Quantum method for hyperpolarization

Abstract

The present disclosure relates to a method, quantum circuit, and computer readable memory for hyperpolarization. Illustratively, a method for a system, the system including a target system, an ancilla system, and a reset system, each having its own energy level, includes applying one or more operations to increase a probability of the target system energy level in a lower energy state and decrease a probability of the target system energy level having a target element in a higher energy state.

Description

Technical Field

[0001] This disclosure relates to a method for spin hyperpolarization. Background Technology

[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 in the corresponding processes. Polarization is proportional to the magnetic field strength at thermal equilibrium and the Boltzmann factor.

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

[0005] The aforementioned methods may have drawbacks: they have a limited number of achievable polarizations or may require undesirable amounts of time, operations, or energy to achieve polarization beyond the polarization source. Accordingly, there is a need for new methods that utilize quantum operations to overcome the limitations of existing approaches. Summary of the Invention

[0006] This disclosure provides methods for increasing the polarization of target elements used in imaging, such as in NMR and MRI systems. The disclosure includes quantum manipulation, which, in at least some example embodiments, is implemented, for example, in quantum circuits or pulse sequences or via optimal control theory for a system having three elements (or alternatively, referred to as a three (3)-spin system). The disclosed methods involve, for example, applying a series of electromagnetic pulses to a sample containing several spins in a magnetic field and using quantum circuits to manipulate the spin states.

[0007] The disclosed method can enhance NMR and MRI signals by several orders of magnitude and enables the detection and characterization of a variety of molecular and biological processes.

[0008] The disclosed method can improve upon the trade-offs in the prior art. For example, the disclosed method can be implemented more quickly, and thus achieve high polarization (compared to a polarization source) or reduce the amount of energy or number of operations required to achieve a comparable or slightly lower amount of polarization. The disclosed method can also achieve so-called "hyperpolarization" in the sense that it can generate greater polarization than certain prior art techniques used to increase polarization in a system (e.g., DNP). Attached Figure Description

[0009] Embodiments of this disclosure will now be described by way of example only, with reference to the accompanying drawings.

[0010] Figure 1A , 1B 1C and 1C are spin states according to embodiments described herein ( Figure 1A ), and example notation for different spin states ( Figure 1B ) and example notation for the states of a three-spin system ( Figure 1C (The image is missing from the original text.) Figure 2A , 2B 2C and 2C are diagrams that illustrate different representations of quantum operations. Figure 2A The single-spin operation and its associated notation are shown. Figure 2B The two-spin operation and the associated notation are shown. Figure 2C It shows the relationship with Figure 2A and 2B The Pauli spin matrix associated with the notation method in the text; Figure 3A and 3B This is a schematic diagram illustrating examples of quantum circuits operating on three spins according to various embodiments described herein; Figure 4 This is a diagram illustrating the example quantum circuit of Figure 3 implemented in an NMR system; Figure 5 The illustration shows an example of how dual spingates can be implemented in an NMR pulse sequence; Figure 6 This demonstrates how it can be applied when spins S1 and S2 are in the same channel (e.g., when they are the same type of spin). Figure 4 The diagram shows the pulse sequence; and Figure 7 This demonstrates how it can be applied when spins S2 and S3 are in the same channel (e.g., when they are the same type of spin). Figure 4 The diagram shows a pulse sequence. Detailed Implementation

[0011] Illustratively, the disclosed quantum operations can be implemented via quantum circuits composed of sequences of quantum gates. The disclosed systems can be adapted and directly implemented for, for example, NMR or MRI-based systems. These include single-spin rotations about any axis in the XY plane of a Bloch sphere (NMR pulse) that can be realized via electromagnetic pulses. The disclosed quantum circuits also include two-spin or multi-spin rotations realized by spin coupling in the system of interest.

[0012] The disclosed system consists of a set of target spins to be hyperpolarized (hereinafter referred to as "target spins") and other spins in the system (hereinafter referred to as "auxiliary spins"). In some cases, some of the auxiliary spins have short relaxation times or can be reset (e.g., by waiting for the 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".

