A chemical ground state energy solving method and device based on dissipative dynamics simulation

Abstract

The application discloses a chemical ground state energy solving method and device based on dissipation dynamics simulation, and the method comprises the following steps: a Lindblad dissipation generator containing only a single transition operator is constructed, the transition operator is configured to force the quantum state to only transition from a high energy level to a low energy level; a single auxiliary quantum bit is introduced, a non-unitary dissipation evolution corresponding to the transition operator is mapped to a unitary evolution on a joint main system and auxiliary quantum bit, and a partial trace operation is performed on the auxiliary quantum bit to construct a dissipation quantum channel; the dissipation quantum channel is combined with a coherent evolution driven by a system Hamiltonian to form a single complete evolution mapping at each time step; the single complete evolution mapping is iteratively performed until the system converges, and the ground state energy is measured and output. By constructing a one-way dissipation Lindblad generator and introducing a single auxiliary quantum bit, the system is determined to converge to the ground state from an arbitrary initial state, the quantum resource requirement is reduced, and high-precision ground state energy solving is realized.

Description

Technical Field

[0001] This invention relates to the fields of quantum computing and quantum simulation technology, and in particular to a method and apparatus for solving the chemical ground state energy based on dissipative dynamics simulation. Background Technology

[0002] In the interdisciplinary field of modern quantum information science and computational chemistry, simulating the ground-state properties of many-body quantum systems using quantum computers is considered one of the most promising killer applications. From the analysis of strongly correlated electron systems in materials science to the study of catalytic reaction mechanisms of complex drug molecules, the precise solution of ground-state energy has always been a core physical requirement. However, from the rigorous perspective of computational complexity theory, solving for the ground state of arbitrarily few-body Hamiltonians is a QMA-hard (Quantum Merlin Arthur-hard) problem. This means that academia and industry generally do not expect the existence of a universal and efficient quantum algorithm that can efficiently prepare the ground state for all many-body Hamiltonians in polynomial time. Due to this limitation of theoretical computational hardness in the worst case, the academic community has turned to developing quantum algorithms that rely on specific physical assumptions or heuristic mechanisms, hoping to achieve breakthroughs in systems with practical physical and chemical significance.

[0003] In the current landscape of quantum chemical ground state energy solutions, two main types of representative algorithms dominate: quantum phase estimation (QPE) algorithms for the era of fault-tolerant quantum computing (FTQC), and variational quantum eigensolvers (VQE) for the era of noisy intermediate-scale quantum (NISQ).

[0004] Quantum phase estimation (QPE), a cornerstone theoretical algorithm in quantum computing, operates primarily through a "post-selection" operation within the energy domain. The QPE algorithm first requires constructing a pure or mixed state that is easily prepared on a quantum circuit as a trial state. Subsequently, phase information is extracted using complex controlled unitary evolution and inverse quantum Fourier transform, and its energy state is measured and evaluated. The success rate of the algorithm is strictly dependent on the initial experimental state and the target true ground state. The degree of overlap between them is defined as follows: Depending on the specific implementation path of different algorithms, the computational resource cost of the standard QPE algorithm is typically... or There is a positive correlation, and currently known post-QPE derivative algorithms that are close to optimal complexity also exist. The scaling dependency. This means that in order for the QPE algorithm to provide theoretical guarantees within a reasonable computation time, it is necessary to presuppose the existence of a state that can be efficiently prepared and has a sufficiently large (usually required) similarity to the true ground state. The quantum state of overlap.

[0005] Variational quantum eigenvalue solvers (VQEs) employ a radically different theoretical paradigm. Based on the classical Rayleigh-Ritz variational principle, they aim to adapt to current noisy physical hardware by significantly reducing the depth requirements of quantum circuits. VQE algorithms operate through a hybrid closed-loop architecture of classical and quantum computers: the quantum processor executes a parameterized quantum circuit (Ansatz) consisting of a series of parametric quantum gates (such as single-qubit rotation gates and multi-qubit entanglement gates) to prepare the experimental wavefunction and measure the expected energy of the system; subsequently, a classical optimizer takes over control, updating the parameters in the quantum circuit using gradient descent or gradient-free optimization strategies based on the measured energy feedback or energy gradient information, driving the experimental state to slide towards the lower energy bound in Hilbert space. Because it does not require maintaining an extremely long quantum coherence time, VQE is widely considered the most practical tool for chemical simulations on recent quantum devices.

