Patent Application
20230267358
The present application claims the priority of Chinese Patent Application 202010923077.1, filed in the State Intellectual Property Office of China on Sep. 04, 2020, and entitled “Distributed Quantum Computing Simulation Method and Apparatus”, the entire contents of which are herein incorporated by reference.
The present invention relates to the field of quantum computing, and in particular, to a distributed quantum computing simulation method and apparatus.
Quantum computing is a novel computing mode using the principles of quantum entanglement and state superposition, which may bring powerful quantum parallelism, and bring a new solution to the problem of insufficient computing power in the Post-Moore era. In practice, for the problem of an exponential increase in the memory overheads of a classical computer simulation quantum system, Feynman has put forward the concept of quantum computing decades ago. After decades of development, quantum computing has made great progress in both hardware and algorithm, especially with Google claiming to realize “quantum hegemony”, quantum computing has come into the public view. However, as a whole, quantum computing is still in a primary stage, and there is still a long way to go before large-scale fault-tolerant quantum computers are implemented. In this context, it is of great significance to construct a quantum computing simulation platform based on a classical computer: (1) it may provide a verification platform for a quantum algorithm, and may also verify the reliability of quantum software and quantum fault tolerance; and (2) it helps understand the boundary between classical computing and quantum computing, and promote the development of quantum computing field.
The construction of the quantum computing simulation platform is a relatively new direction, and there are a full-amplitude mode and a single-amplitude mode at present. In the full-amplitude mode, all amplitudes of a quantum state need to be stored, the amplitudes are regulated and controlled by a quantum gate, a vector dimension required for storing the amplitude of one N quantum bit is 2N, the storage requirement is increased along with the increase index of the quantum bit, and even if one large-scale supercomputer is difficult to simulate a quantum system exceeding 45 quantum bits. Recently, a great progress has also been made in full-amplitude simulation, for example, partial amplitude simulation, and double-bit-gate decomposition. The MPS (Matrix Product State, matrix product state) and PEPS (Projective Entangled Pair States, projective entangled pair states) technologies based on quantum states of associated electronic systems also belong to full-amplitude simulation. These new techniques may enable the scale of full-amplitude simulation to break through 45 quantum bits.
Single-amplitude simulation is a recently developed strategy, in which there is no need to store all amplitudes of the quantum state, and it is only necessary to compute a probability amplitude of a POVM (Positive Operator Value Measurement, positive operator value measurement) element. It is very easy for a single-amplitude strategy to simulate a quantum supremacy circuit and even a shallow quantum circuit exceeding 100 quantum bits. In the single-amplitude mode, a quantum circuit is generally mapped to a tensor network, and a zero-order tensor obtained by contraction and merging is the required probability amplitude. At present, there are two strategies based on path integral and density matrix, and there are relatively many researches based on the path integral strategy. At present, a quantum supremacy circuit capable of simulating 40 layers of 9*9 quantum bits is the best result.
However, for a density matrix-based quantum computing simulation strategy, there are no specific and feasible solutions at home and abroad for running on a distributed supercomputer, and there is only a multi-thread supporting solution, which runs on a plurality of cores in a processor. In view of the problem in the prior art that density matrix-based single-amplitude strategy quantum computing simulation does not support a distributed computing system, there is still no effective solution at present.
In view of this, the objective of the embodiments of the present invention is to provide a distributed quantum computing simulation method and apparatus, which may perform density matrix-based single-amplitude strategy quantum computing simulation on a distributed computing system, thereby improving the universality and usability of single-amplitude strategy quantum computing simulation.