[0013] In one aspect, this disclosure provides a method for managing a system comprising having target elements (e.g., 1 H, 13 C or 15 A target system (N) has a target system energy level, the system includes an auxiliary element with an auxiliary system energy level, the system includes a reset system with a reset system energy level, and the system has a set of system energy levels comprising combinations of target system energy levels, auxiliary energy levels, and reset system energy levels (identified by target, auxiliary, and reset, respectively). The method includes applying one or more operations to increase the probability of a target system energy level for a target element in a lower energy state and decrease the probability of a target system energy level for a target element in a higher energy state.

[0014] Each of the target system energy level, auxiliary energy level, and reset system energy level can be binary. The one or more operations can generate a state permutation of the system energy levels such that the first system energy state 011 is moved to any one of the second system energy states 100, 101, 110, and 111, or the first system energy state 100 is moved to any one of the second system energy states 000, 001, 010, and 011. In this document, the term "moved" or the arrow (→) indicates a change in the probability of finding the indicated system state in the resulting state (also referred to as the state population). Alternatively, this change can be indicated by "swapping," since the energy state itself does not move, but the probability of finding the system in that state changes.

[0015] One or more operations can generate state substitutions of system energy levels, such that system energy states 000, 001, and 010 are moved to the system energy state of the target element in a lower energy state.

[0016] One or more operations can generate state substitutions of system energy levels, such that system energy states 111, 101, and 110 are moved to the system energy state of the target element in a higher energy state.

[0017] The one or more operations can generate state permutations of the system energy levels such that at least one of the following permutations occurs: first system energy states 001 and 011 are moved to any of the following second system energy states: 100, 101, 110, or 111; or first system energy states 100 and 110 are moved to any of the following second system energy states: 000, 001, 010, or 011.

[0018] The one or more operations can generate state permutations of the system energy levels such that at least one of the following permutations occurs: the first system energy states 000 and 010 are moved or maintained to any of the second system energy states: 000, 001, 010, or 011; or the first system energy states 111 and 101 are moved or maintained to any of the second system energy states: 100, 101, 110, or 111.

[0019] One or more operations can generate state permutations of the system's energy levels, such that the following permutation occurs: First system energy state 000 → Second system energy state 000; First system energy state 100 → Second system energy state 001; First system energy state 001 → Second system energy state 010; First system energy state 010 → Second system energy state 011; First system energy state 111 → Second system energy state 100; First system energy state 011 → Second system energy state 101; First system energy state 101 → Second system energy state 110; and First system energy state 110 → Second system energy state 111.

[0020] The method may include substitution operations, wherein one or more substitution operations affect auxiliary and reset elements without affecting the polarization of the target element.

[0021] Each target element can be a spin (i.e., a nucleus with spin), and the one or more operations can include the application of an electromagnetic pulse.

[0022] Some or all of the target, auxiliary, or reset elements can be fully or partially pre-polarized. Pre-polarization can be achieved by DNP, distortionless enhancement via polarization transfer (DEPT), insensitive nucleus enhancement via polarization transfer (INEPT), signal amplification via reversible exchange (SABRE), or other known magnetic resonance hyperpolarization techniques. This means that current methods can be combined with other hyperpolarization techniques to achieve higher polarization.

[0023] The target element can be 1 H, 13 C and 15 One of N.

[0024] The system can be based on magnetic resonance imaging or nuclear magnetic resonance.

[0025] In an example embodiment, the one or more operations swap a target system level in a lower energy state with a low-probability instance with a target system level in a higher energy state with a high-probability instance.

[0026] In another aspect, a quantum circuit comprising one or more gates is configured to perform any of the methods described above.

[0027] 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 of the methods described above.

[0028] This disclosure describes a method for hyperpolarizing a target spin in a spin system by reducing the entropy of the quantum system.

[0029] For the sake of simplicity and clarity, reference numerals may be repeated in the figures to indicate corresponding or similar elements. Numerous details are set forth to provide an understanding of the embodiments described herein. Embodiments may be practiced without these details. In other instances, well-known methods, processes, and components have not been described in detail to avoid obscuring the described embodiments.

[0030] In this document, the term "hyperpolarization" refers to an increase in the polarization aspect of an element within a quantum system (as described herein) compared to existing systems. As used in this disclosure, hyperpolarization can mean that the achieved polarization is larger than that in existing systems. It should be noted that the term "hyperpolarization" is not intended to be limiting.