[0006] Although quantum phase estimation algorithms and variable quantum eigenvalue solvers have achieved a great deal of research results within their respective applicable theoretical frameworks, existing technologies have revealed insurmountable systemic defects and objective bottlenecks when faced with the task of solving the ground state of complex chemical molecules on a large scale and with strong correlations.

[0007] In quantum phase estimation (QPE) algorithms, the primary challenge is the extremely demanding hardware resource overhead. The controlled evolution module of the QPE algorithm not only requires the introduction of a large number of ancilla qubits, but its quantum circuit depth also increases exponentially or in higher-order polynomial terms with the required energy precision. This rigid requirement for ultra-deep quantum circuits, ultra-long coherence times, and extremely high quantum gate fidelity is completely unattainable on existing and even early fault-tolerant quantum computing hardware. Besides the hardware gap, the QPE algorithm also suffers from a fatal "post-selection collapse" risk in its algorithmic logic. Since the algorithm essentially projects and truncates the energy eigenspace of the input state, it only attempts to retain components that have non-zero overlap with the target ground state. Once the input experimental state is completely orthogonal to the real ground state (i.e., the initial overlap is zero), the algorithm suffers from a critical "post-selection collapse" risk. In strong correlated chemical systems, the overlap of experimental states decays exponentially with the number of particles in the system, tending towards zero. In such cases, the QPE algorithm based on post-selection will completely fail, and the success probability will drop directly to zero. In practical large-scale many-body physics and complex chemical systems, finding or guessing a high-quality initial experimental state that satisfies the assumption of non-zero overlap is itself an extremely difficult technical barrier.

[0008] In the realm of variational quantum eigenvalue solvers (VQE), the core flaw stems from the scalability failure of classical-quantum hybrid optimization architectures in large-scale complex systems. First, VQE algorithms suffer from the "Barren Plateaus" phenomenon. As the scale of molecular systems and the number of qubits increase, the cost function of parameterized quantum circuits becomes extremely flat across a vast parameter space, causing its gradient with respect to the circuit parameters to decay exponentially to zero. In this extremely flat region where gradients vanish, classical optimizers not only fail to obtain effective guidance but also require an exponential increase in the number of measurement samples, completely negating the potential advantages of quantum computing. Second, even if the Barren Plateaus are avoided, the optimization landscape of the VQE algorithm's loss function is extremely complex and rugged, riddled with numerous high-dimensional local minima. Recent academic research indicates that even finding local minima in thermally perturbed quantum systems often constitutes a computational hardness barrier for classical computers. Since ground state solution is essentially about finding the global optimum, VQE is extremely prone to getting stuck in local optima in complex parametric terrains, and cannot output the true ground state energy. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method and apparatus for solving the chemical ground state energy based on dissipative dynamics simulation. This method addresses the problems of post-selection collapse risk and excessive hardware resource consumption faced by existing quantum phase estimation algorithms due to their reliance on the overlap between the initial experimental state and the target ground state, as well as the problems encountered by existing variable quantum eigenvalue solvers in large-scale systems due to their classical-quantum hybrid optimization architecture, which suffer from gradient exponential decay and local minima traps.

[0010] To achieve the above objectives, this invention provides a method for solving the chemical ground state energy based on dissipative dynamics simulation, comprising the following steps: constructing a Lindeblad dissipative generator containing only a single transition operator, wherein the transition operator is configured to force the quantum state to transition only from a high energy level to a low energy level; introducing a single auxiliary qubit, mapping the non-unitary dissipative evolution corresponding to the transition operator to a unitary evolution on the joint main system and the auxiliary qubit, and performing a bias operation on the auxiliary qubit to construct a dissipative quantum channel; combining the dissipative quantum channel with the coherent evolution driven by the system Hamiltonian to form a single complete evolution mapping in each time step; iteratively executing the single complete evolution mapping until the system converges, measuring and outputting the ground state energy.