Based on the above objective, a first aspect of the embodiments of the present invention provides a distributed quantum computing simulation method, including the following steps:
In some embodiments, the step of converting the quantum circuit to be simulated into the tensor network that is represented by the undirected graph, includes:
In some implementations, the step of segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system, includes:
In some embodiments, the step of determining, on the basis of the number of times for segmentation and by using the genetic algorithm, the edge set for segmenting the undirected graph, includes:
In some implementations, the step of computing the width of the undirected graph tree, includes:
In some embodiments, the step of respectively performing, on the sub-process nodes, tensor contraction and merging on the plurality of sub-graphs for the connected tensors until only one tensor is left, so as to finally obtain the zero-order tensors of the plurality of sub-graphs at the same time, includes: respectively performing, by the sub-process nodes, tensor contraction and merging for different nodes in the plurality of sub-graphs in sequence by using the same tensor contraction and merging sequence, consuming the same computing resources within a unit computing time, and enabling the sub-process nodes with the same computing capability to obtain the zero-order tensors of the plurality of sub-graphs at the same time.
In some embodiments, the step of converting the quantum circuit to be simulated into the tensor network that is represented by the undirected graph, and segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system; and the step of acquiring and superposing the zero-order tensors of the plurality of sub-graphs from the sub-process nodes at the same time, so as to determine the zero-order tensor of the undirected graph, and using the zero-order tensor of the undirected graph as the probability amplitude of the positive operator value measurement element, so as to perform quantum computing simulation, are all performed on a main process node of the distributed system.
Based on the above objectives, a second aspect of the embodiments of the present invention provides a distributed quantum computing simulation apparatus, including a main process node and a plurality of sub-process nodes, wherein:
In some embodiments, the main process node segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system includes:
In some embodiments, the main process node determining, on the basis of the number of times for segmentation and by using the genetic algorithm, the edge set for segmenting the undirected graph includes:
The present invention has the following beneficial technical effects: according to the distributed quantum computing simulation method and apparatus provided in the embodiments of the present invention, by means of the technical solutions of converting the quantum circuit to be simulated into the tensor network that is represented by the undirected graph, and segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system; respectively performing, on the sub-process nodes, tensor contraction and merging on the plurality of sub-graphs for the connected tensors until only one tensor is left, so as to finally obtain the zero-order tensors of the plurality of sub-graphs at the same time; and acquiring and superposing the zero-order tensors of the plurality of sub-graphs from the sub-process nodes at the same time, so as to determine the zero-order tensor of the undirected graph, and using the zero-order tensor of the undirected graph as the probability amplitude of the positive operator value measurement element, so as to perform quantum computing simulation, density matrix-based single-amplitude strategy quantum computing simulation can be performed on a distributed computing system, thereby improving the universality and usability of single-amplitude strategy quantum computing simulation.
To illustrate technical solutions in the embodiments of the present invention or in the prior art more clearly, a brief introduction on the drawings which are needed in the description of the embodiments or the prior art is given below. Apparently, the drawings in the description below are merely some of the embodiments of the present invention, based on which other drawings may be obtained by those ordinary skilled in the art without any creative effort.
In order to make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below in combination with specific embodiments and with reference to the drawings.
It should be noted that, all expressions using “first” and “second” in the embodiments of the present invention are to distinguish two different entities or different parameters of the same name. Therefore, “first” and “second” are only for the convenience of expression, and should not be construed as limitations to the embodiments of the present invention, which will not be illustrated in subsequent embodiments one by one.
Based on the above objectives, a first aspect of the embodiments of the present invention provides an embodiment of a distributed quantum computing simulation method, which is capable of performing density matrix-based single-amplitude strategy quantum computing simulation on a distributed computing system.
The distributed quantum computing simulation method, as shown in
Those ordinary skilled in the art may understand that all or some processes in the embodiments of the method described above may be implemented by instructing relevant hardware by means of a computer program, the program may be stored in a computer-readable storage medium, and when executed, the program may include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a read-only storage memory (ROM), or a random storage memory (RAM), etc. The embodiments of the computer program may achieve the same or similar effects as any of the foregoing method embodiments corresponding thereto.
