the system energy levels such that at least one of:The first system energy states of 000 and 010 are moved or maintained to any one of the system energy states of: 000, 001 , 010 and 011 ; and the first system energy states of 111 and 101 are moved or maintained to any one of the system energy states of: 100, 101 , 110 and 111.

8. The method of claim 2, wherein the one or more operations generate state permutations of the system energy levels such that the below permutations occur: i. a system energy state of 000 is maintained; ii. a first system energy state of 100 is moved to a second system energy state of 001 ; iii. a first system energy state of 001 is moved to a second system energy state of 010; iv. a first system energy state of 010 is moved to a second system energy state of 011 ; v. a first system energy state of 111 is moved to a second system energy state of 100; vi. a first system energy state of 011 is moved to a second system energy state of 101 ; vii. a first system energy state of 101 is moved to a second system energy state of 110; and viii. a first system energy state of 110 is moved to a second system energy state of 111.

9. The method of claim 1 , further comprising one or more substitute operations, or wherein the one or more operations affect the auxiliary element and the reset element without affecting the polarization of the target element.

10. The method of claim 1 , wherein each target element is a spin.

11. The method of claim 1 , wherein the one or more operations comprise applying electromagnetic pulses.

12. The method of claim 1 , wherein one or more of the target element, the auxiliary element and the reset element are completely or partially pre-polarized.

13. The method of claim 12, wherein the pre-polarization is achieved by a magnetic resonance hyperpolarization technique.

14. The method of claim 13, wherein the magnetic resonance hyperpolarization technique is one of: dynamic nuclear polarization, distortionless enhancement by polarization transfer, insensitive nuclei enhancement by polarization transfer and signal amplification by reversible exchange.

15. The method of claim 1 , wherein the target element is one of:1H,13C, and15N.

16. The method of claim 1 , wherein the system is a magnetic resonance imaging system or a nuclear magnetic resonance system.

17. The method of claim 1 , wherein the one or more operations swap instances of the target system energy levels in the lower energy state and having a low probability with instances of the target system energy levels that have the target element in the higher energy state and having a high probability.

18. The method of claim 1 , wherein the one or more operations are expressed as a quantum circuit.

19. A quantum circuit comprising one or more gates configured to perform the method of any one of claims 1-16.

20. A computer readable medium comprising computer executable instructions that, when executed, cause a computing device to perform the method of any one of claims 1- 16.

Images