[0011] The transition operator in the eigenstate of the target quantum system Expand below:

[0012]

[0013] Wherein, K is the transition operator; , For the eigenstates of the target quantum system; , A represents the corresponding eigenvalue; A is the local Hermitian coupling operator. Let H be the system Hamiltonian, s be the time-integral variable, and i and j be the eigenstate indices. This is a time-domain filtering function. It is a frequency domain filtering function; The energy is the ground state energy; the frequency domain filtering function is applicable to any non-negative energy difference. satisfy , making

[0014]

[0015] The step of introducing a single auxiliary qubit, mapping the non-unitary dissipative evolution corresponding to the transition operator to a unitary evolution on the joint master system and the auxiliary qubit, and performing a bias operation on the auxiliary qubit to construct a dissipative quantum channel includes:

[0016] Hermitian-expanded Hamiltonians of the joint master system and auxiliary qubits are constructed based on the aforementioned transition operator K. The non-unitary dissipative evolution is mapped to a unitary evolution on the joint system. , where τ is the short time step; The conjugate transpose of the transition operator K;

[0017] After each of the aforementioned short time steps, a bias operation is performed on the auxiliary qubit:

[0018]

[0019] in, This is the system density matrix after the partial trace operation; This indicates the calculation of the bias trace over the auxiliary qubit. The initial state for the auxiliary qubit; The system density matrix;

[0020] The deviation operation is

[0021]

[0022] Approaching the Lindblad dissipative evolution, in which... For Lindblad dissipative supercomputers.

[0023] The frequency domain filtering function Constructed using Gevrey-class functions, the time-domain transformation of the Gevrey-class functions. With superpolynomial-level decay, the time integral in the transition operator is discretized and truncated by the Gevrey-type function within a finite time-domain truncation interval.

[0024] The discretization truncation includes: setting a truncation upper limit. and grid spacing With a uniform grid and trapezoidal integral weights Sampling was performed; among which, This is the sampling point index, with a value range of [value range missing]. The transition operator is approximately in discretized form:

[0025]

[0026] in, For discretized transition operators, Number of grid divisions, For the first One sampling point;

[0027] The Hermitian dilatation Hamiltonian is approximately decomposed into:

[0028]

[0029] in, For discretized Hermitian dilatational Hamiltonian; For auxiliary bit control matrix, , For Pauli operators, Indicates taking the real part, This indicates taking the imaginary part; It is a sequence operator.

[0030] For the sequence operator Applying second-order Trout decomposition, the unitary evolution on the joint system is approximated as:

[0031]

[0032] The coherent evolution combination driven by the dissipative quantum channel and the system Hamiltonian is implemented using a first-order Trout formula, and a single complete evolution mapping is:

[0033] ;

[0034] in, This is the system density matrix after the (m+1)th iteration; H is the system density matrix after the m-th iteration; H is the system Hamiltonian; τ is the short time step. The coherent unitary evolution driven by the system Hamiltonian; This is a dissipative quantum channel.

[0035] The total number of iterations M performed in the iteration process satisfies the following relationship with the preset tolerance error ε:

[0036]

[0037] in, Indicates an asymptotic upper bound.

[0038] In another aspect, the present invention provides a device for solving the chemical ground-state energy based on dissipative dynamics simulation, comprising:

[0039] A dissipation generator building module is used to build a Lindblad dissipation generator containing only a single transition operator, which is configured to force quantum states to transition only from high energy levels to low energy levels.

[0040] An auxiliary bit mapping module is used to introduce a single auxiliary qubit, map the non-unitary dissipative evolution corresponding to the transition operator to a unitary evolution on the joint master system and the auxiliary qubit, and perform a bias operation on the auxiliary qubit to construct a dissipative quantum channel.

[0041] The evolutionary combination module is used to combine the dissipative quantum channel with the coherent evolution driven by the system Hamiltonian to form a single complete evolutionary mapping in each time step.

[0042] The iterative convergence module is used to iteratively execute the single complete evolution mapping until the system converges to the target ground state and outputs the ground state energy.

[0043] In another aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method for solving the chemical ground state energy based on dissipative dynamics simulation.

[0044] As can be seen from the above technical solutions, the advantages of the present invention are:

[0045] In this invention, the Lindeblad dissipative generator constructed by the transition operator is a fully positive definite trace-preserving mapping. The repeated iterations of its single complete evolution mapping constitute a deterministic dissipative cooling trajectory, enabling the system to converge to the target ground state from any initial state without the need for searching or optimizing in the parameter space. This fundamentally eliminates the dependence on the overlap between the initial experimental state and the ground state and completely avoids gradient vanishing and local minima traps that occur during parameter optimization. At the same time, the expanded Hamiltonian only requires a single auxiliary qubit to map the non-unitary dissipative evolution to a unitary evolution and perform a biased trace operation to construct a dissipative quantum channel, which greatly reduces the quantum hardware resource requirements. This provides a chemical ground state energy solution scheme with strict convergence guarantee and optimal time-precision complexity for the early era of fault-tolerant quantum computing.