[0031] As used in this disclosure, "spin system" or "quantum system" (also referred to herein as "system") means a physical system having discrete energy levels called system energy levels. Quantum systems include systems that can be considered classical or quasi-classical systems, such as NMR samples.

[0032] The system comprises a target spin, an auxiliary spin, and a reset spin. The target system comprises one or more target elements, the auxiliary system comprises one or more auxiliary elements, and the reset system comprises one or more reset elements. The target and reset elements can be of any size, such as spin-1 / 2 particles or multilevel quantum systems. Multilevel quantum systems comprise elements having more than two states or energy levels. Multilevel quantum systems can include, for example, spin-1 particles and nitrogen-vacancy (NV) centers.

[0033] The target system has multiple target system energy levels, the auxiliary system has multiple auxiliary system energy levels, and the reset system includes multiple reset system energy levels. For example, when the target element and the reset element include 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 be separated 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 an associated target system energy level, an associated auxiliary system energy level, and an associated reset system energy level, respectively. In this disclosure, "state" and "energy level" are used interchangeably.

[0034] Now refer to the figures, Figure 1A , 1B Figures 1 and 1C are illustrations of the labeling method used in this disclosure. The labeling method is related to quantum systems. Figure 1A A notation for the spin states of a single element (e.g., a target element, as discussed herein) is defined. Up arrow 10 indicates spin alignment with an external magnetic field (first energy level or ground state), and down arrow 12 indicates alignment in the opposite direction to the external magnetic field (second energy level or excited state). In this notation, the ground state is denoted as |0>, and the excited state is denoted as |1>. Figure 1B The notation used to represent a three-spin system (as described herein) and the constituent target spin 102, auxiliary spin 104, and reset spin 106 is shown. KET notation from quantum physics is used, i.e., |s1, s2, s3>, where s1 refers to the first spin state (in this case, target spin 102), s2 refers to the second spin state (in this case, auxiliary spin 104), and s3 refers to the third spin state (in this case, reset spin 106). Figure 1C The notation for all combinations / energy states of the target, auxiliary, and reset system energy levels within a 3-spin quantum system is shown.

[0035] Figure 2A , 2B Both 2C and 2C illustrate the additional notation used within this disclosure. Figure 2A The diagram shows the effect on spin. s n The notation for the single-spin operation 202. The single-spin operation is derived from... Figure 2A The middle is marked as α , β and γ It consists of three Euler rotations, which describe a sequence of active rotations about the y-axis and z-axis. ,in These angles can be translated to x- and y-rotations that can be directly achieved by electromagnetic pulses in an NMR device.

[0036] Figure 2B This shows the effect on spin n and m above as The notation for the double spin operation 204. The double spin operation 204, alternatively referred to as the Rzz ​​gate, is defined by... Figure 2B The middle is marked as θ The evolution angle provided indicates the duration of evolution under scalar coupling between two spins of interest. This can be achieved in liquid NMR experiments via scalar J coupling between nuclei. The full evolution time of the Rzz ​​gate in the experiment... T Through equations And related to the evolution angle, among which J It represents the coupling strength between two nuclei of interest, given in Hz.

[0037] Figure 2C It shows the formation Figure 2A and 2B A portion of the Pauli spin matrix.

[0038] Figure 2B Each of the Rzz ​​gates described herein has a certain free parameter. The free parameter is set to give a specific permutation, including the permutations described below.

[0039] Quantum operations can be expressed as a predetermined set of permutation operations on the energy states of a system. The set of permutation operations can be performed on the system by applying a set of electromagnetic (EM) pulses.

[0040] For the sake of simplicity, the methods for the elements mentioned in this paper are discussed as including two energy states, such as a target element, an auxiliary element, and a reset element that include two energy states. This could, for example, include spin-1 / 2 particles or qubits for the target system or the reset system.

[0041] As disclosed herein, achieving hyperpolarization of one or more target spins involves increasing the probability of the system being in a state of a target element having a ground state of 0. Quantum operations that increase the probability of a target element having a state in ground state 0 (e.g., 000, 001, 010, 011) and decrease the probability of a target element having a state in excited state 1 (e.g., 100, 101, 110, 111) can be performed to increase hyperpolarization.