In some embodiments, the step of converting the quantum circuit to be simulated into the tensor network that is represented by the undirected graph, includes:
In some implementations, the step of segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system, includes:
In some embodiments, the step of determining, on the basis of the number of times for segmentation and by using the genetic algorithm, the edge set for segmenting the undirected graph, includes:
In some implementations, the step of computing the width of the undirected graph tree, includes:
In some embodiments, the step of respectively performing, on the sub-process nodes, tensor contraction and merging on the plurality of sub-graphs for the connected tensors until only one tensor is left, so as to finally obtain the zero-order tensors of the plurality of sub-graphs at the same time, includes: respectively performing, by the sub-process nodes, tensor contraction and merging for different nodes in the plurality of sub-graphs in sequence by using the same tensor contraction and merging sequence, consuming the same computing resources within a unit computing time, and enabling the sub-process nodes with the same computing capability to obtain the zero-order tensors of the plurality of sub-graphs at the same time.
In some embodiments, the step of converting the quantum circuit to be simulated into the tensor network that is represented by the undirected graph, and segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system; and the step of acquiring and superposing the zero-order tensors of the plurality of sub-graphs from the sub-process nodes at the same time, so as to determine the zero-order tensor of the undirected graph, and using the zero-order tensor of the undirected graph as the probability amplitude of the positive operator value measurement element, so as to perform quantum computing simulation, are all performed on a main process node of the distributed system.
The specific embodiments of the present invention will be further described below according to specific embodiments.
A tensor network is formed by connecting different tensors via topology, and may be generally represented by an undirected graph, and we define the tensor network to be G=(V,E), wherein V is a vertex set, and E is an edge set. For example, a quantum circuit as shown in
A tensor in the tensor network is a data structure having an order and a dimension, wherein the order refers to that a tensor is connected to how many edges, and may be represented by different exponential indexes (for example, i, j, k, l); and the dimension refers to that each index many have several possible accesses. Under the framework of quantum computing, the dimension of the tensor is a 4-component density operator, and the value thereof isΠ={|0><0]|,|0><1|,|1><0|,|1><1]}. Therefore, for a k-order tensor, we can use a one-dimensional array for storage, and it is necessary to store 4k complex numbers.
A method for constructing a tensor network has been disclosed in the related art: for an input state p within a single quantum bit, the tensor of which is _σ=tr(ρ·σ) (wherein σ ∈ Π); for an operation gate within a single quantum bit, the tensor of which is T_(σ,τ)=tr(τ^+ G(σ)); for an operation gate with two quantum bits, the tensor of which is T_(σ_1,σ_2 τ_1,τ_2)=tr((τ_1⊗τ_2)^+ G(σ_1⊗σ_2)); and the tensor of a quantum measurement is T_τ=tr(E·τ), wherein E is a POVM element operator, and G is a unitary evolution operator.
Tensor contraction and merging is a tensor operation, in which two tensors are contracted and merged into one tensor in a manner as shown in
After the contraction and merging operation of a plurality of tensors in the tensor network is completed in sequence, a zero-order tensor is obtained, and the zero-order tensor is a probability amplitude corresponding to the POVM (positive operator value measurement) element.
The maximum memory overhead of the contraction and merging of the tensor network depends on the tensor of the maximum order in the contraction and merging process. Generally, with the progress of the contraction and merging of the tensor network, the maximum order of an intermediate process tensor will first increase and then decrease. For example, after the contraction and merging operation of a (3+2)-order tensor and a (2+3)-order tensor, a (3+3)-order tensor is obtained. The maximum order of the intermediate tensor is related to the contraction and merging sequence of the tensors, each contraction and merging sequence corresponds to tree decomposition of one graph, and an optimal elimination sequence is tree decomposition with the minimum tree width.
It is set that G=(V,E) is an undirected graph, a node subset of the graph G constitutes a bag (bag), which is denoted as Bi, and the tree decomposition of the graph G is a tree T, which is composed of the bag Bi. One tree decomposition of the graph G may be represented as the mapping of a vertex V(G) of the graph to the bag Bi, and meets the following conditions:
With regard to the tree decomposition T, the width of which is defined as max(|Bν∈v(T)| - 1). The tree decomposition of a graph G is not unique, and the tree width of the graph G refers to a minimum value of the width in all possible tree decompositions of the graph G, which is denoted as tw(G). How to compute the tree width and the tree decomposition is an NP (Non-deterministic polynominal, non-deterministic polynominal) problem, but open-source software may be applied in actual computing, such as QuickBb. In fact, the time overheads of the contraction and merging of the tensor network are also related to the tree width.