[0046] Without any classical cost optimizer intervention or training process, this invention simplifies the control logic and reduces the size of the quantum circuit by constructing a Lindeblad dissipation generator containing only a single transition operator and forcing quantum states to transition only from high to low energy levels, utilizing a single auxiliary bit. The dissipation quantum channel constructed by the algorithm and the coherent evolution driven by the system's Hamiltonian combine to form a single complete evolutionary mapping. This mapping is iterated repeatedly until the system converges, ensuring that even when the dissipation generator, which is the essence of the CPTP mapping, is orthogonal to the ground state (zero initial overlap), the system can still reach the target energy state with 100% determinism along the dissipation cooling trajectory, completely eliminating the "post-selection collapse" and "local minima trap" crises in existing technologies. This ensures that even in the era of early fault-tolerant quantum computers with extremely limited computing resources, this invention can still achieve ultra-large-scale and high-precision calculations of ground-state physical properties and energy calibration for strongly correlated electronic systems and complex chemical catalytic reaction molecules. Attached Figure Description

[0047] Figure 1 A flowchart of a method for solving the chemical ground state energy according to an embodiment of the present invention;

[0048] Figure 2 A single complete evolution mapping quantum circuit diagram provided for embodiments of the present invention;

[0049] Figure 3 for Figure 1 Iterative evolution flowchart of step S4;

[0050] Figure 4 This is a schematic diagram of a chemical ground state energy solving device provided in another embodiment of the present invention;

[0051] In the attached figures, the following labels are used:

[0052] 1-Methods for solving chemical ground state energy;

[0053] 2-Apparatus for solving the chemical ground state energy;

[0054] 20 - Dissipation generator building blocks;

[0055] 21-Auxiliary bit mapping module;

[0056] 22-Evolutionary Combinatorial Module;

[0057] 23-Iterative convergence module;

[0058] Steps S1~S4. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0060] The chemical ground state energy solution proposed in this invention is based on dissipative dynamics simulation. Its formation process is a deep exploration of thermodynamic physical intuition, accompanied by the design and analysis of digital simulation algorithms for open quantum systems.

[0061] The initial physical intuition of this invention derives from macroscopic thermodynamic phenomena: whether preparing the ground state or preparing a state with a large inverse temperature. Low-energy Gibbs state ( In nature, this should be a spontaneous and easy process—simply placing the target physical system in an extremely low-temperature fridge / bath environment will cause the system to spontaneously cool to a low-energy state through heat exchange with the fridge / bath. Inspired by this thermodynamic picture, an open system is constructed to simulate this process. The dynamic equations for the weak system-fridge / bath interaction are derived using Lindblad dynamics as a mathematical tool.

[0062] The main technical challenge lies in the catastrophic consumption of hardware control resources by simulating the dynamics of open systems. Although the GKLS (Gorini-Kossakowski-Lindblad-Sudarshan) theorem states that the generator of any quantum Markov semigroup must take the Lindblad form, accurately simulating time evolution operators on a quantum computer remains a significant challenge. Traditional methods all face extremely high control costs. Most existing Lindblad simulation algorithms presuppose the ability to control transition operators. Perform block encoding. Because... Often expressed as a linear combination of Heisenberg evolution operators, constructing its block encoding inevitably requires invoking the Linear Combination of Unitaries (LCU) mechanism and complex frequency filter preparation oracles. This means that existing analog algorithms require a massive number of auxiliary qubits, directly pushing these algorithms into the era of deep fault-tolerant quantum computing, completely contradicting the original intention of designing algorithms to "run in the early fault-tolerant stage".

[0063] The evolution of this invention departs from the simulation of a real thermodynamic cold bath. Through the artificially constructed unidirectional transition operator (i.e., only allowing transitions from high energy levels to low energy levels), a set of dissipation dynamics simulation and ground state energy solvers based on a single auxiliary bit framework, with rigid theoretical guarantees and high efficiency can be formed.