[0042] The conditions for generating (1) a state with a target element in ground state 0 or (2) a state with a target element in excited state 1 may include: exchanging (a) a state with a target spin in state 0 and a low probability with (b) a state with a target spin in state 1 and a higher probability.

[0043] Various quantum operations can be conceived to achieve the operations mentioned above. For example, U.S. Patent No. 10,560,096 describes example quantum operations that can be arranged to generate at least some of the conditions mentioned above.

[0044] Some quantum operations involve permutations that are challenging to implement. These challenging operations may require undesirably longer quantum circuits, longer operation times, etc. Efficient permutations are desirable.

[0045] In at least some example embodiments, this disclosure provides quantum operations that can partially optimize both polarization (hyperpolarization) and operation time in a single iteration (with only one iteration). For example, in at least some example embodiments, the quantum operation can be applied between the populations of the system's states according to the following: First system energy state 000 → Second system energy state 000; First system energy state 100 → Second system energy state 001; First system energy state 001 → Second system energy state 010; First system energy state 010 → Second system energy state 011; First system energy state 111 → Second system energy state 100; First system energy state 011 → Second system energy state 101; First system energy state 101 → Second system energy state 110; and First system energy state 110 → Second system energy state 111.

[0046] In the following text, the above permutation is generally referred to as the optimized permutation.

[0047] The optimized permutation can also be expressed as: (P000, P100, P001, P010, P111, P011, P101, P110).

[0048] To be further clear, if Given the population or probability of state |s1, s2, s3>, the population of the system's states can initially be expressed as: (P000, P001, P010, P011, P100, P101, P110, P111).

[0049] The optimized quantum operation (i.e., the optimized permutation above) will change the sequence to: (P000, P100, P001, P010, P111, P011, P101, P110).

[0050] The optimized quantum operations can also be expressed as the following matrices.

[0051] .

[0052] Consider variations of optimized quantum operations. For example, consider optimized permutations that include operations on additional elements other than the target element, or removal of certain operations, or include rearrangement (e.g., using inverse elements) and rearrangement or reordering of the sequence.

[0053] Optimized quantum operations can be achieved via electromagnetic pulses that drive transitions in a spin system.

[0054] Figure 3A This is a schematic diagram illustrating an example quantum circuit 302 acting on a three-spin system according to the described optimized quantum operations. Figure 3A In the circuit 302, the circuit corresponds to a process with a single iteration (quantum operation), where the horizontal lines indicate spin states or qubits, the top line is the target spin or qubit s1, and the middle and bottom horizontal lines indicate the auxiliary spin s2 and the reset spin s3, respectively. Figure 3A The quantum circuits include single-spin rotation and two-spin free evolution (Rzz) gates. Single-spin rotation operates on a single spin (one of the three spins s1, s2, or s3), while Rzz ​​gates operate on two spins (e.g., s1 and s2, s1 and s3, or s2 and s3).

[0055] The circuit 302 shown is used to hyperpolarize the first spin, represented as S1. Figure 3A and 3BAs shown, various operations can be performed on each of the three spins, where unconnected horizontally aligned operations can occur simultaneously or sequentially. Furthermore, according to various embodiments, if an operation occurs directly after or before a blank space on one or more of its spin channels, it can be moved to an earlier or later time.

[0056] think Figure 3A The quantum circuits in this context will correspond to or provide variants with similar performance to optimized quantum operations. For example, Figure 3B The quantum circuit 303 involves: additional single-spin rotations 304 on the second and third spins will achieve the same amount of hyperpolarization for the target spin after a single iteration. In another example (not shown), the adjustment... Figure 3A The angle of rotation in the middle, while keeping the rotation the same (for example, ( Alternatively, the evolution angle can be adjusted, which alters the evolution itself, but in conjunction with other operations (e.g., ,in Indicates the relationship with spin n about the z-axis π When rotations combine, they lead to equivalent evolution, and so on.

[0057] The rotations and manipulations in quantum circuits 302 and 303 can be translated into NMR / MRI pulse sequences. For example, these pulse sequences can be programmed into an NMR / MRI machine and implemented using the machine's firmware.