On the basis of the specific means of the above tensor contraction and merging, the problem of computing space complexity and application requirements on a distributed computing system are met, the embodiments of the present invention specifically propose a tensor network contraction and merging algorithm, which better adapts to the distributed computing system and reduces the tree width: rather than eliminating a vertex, but eliminating an edge. In the tensor network, each edge has four different indexes: |0><0|, |0><1|, |1><0| and |1><1|. As shown in
This fact means that the contraction and merging of different sub-graphs may be computed on different cores, respectively, thereby realizing distributed contraction and merging of the tensor network. At the same time, it must be noted that, the sub-graph subjected to edge cutting has a smaller tree width, which means that the sub-graph contraction and merging have smaller memory occupancy and lower time algorithm complexity. For example, if the tree width of the original undirected graph in
This will bring a plurality of preferred technical effects. In the embodiments of the present invention, it is only necessary to collect the contraction and merging result (i.e., only a complex number) of each sub-process in a main process, and there is no need for sub-processes, which perform a complete vertical operation, to communicate with each other, then the communication between super-computing nodes will be reduced to be very low, and therefore, the bottleneck is no longer a bottleneck. At the same time, the structure of each sub-graph obtained by the contraction and merging of each process is completely consistent, so that the used computing time is also consistent, thereby being free of the situation in which some processes are idle, and then the utilization rate of the distributed computing system is also fully improved.
At this time, the only remaining problem is to determine how to cut edges. The tree widths of sub-graphs generated by eliminating different edges differ a lot, therefore, it is crucial to improving the performance of the algorithm by finding a set of optimal eliminated edges. Search for the optimal set itself is an NP problem, and when the scale of the graph is large, it is obviously impossible to find the set of optimal eliminated edges by means of exhaustion within a limited time. As an approximate alternative, the embodiments of the present invention propose a heuristic algorithm-based strategy for finding the optimal eliminated edges.
First, the genetic algorithm is initialized, an iteration counter is set to be t=0, the maximum number of iterations T is set, and a population P is initialized, wherein the population P has N individuals, and each individual is a set of M edges (eliminated), which are randomly selected from an undirected graph.
The following steps are then repeated:
Step 1: individual evaluation. The tree widths of corresponding graphs of the N individuals in the population P are computed and sorted.
Step 2: cross operation (chromosome variation). In addition to the individual with the minimum tree width, every two adjacent individuals are crossed, the cross mode is that the latter [N] elements in the two sets are exchanged, and if there are repeated elements in the crossed set, elements, which do not exist in one set, are randomly generated.
Step 3: variation operation (gene mutation). An individual except the optimal individual is selected from the population for variation, an edge is randomly selected from the set of the individual edges, and then an edge, which does not exist in the set, is randomly generated then.
Step 4: add 1 to the iteration counter. t=t+1, Until (until) t >T.
Finally, at the end of the circulation, the individuals in the population are evaluated, and an optimal individual is returned to cut the edges.
It can be seen from the above-mentioned embodiments that, the distributed quantum computing simulation method provided in the embodiments of the present invention has technical effects as follows: by means of the technical solutions of converting the quantum circuit to be simulated into the tensor network that is represented by the undirected graph, and segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system; respectively performing, on the sub-process nodes, tensor contraction and merging on the plurality of sub-graphs for the connected tensors until only one tensor is left, so as to finally obtain the zero-order tensors of the plurality of sub-graphs at the same time; and acquiring and superposing the zero-order tensors of the plurality of sub-graphs from the sub-process nodes at the same time, so as to determine the zero-order tensor of the undirected graph, and using the zero-order tensor of the undirected graph as the probability amplitude of the positive operator value measurement element, so as to perform quantum computing simulation, density matrix-based single-amplitude strategy quantum computing simulation can be performed on the distributed computing system, thereby improving the universality and usability of single-amplitude strategy quantum computing simulation.