[0064] To address the technical obstacles of existing fault-tolerant quantum computing algorithms (such as quantum phase estimation, QPE) which heavily rely on and are limited by the assumption of overlap between the initial experimental state and the true ground state, and existing heuristic algorithms for the noisy era (such as variable quantum eigenvalue solvers, VQE) which are prone to getting trapped in cost function-poor plateaus or local optima caused by complex optimization landscapes in large-scale parameter spaces, this invention adopts an algorithm architecture based on non-unitary dissipative dynamics simulation. By constructing a specific artificial Lindbladian evolution generator, it induces the target system to spontaneously relax to the ground state through a Markov chain, fundamentally bypassing the energy post-selection filtering mechanism. This invention can significantly reduce the circuit size requirements for complex controlled quantum gates and multiple auxiliary qubits while maintaining a 100% convergence success rate, thus providing an effective path for ground state preparation and energy solution with optimal time and accuracy complexity guarantees for quantum hardware devices limited in the early stages of fault tolerance.

[0065] The core concept of this invention is to abandon the traditional phase measurement or variational parameter closed-loop iteration mechanism based on Schrödinger unitary evolution, and instead utilize the dissipative dynamics method based on the characteristics of complete positive trace preservation mapping (CPTP). By constructing a single jump operator with strict frequency domain filtering characteristics, the high-energy quantum state components are forced to undergo unidirectional continuous "energy shoveling" to the low-energy level, thereby guiding the quantum system to evolve naturally and collapse to a unique absolute fixed point - the target ground state, and finally achieving a high-precision solution for the ground state energy.

[0066] The embodiments of this invention provide a highly refined and rigorously mathematical quantum circuit mapping process, aiming to transform the abstract Lindebride Markov semigroup evolution into a single-auxiliary-qubit quantum circuit with low resource requirements. The implementation logic of this invention is deconstructed below into several progressively detailed steps, each of which retains and analyzes the key formulas and core mechanisms for achieving unidirectional energy dissipation and error suppression.

[0067] Premise of the target system: Given a many-body target quantum system, its coherent evolution is determined by the system's Hamiltonian. Control. (Among them) Represents the true target ground state of the system. This corresponds to the ground state energy. It is assumed that the system has a finite positive energy gap, i.e., the difference between the first excited state energy and the ground state energy (Spectral gap). .

[0068] like Figure 1 The diagram shows a flowchart of a chemical ground state energy solution method 1 based on dissipative dynamics simulation according to an embodiment of the present invention. This chemical ground state energy solution method 1 includes the following steps:

[0069] S1: Construct a Lindeblad dissipation generator containing only a single transition operator, which is configured to force quantum states to transition only from higher energy levels to lower energy levels.

[0070] Unlike constructing a thermodynamic cold bath network that satisfies detailed equilibrium conditions, step S1 proposes designing a purely artificial algorithmic Lindbergh equation containing only a single controlled dissipation channel. System density matrix. (Assuming) (qubit) over time The continuous evolution dynamics are defined as the Lindeblad equations containing only a single transition operator:

[0071]

[0072] The coherent driving part on the right side of the equation Directly from the original Hamiltonian The generation, and the purely dissipative component that plays a decisive role. Then by a single transition operator Parametric configuration.

[0073] In order to force the dynamics of the entire system to converge to the ground state transition operator Using a local Hermitian coupling operator Heisenberg time-varying evolution (which can be considered as an artificial cold bath perturbation source) and a pre-designed filtering function It is defined by time integration:

[0074]

[0075] in, , For the eigenstates of the target quantum system; , A represents the corresponding eigenvalue; A is the local Hermitian coupling operator. Let H be its Heisenberg time-varying evolution, and H be the system Hamiltonian; This is a time-domain filtering function. This is a frequency domain filtering function.

[0076] Here, the integrator kernel is represented in the frequency domain. This constitutes the engine of unidirectional energy flow. The filter function must satisfy the strict negative frequency support property: for any energy difference greater than or equal to zero in the system... All are mandatory This condition perfectly blocks the matrix elements that transition from a low-energy state to a high-energy state, i.e., when... At this time, the energy conversion weight is zero. Applying it to the true ground state, we obtain:

[0077]

[0078] The above identity (where the energy of all eigenstates) All are greater than or equal to the ground state energy This ensures that the dissipation generator has no effect on the ground state, i.e. Furthermore, since coherent evolution stagnates at the ground state, it can be rigorously deduced that the target state is the asymptotic attractor and fixed point of the entire mapping.