[0058] Figure 4 This is a schematic diagram illustrating an example of how the quantum circuit depicted in Figure 3 can be implemented in an NMR system. Figure 4 In the diagram, each row represents a spin (i.e., s1, s2, and s3), and horizontally aligned pulses can be applied simultaneously or sequentially. A two-spin operation (e.g., exemplary two-spin operation 403) is implemented using free evolution periods of the two spins of interest, marked by segments listing the two spins and their associated evolution angles.

[0059] A single-spin operation (e.g., a single-spin rotation 402) is shown as a translation from ZYZ Euler angles to XYX Euler angles to allow for implementation on a spectrometer. This can be accomplished using one, two, or three pulses according to the precise angle. Alternatively, the same effect of a ZYZ rotation can be achieved via a single pulse with a certain phase in the xy plane, depending on the initial magnetization of the spin, even if the precise operator representations of the two rotations are not equal (i.e., a ZYZ rotation of a single vector can always be performed by a rotation axis about the xy plane). φ Angle θIt can be reproduced by a single rotation, but this is not the case for rotations of a set of vectors.

[0060] The frequency of the EM pulses influencing the substitution operation can be determined based on the energy difference between system levels corresponding to the exchange states. The energy difference associated with each pair of system levels can be determined, for example, by a spectroscopic measurement performed on the system. Each exchange operation can be associated with one EM pulse from a set of pulses or with multiple EM pulses. For example, multiple EM pulses can be applied such that the substitution operation is influenced via intermediate system levels. Furthermore, since the EM pulses are determined based on the energy difference between the states corresponding to a specific transition, it is possible that if multiple pairs of system levels are separated by the same energy difference, a single EM pulse can be associated with multiple pairs of system levels. The EM pulses can be... π pulse.

[0061] Figure 4 The set of EM pulses applied to different spins can be applied simultaneously or sequentially, or some can be applied simultaneously while others are applied sequentially.

[0062] For the Rzz ​​gate / quantum operation 403, the spins of interest are preferably decoupled together from the other spins and the environment to allow evolution under J-coupling, which has two spins. n and m The form between Therefore, the time during which other spins and the environment are decoupled from these spins allows for decoupling via the operator. The evolution, in which T It refers to the duration of the evolutionary period. This is achieved through the time span of evolution. π Pulses are used to decouple interactions with other spins and the environment. Spin n and m The simultaneous application of π pulses at the halfway point of the evolutionary period on both may render all other interactions ineffective on the state of these spins at the end of the evolutionary period.

[0063] The effect of the π pulse itself can be removed by applying a second identical π pulse at the end of the evolutionary period.

[0064] When considering more than two spins, it is preferable to also decouple the third spin from the environment, while ensuring that it remains decoupled from the two spins intended to evolve under its J coupling. This can be accomplished by applying two π pulses to the third spin, but placing these pulses at a time such that the first two spins remain unaffected by the third spin at the end of the evolution period. In a simplified example, at the end of the evolution period... and A π pulse is added to the third spin at the point. If the spin is coupled to an environment in which magnetization rapidly relaxes, more complex decoupling schemes are possible and may be necessary.

[0065] Figure 5 An example of the above implementation in an NMR pulse sequence is shown, where four π pulses are used to help maintain the signal by reducing the intermittent transfer of magnetization to the environment, which can then relax rapidly and lead to signal loss. Additionally, this type of scheme, generally referred to in the literature as dynamic decoupling, utilizes the variable phase of the pulses, which can help reduce the effects of errors in the pulse power.

[0066] In the illustrated embodiment, a dual spin gate appears between spins S1 and S3 and follows a dynamic decoupling scheme to decouple the two spins from S2 and the environment, thereby allowing the desired evolution to occur within a single Rzz ​​gate. The phase of this scheme can reduce the influence of experimental errors. The delay time τ is determined based on the gate's evolution angle, the coupling strength between spins S1 and S3, and the pulse length. A refocusing pulse is also applied to the uncoupled spin S2 to ensure it is decoupled from the environment.

[0067] It may also be necessary to require inverted pulses on other spins in the system to ensure that those are also decoupled from the environment.

[0068] Various implementations of dynamic decoupling have been previously studied.