It should be particularly pointed out that, in various embodiments of the foregoing distributed quantum computing simulation method, the various steps may be exchanged, replaced, increased and decreased, therefore these reasonable permutation and combination transformations should also fall within the protection scope of the present invention with respect to the distributed quantum computing simulation method, and the protection scope of the present invention should not be limited to the embodiments.
Based on the above objectives, a second aspect of the embodiments of the present invention provides an embodiment of a distributed quantum computing simulation apparatus, which is capable of performing density matrix-based single-amplitude strategy quantum computing simulation on a distributed computing system. The distributed quantum computing simulation apparatus includes a main process node and a plurality of sub-process nodes, wherein:
In some embodiments, the main process node segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system includes:
In some embodiments, the main process node determining, on the basis of the number of times for segmentation and by using the genetic algorithm, the edge set for segmenting the undirected graph includes:
It can be seen from the above-mentioned embodiments that, the distributed quantum computing simulation apparatus provided in the embodiments of the present invention has technical effects as follows: by means of the technical solutions of converting the quantum circuit to be simulated into the tensor network that is represented by the undirected graph, and segmenting the undirected graph into the plurality of sub-graphs by using the genetic algorithm that is based on the operation resources of the distributed system; respectively performing, on the sub-process nodes, tensor contraction and merging on the plurality of sub-graphs for the connected tensors until only one tensor is left, so as to finally obtain the zero-order tensors of the plurality of sub-graphs at the same time; and acquiring and superposing the zero-order tensors of the plurality of sub-graphs from the sub-process nodes at the same time, so as to determine the zero-order tensor of the undirected graph, and using the zero-order tensor of the undirected graph as the probability amplitude of the positive operator value measurement element, so as to perform quantum computing simulation, density matrix-based single-amplitude strategy quantum computing simulation can be performed on the distributed computing system, thereby improving the universality and usability of single-amplitude strategy quantum computing simulation.
It should be particularly pointed out that, the embodiment of the distributed quantum computing simulation apparatus uses the embodiment of the distributed quantum computing simulation method to specifically describe the working process of each module, and those skilled in the art may readily think that these modules are applied to other embodiments of the distributed quantum computing simulation method. Of course, since the various steps in the embodiment of the distributed quantum computing simulation method may be exchanged, replaced, increased and decreased, these reasonable permutation and combination transformations should also fall within the protection scope of the present invention with respect to the distributed quantum computing simulation apparatus, and the protection scope of the present invention should not be limited to the embodiments.
The above descriptions are exemplary embodiments disclosed in the present invention, but it should be noted that various changes and modifications may be made without departing from the scope of the embodiments of the present invention defined by the claims. The functions, steps and/or actions of the method claims according to the disclosed embodiments described herein need not be performed in any particular order. In addition, although the elements disclosed in the embodiments of the present invention may be described or claimed in an individual form, it may be understood that there are a plurality of elements, unless explicitly limited to be singular.
Those ordinary skilled in the art to which the present invention belongs should understand that, the discussion of any of the above embodiments is merely exemplary, and is not intended to imply that the scope (including the claims) disclosed in the embodiments of the present invention is limited to these examples; and in the idea of the embodiments of the present invention, the technical features in the above embodiments or different embodiments may also be combined with each other, there are many other changes in different aspects of the embodiments of the present invention as described above, and are not provided in detail for the sake of brevity. Therefore, any omissions, modifications, equivalent replacements, improvements, and the like, made within the spirit and principles of the embodiments of the present invention, shall fall within the protection scope of the embodiments of the present invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 202010923077.1 | Sep 2020 | CN | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/CN2021/103305 | 6/29/2021 | WO |