[0079] The frequency domain filtering function Constructed using Gevrey-class functions, the time-domain transformation of the Gevrey-class functions. With superpolynomial-level decay, the time integral in the transition operator is discretized and truncated by the Gevrey-type function within a finite time-domain truncation interval.

[0080] Specifically, to implement the above integration on finite quantum hardware, this implementation introduces a Gevrey-like function to construct a frequency domain filtering function. This special smooth distribution ensures that the function strictly conforms to... While its time domain is always zero, its time domain transformation Maintain rapid decay of the superpolynomial hierarchy over time. Set a cutoff upper limit with a sufficiently large coverage width. Then, use a grid spacing of Uniform grid and its trapezoidal area weight Sampling is performed, and the optimal quadrature discretization of the integral operator is completed using the Nyquist-Shannon sampling theorem. The transition operator is approximately in discretized form:

[0081]

[0082] in, For discretized transition operators, To determine the number of grid divisions within the truncation interval, For the first There are sampling points, and the total number of sampling points is . .

[0083] S2: Introduce a single auxiliary qubit, map the non-unitary dissipative evolution corresponding to the transition operator to a unitary evolution on the joint master system and the auxiliary qubit, and perform a bias operation on the auxiliary qubit to construct a dissipative quantum channel.

[0084] Step S2 further includes: constructing the Hermitian expanded Hamiltonian of the joint master system and the auxiliary qubit based on the transition operator K, mapping the non-unitary dissipative evolution to the unitary evolution on the joint system; and performing a bias operation on the auxiliary qubit after each short time step.

[0085] Specifically, to avoid the exponential overhead of auxiliary quantum registers caused by multi-operator block encoding, this implementation uses irreversible dissipative operators that are difficult to simulate directly. This is mapped to a unitary evolution process in a higher dimension. Only one additional auxiliary qubit is introduced (initially prepared in the ground state). And construct the joint Hermitian expanded Hamiltonian for the main system-auxiliary composite system:

[0086]

[0087] in, This is the conjugate transpose of the transition operator. Through this extension operation, the original exponential form of dissipative evolution can be simulated using ordinary quantum Hamiltonian time on composite systems. To achieve indirectly, among which For short time steps. By using each short time step... After completion, a partial trace is performed on the auxiliary qubit, which physically corresponds to the measurement and is discarded if the result is useless, and then the qubit is reset. )operate:

[0088]

[0089] in, This indicates that the auxiliary qubit is used to find the bias path. To assist the initial state of the qubit, Let be the system density matrix. This trajectory projection can be... It approximates the true dissipative Markov process with extremely high precision. Theoretically, it can be rigorously proven in the sense of trace norm using Taylor expansion:

[0090] ,

[0091] in, For Lindblad dissipative superoperators, This represents the trace norm. This means that the single-bit expansion plus reset operation, as a first-order precision scheme, successfully incorporates complex non-unitary dynamics into the conventional unitary execution class of quantum circuits.

[0092] To integrate the time from negative infinity to positive infinity included in K in step S1 Implemented within a fixed-length execution cycle of quantum hardware, the discretized transition operator is... Substituting the expanded Hamiltonian and approximating the Hermitian expanded Hamiltonian as follows:

[0093]

[0094] in, For discretized Hermitian dilatational Hamiltonian; For auxiliary bit control matrix, , For Pauli operators, Indicates taking the real part, This indicates taking the imaginary part; It is a sequence operator.

[0095] When implementing discretized operator sequences using quantum gates, second-order trotter decomposition is employed. ,Right now

[0096]

[0097] This effect will be applied later. The unitary change on a qubit is denoted as Therefore, the corresponding transition operator The dissipative quantum channel can be expressed as:

[0098] .

[0099] S3: Combine the dissipative quantum channel with the coherent evolution driven by the system Hamiltonian to form a single complete evolutionary mapping in each time step.