[0069] In systems where one of the three sets of dual-spin evolution periods requires a significantly longer evolution time than the other two, it is possible to reduce the required time using a compound gate, according to the precise J-coupling value. Specifically, in the spin... i and j Executing the Rzz ​​gate in between is equivalent to executing the next three operations sequentially: spin. i and k The SWAP gate between them, followed by spin. k and j The Rzz ​​gate between them, followed by spin. i and k Another SWAP gate between, where spin i , j and k This represents any permutation of spins 1, 2, and 3.

[0070] The disclosed method for exchanging the target state and the optimized permutation operation can be used once (single iteration) or iteratively. Iterative implementation can achieve higher polarization. The number of EM pulse sets applied to achieve convergence, or the number of iterations, can be determined by, for example, the desired accuracy and precision of the operation. The number of iterations can be a predetermined number of iterations, which is related to the number of iterations predicted when the system reaches the desired fidelity or when the system changes from the ideal state by a predetermined amount. Alternatively or additionally, the system can be monitored such that the EM pulse set is applied until it is determined that the system has reached the desired fidelity or when the system has changed from the ideal state by a predetermined amount. The ideal state can be a maximum mixture state (MMS).

[0071] In an iterative implementation, after each step, reset elements may need to be reset. This may involve waiting for the relaxation time of the reset elements to facilitate the reset of at least some of them from a higher reset system level to a lower reset system level. This partially resets the state of the reset elements to their initial (equilibrium) state. The elapsed time period can be on the order of the relaxation time of the reset system.

[0072] In some embodiments, the relaxation time of the reset system can be an effective relaxation time that is shorter than the inherent relaxation time of the reset system. The effective relaxation time can be the result of manipulating the reset system to reduce the relaxation time from the inherent relaxation time to the effective relaxation time. For example, manipulating the reset system can include performing optical polarization, optical pumping, or dynamic nucleation polarization during the elapsed time period.

[0073] The disclosed methods for exchanging target states and optimizing permutation operations may involve a pre-polarization step. Pre-polarization may involve using techniques for first polarizing the target system (and / or auxiliary system) and then applying the operations as described herein.

[0074] For example, in one of them is 13 C and one of them is 1 In the realization of H nuclear spin (discussed in more detail below), techniques such as refocusing INEPT can be used to first target the nuclear spin of H. 13 The C nuclear spin is polarized and then the quantum operations described above are applied. Similarly, in implementations involving electron spin, techniques such as dynamic nuclear polarization (DNP) can be used to first increase the polarization of all nuclear spins in the system, and then follow up with the use of... Figure 3A , 3B Hyperpolarization is performed by one of the quantum circuits 302 and 303 in the process.

[0075] The following describes exemplary embodiments. It should be understood that the exemplary embodiments are not intended to limit the scope of this disclosure to the embodiments described herein. Those skilled in the art can make changes, modifications, and variations to the embodiments without departing from the scope defined solely by the appended claims.

[0076] Example Implementation I: Metronidazole - 15 Hyperpolarization of N3 The disclosed pathway can be used to assist spin-active nitrogen nuclei. 15 Imaging of N-type metronidazole. 15 N is significantly less sensitive to magnetic fields than protons, and is therefore much more difficult to observe in experiments.

[0077] exist Figure 6 In the embodiments disclosed in A and 6B, the N1 site of metronidazole is taken into consideration. 15 Hyperpolarization of the N nucleus, thereby utilizing another [site] at the N3 site 15 The N nucleus and the proton at the H4 site.

[0078] Figure 6 illustrates the effect when applied to systems with S1 and S2 in the same channel (such as for the three spins listed above). Figure 4 An example implementation of a pulse sequence is provided. To ensure that the pulse affects only one of those spins at a time, a selective pulse (such as a Gaussian pulse) is used, and the transmitter frequency is shifted between two resonant frequencies such that it resonates with the indicated spin when the pulse is applied. The transmitter frequency can be shifted either by explicitly changing the transmitter frequency or by adding a linearly varying phase to the pulse to create an effective frequency offset. A 2 ms length was found. The pulse is used to fully excite the spin of interest while leaving other spins largely unaffected.

[0079] The length of the evolution period is determined by the intramolecular J coupling constant, which can be obtained by measuring the distance between splitting peaks in the spectrum. For example, the values ​​of the three spins of interest are... J 12 = 1.65 Hz J 13 = 2.01 Hz and J 23 =9.15 Hz. Based on these values, Figure 6 The lengths of the evolution periods shown are 54.6 ms, 248.8 ms, 404.0 ms, 72.9 ms, and 248.8 ms from left to right.