[0100] The full Lindbladian evolution includes a coherent part and a dissipative part. At an extremely short time step , the algorithm uses the first-order Trotter formula to separate these two parts, which is approximately expressed as a serial product. The coherent part can be completed using conventional Hamiltonian simulation techniques , and the dissipative part is implemented by the dissipative quantum channel constructed in step S2 above . Therefore, the total single evolution mapping is:

[0101] ,

[0102] is the system density matrix after the m+1-th iteration; is the system density matrix after the m-th iteration; is the coherent unitary evolution driven by the system Hamiltonian.

[0103] Specifically, the quantum circuit structure of the single complete evolution mapping is as follows: the system register contains n qubits, and the auxiliary register contains 1 qubit. The system density matrix first enters the dissipative quantum channel , which acts on all n+1 qubits; then the partial trace operation is performed on the auxiliary qubit and it is discarded; the states of the remaining n system qubits enter the coherent evolution module , and the updated system density matrix is output . The coherent evolution only acts on the system qubits, and the auxiliary qubit does not participate in this stage. The quantum circuit diagram corresponding to the above single evolution is shown in Figure 2 .

[0104] S4: Iteratively execute the single complete evolution mapping until the system converges, measure and output the ground state energy.

[0105] Initialization: Introduce a single auxiliary qubit, set the initial quantum state , set the total number of evolution steps (i.e., the total number of iteration steps) to M, and the counter m=0. The total number of iteration steps is determined according to a preset allowable error , and the relationship is , that is, the total number of iteration steps increases logarithmically as the allowable error decreases.

[0106] Determine whether the current counter reaches the preset total number of steps M: if m<M, perform a single-step iterative evolution, and apply the single complete mapping constructed in step S3 to the current system density matrix to obtain Then update the counter m = m + 1 and continue the loop. If m = M, terminate the iteration and output the final quantum state. The ground state preparation is completed, and the ground state energy is measured and output. A detailed iterative flowchart is shown below. Figure 3 As shown.

[0107] The following are apparatus embodiments corresponding to the above method embodiments. This embodiment can be implemented in conjunction with the above embodiments. The relevant technical details mentioned in the above embodiments remain valid in this embodiment, and will not be repeated here to reduce repetition. Correspondingly, the relevant technical details mentioned in this embodiment can also be applied to the above embodiments.

[0108] like Figure 4 As shown, another embodiment of the present invention provides a chemical ground state energy solution device 2 based on dissipative dynamics simulation, comprising:

[0109] Dissipation generator building module 20 is used to build a Lindblad dissipation generator containing only a single transition operator, which is configured to force quantum states to transition only from high energy levels to low energy levels.

[0110] The auxiliary bit mapping module 21 is used to introduce a single auxiliary qubit, map the non-unitary dissipative evolution corresponding to the transition operator to the unitary evolution on the joint master system and the auxiliary qubit, and perform a bias operation on the auxiliary qubit to construct a dissipative quantum channel.

[0111] Evolutionary combination module 22 is used to combine the dissipative quantum channel with the coherent evolution driven by the system Hamiltonian to form a single complete evolutionary mapping in each time step.

[0112] The iterative convergence module 23 is used to iteratively execute a single complete evolution mapping until the system converges to the target ground state, and measure and output the ground state energy.

[0113] Furthermore, those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the chemical ground state energy solving device 2 can be referred to the corresponding process in the aforementioned embodiment of the chemical ground state energy solving method 1, and will not be repeated here.

[0114] Another embodiment of the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method for solving the chemical ground-state energy based on dissipation kinetics simulation (e.g.) Figure 1 (The steps shown).

[0115] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms fall within the scope of protection of the present invention.

Claims

1. A method for solving the chemical ground-state energy based on dissipative dynamics simulation, characterized in that, Includes the following steps: Construct a Lindeblad dissipation generator containing only a single transition operator, which is configured to force quantum states to transition only from higher energy levels to lower energy levels; A single auxiliary qubit is introduced to map the non-unitary dissipative evolution corresponding to the transition operator to a unitary evolution on the joint master system and the auxiliary qubit, and a bias operation is performed on the auxiliary qubit to construct a dissipative quantum channel. The dissipative quantum channel is combined with the coherent evolution driven by the system Hamiltonian to form a single complete evolutionary mapping in each time step; The single complete evolutionary mapping is iteratively executed until the system converges, and the ground state energy is measured and output.

2. The method for solving the chemical ground-state energy based on dissipative dynamics simulation according to claim 1, characterized in that, The transition operator in the eigenstate of the target quantum system Expand below: Wherein, K is the transition operator; , For the eigenstates of the target quantum system; , Here, A represents the corresponding eigenvalue; A is the local Hermitian coupling operator. Let H be the system Hamiltonian, s be the time-integral variable, and i and j be the eigenstate indices. This is a time-domain filtering function. It is a frequency domain filtering function; The energy is the ground state energy; the frequency domain filtering function is applicable to any non-negative energy difference. satisfy , making 3. The method for solving the chemical ground-state energy based on dissipative dynamics simulation according to claim 2, characterized in that, The step of introducing a single auxiliary qubit, mapping the non-unitary dissipative evolution corresponding to the transition operator to a unitary evolution on the joint master system and the auxiliary qubit, and performing a bias operation on the auxiliary qubit to construct a dissipative quantum channel includes: Hermitian-expanded Hamiltonians of the joint master system and auxiliary qubits are constructed based on the aforementioned transition operator K. The non-unitary dissipative evolution is mapped to a unitary evolution on the joint system. , where τ is the short time step; The conjugate transpose of the transition operator K; After each of the aforementioned short time steps, a bias operation is performed on the auxiliary qubit: in, This is the system density matrix after the partial trace operation; This indicates the calculation of the bias trace over the auxiliary qubit. The initial state for the auxiliary qubit; The system density matrix; The deviation operation is Approaching the Lindblad dissipative evolution, in which... For Lindblad dissipative supercomputers.

4. The method for solving the chemical ground-state energy based on dissipative dynamics simulation according to claim 3, characterized in that, The frequency domain filtering function Constructed using Gevrey-class functions, the time-domain transformation of the Gevrey-class functions. With superpolynomial-level decay, the time integral in the transition operator is discretized and truncated by the Gevrey-type function within a finite time-domain truncation interval.

5. The method for solving the chemical ground-state energy based on dissipative dynamics simulation according to claim 4, characterized in that, The discretization truncation includes: Set truncation limit and grid spacing With a uniform grid and trapezoidal integral weights Sampling was performed; among which, This is the sampling point index, with a value range of [value range missing]. The transition operator is approximately in discretized form: in, For discretized transition operators, Number of grid divisions, For the first One sampling point; The Hermitian dilatation Hamiltonian is approximately decomposed into: in, For discretized Hermitian dilatational Hamiltonian; For auxiliary bit control matrix, , For Pauli operators, Indicates taking the real part, This indicates taking the imaginary part; It is a sequence operator.

6. The method for solving the chemical ground-state energy based on dissipative dynamics simulation according to claim 5, characterized in that, For the sequence operator Applying second-order Trout decomposition, the unitary evolution on the joint system is approximated as:

7. The method for solving the chemical ground-state energy based on dissipative dynamics simulation according to claim 1, characterized in that, The coherent evolution combination driven by the dissipative quantum channel and the system Hamiltonian is implemented using a first-order Trout formula, and a single complete evolution mapping is: in, This is the system density matrix after the (m+1)th iteration; H is the system density matrix after the m-th iteration; H is the system Hamiltonian; τ is the short time step. The coherent unitary evolution driven by the system Hamiltonian; This is a dissipative quantum channel.

8. The method for solving the chemical ground-state energy based on dissipative dynamics simulation according to claim 1, characterized in that, The total number of iterations M performed in the iteration process satisfies the following relationship with the preset tolerance error ε: in, Indicates an asymptotic upper bound.

9. A device for solving the chemical ground-state energy based on dissipative dynamics simulation, characterized in that, include: A dissipation generator building module is used to build a Lindblad dissipation generator containing only a single transition operator, which is configured to force quantum states to transition only from high energy levels to low energy levels. An auxiliary bit mapping module is used to introduce a single auxiliary qubit, map the non-unitary dissipative evolution corresponding to the transition operator to a unitary evolution on the joint master system and the auxiliary qubit, and perform a bias operation on the auxiliary qubit to construct a dissipative quantum channel. The evolutionary combination module is used to combine the dissipative quantum channel with the coherent evolution driven by the system Hamiltonian to form a single complete evolutionary mapping in each time step. The iterative convergence module is used to iteratively execute the single complete evolution mapping until the system converges to the target ground state and outputs the ground state energy.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the chemical ground state energy solution method based on dissipative dynamics simulation as described in any one of claims 1 to 8.

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