[0080] The system has been simulated in MATLAB® by time evolution of the density matrix describing all spins in the system based on the Hamiltonian, characterized by terms describing the Zeeman interaction, J-coupling, and the applied RF pulses. When the nitrogen nucleus is pre-polarized using the refocused INEPT pulse sequence, the application of the pulse sequence described above results in a polarization at the N1 site that is 1.41 times larger than the polarization obtained solely from refocused INEPT.

[0081] Example Implementation II: Metronidazole - 13 C2, 15 hyperpolarization of N2 As an alternative to Example Example I, metronidazole may also have two... 15 N marker site and 2 13 C-labeled sites. In this embodiment, the target spin is the N3 nitrogen site, where the labeled carbons at C2 and the methyl site act as auxiliary and refresh spins.

[0082] Figure 7 This illustrates the effect when applied to systems with S2 and S3 on the same channel (for the spins listed above). Figure 4 An example implementation of the pulse sequence. Since the three spin ratios under consideration are separated much better in the previous example, shorter band-selective Gaussian pulses can be used. A 0.2 ms pulse was found. The pulse length is sufficient to excite the spin of interest while leaving other spins largely unaffected.

[0083] The length of the evolution period is determined by the intramolecular J-coupling constant, which can be obtained by measuring the distance between splitting peaks in the spectrum. For example, the estimated J-coupling values ​​for the three spins of interest are... J 12 = 15 Hz J 13 = 2 Hz and J 23 = 50 Hz. Based on these values, Figure 7 The evolution time intervals shown are 10 ms, 250 ms, 44.4 ms, 13.3 ms, and 250 ms from left to right.

[0084] The system has been simulated in MATLAB® by time evolution of the density matrix describing all spins in the system based on Hamiltonians characterized by terms describing Zeeman interactions, J-coupling, and the applied RF pulses. When all three nuclei are pre-polarized using a refocused INEPT pulse sequence from a single proton, the application of the pulse sequence described above results in a polarization at the N1 site that is 1.31 times larger than the polarization obtained solely from refocused INEPT.

[0085] In applications that rely on alanine or lactic acid, spin-activated carbon cores 13 C is less sensitive to magnetic fields than protons, and therefore can exhibit an increased signal in observation through transfer polarization from protons. Alanine- 13 C3 and lactic acid - 13 Both C3 and C3 are characterized by similar structures and coupling constants, and are therefore described together.

[0086] In one example embodiment, the C1 site of alanine or lactate is considered. 13 Hyperpolarization of the C nucleus. Other example embodiments may include, for instance, another [core] concentrated at the C2 site. 13 The C nucleus or a proton attached to the C2 site.

[0087] Figure 6 The pulse sequence shown can also be applied to this system because S1 and S2 are again on the same channel. The length of the pulses used must be carefully chosen to ensure that other spins remain largely unaffected, while also ensuring that the pulses adequately excite the full frequency range of the spins of interest. The large J-coupling between S2 and S3 suggests that short pulses are suitable for this system, but the proximity of S3 to the resonance frequency of another proton requires longer pulses to selectively excite S3. A 300 μs pulse was found. The pulse is designed to simultaneously address the requirements arising from large J-coupling and small resonance differences.

[0088] In alanine, the values ​​of the three spins of interest are... J 12 = 54.0 Hz J 13 = 5.0 Hz and J 23 = 145.1Hz. A similar value is estimated for lactic acid. Based on these values, Figure 6 The lengths of the evolution periods shown are 3.4 ms, 100.0 ms, 12.3 ms, 4.6 ms and 100 ms from left to right.

[0089] The system has been simulated in MATLAB® by time evolution of the density matrix describing all spins in the system based on Hamiltonians characterized by terms describing Zeeman interactions, J-coupling, and the applied RF pulses. When the carbon nuclei are pre-polarized using the refocused INEPT pulse sequence, the application of the pulse sequence described above results in polarization at the C1 site that is 1.31 times larger than the polarization obtained solely from refocused INEPT.

[0090] The length of the total pulse sequence can 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 S1 and S3 at the end of the sequence can be replaced by a SWAP gate between S2 and S3 followed by an Rzz gate between S1 and S2. The trailing SWAP gate between S2 and S3 is omitted here because it does not affect the final state of S1. This reduces the required evolution time from 100 ms to 19.6 ms without affecting the finalization of S1. Furthermore, this reduces the amount of relaxation occurring during the sequence (not considered here), and is therefore expected to lead to an overall improvement in performance.

[0091] Embodiments of this disclosure provide a method for managing systems for hyperpolarized spin. The method utilizes a set of EM pulses that influence permutation operations between system state pairs implementing quantum circuits.

[0092] The disclosed method can be executed by software. In light of this description, the coding of the software used to implement this method is within the scope of those skilled in the art. The method may comprise more or fewer processes than those shown and / or described, and may be executed in different orders. Computer-readable code that can be executed by at least one processor of an electronic device to perform the method can be stored in a computer-readable storage medium (such as a non-transitory computer-readable medium). The device can also be configured to apply or initiate applications of EM pulses as described herein, for example via an EM pulse generator.

[0093] Embodiments of this disclosure can be represented as a computer program product stored on a machine-readable medium (also referred to as a computer-readable medium, processor-readable medium, or computer-usable medium having computer-readable program code embodied therein). A machine-readable medium can be any suitable tangible, non-transitory medium, including magnetic, optical, or electrical storage media, including floppy disks, compact disk read-only memories (CD-ROMs), memory devices (volatile or non-volatile), or similar storage mechanisms. A machine-readable medium can contain various sets of instructions, sequences of code, configuration information, or other data that, when executed, cause a processor to perform the steps in the methods according to embodiments of this disclosure. Those skilled in the art will appreciate that other instructions and operations necessary to implement the described implementations can also be stored on a machine-readable medium. Instructions stored on a machine-readable medium can be executed by a processor or other suitable processing device and can be interfaced with circuitry to perform the described tasks.

[0094] While the foregoing description provides examples of one or more apparatuses, methods, or systems, it should be understood that other apparatuses, methods, or systems may fall within the scope of the claims as interpreted by those skilled in the art.

Claims

1. A method for managing a system, the system comprising a target system having a target element having a target system energy level, the system comprising an auxiliary system having an auxiliary element having an auxiliary system energy level, the system comprising a reset system having a reset element having a reset system energy level, the system having a system energy level set, the system energy level set comprising a combination of the target system energy level, the auxiliary energy level, and the reset system energy level, the method comprising: Apply one or more operations to: Increase the probability of the target system's energy level having a target element in a lower energy state; And the probability of reducing the energy level of the target system with the target element in a higher energy state.

2. The method of claim 1, wherein each of the target system level, the auxiliary level, and the reset system level is binary.

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

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

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

6. The method of claim 3, wherein the one or more operations generate a state permutation of the system energy levels such that at least one of the following occurs: The first system energy states 001 and 011 are moved to any of the following second system energy states: 100, 101, 110, and 111; and The first system energy states 100 and 110 are moved to any of the following second system energy states: 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 following occurs: The first system energy states 000 and 010 are either moved or maintained to any of the following system energy states: 000, 001, 010, and 011; and The first system energy states 111 and 101 are moved or maintained to any of the following system energy states: 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 following permutations occur: i. The system energy state 000 is maintained; ii. The first system energy state 100 is moved to the second system energy state 001; iii. The first system energy state 001 is moved to the second system energy state 010; iv. The first system energy state 010 is moved to the second system energy state 011; v. The first system energy state 111 is moved to the second system energy state 100; vi. The first system energy state 011 is moved to the second system energy state 101; vii. The first system energy state 101 is moved to the second system energy state 110; as well as viii. The first system energy state 110 is moved to the second system energy state 111.

9. The method of claim 1, further comprising one or more alternative 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 include applying an electromagnetic pulse.

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

13. The method of claim 12, wherein the prepolarization is achieved by magnetic resonance hyperpolarization technology.

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

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

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

17. The method of claim 1, wherein one or more operations exchange an instance of a target system energy level that is in the lower energy state and has a low probability of being in the lower energy state with an instance of a target element that has a high probability of being in the higher energy state and has a high probability of being in the higher energy state.

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 as described in 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 as described in any one of claims 1-16.

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