计算张量网络状态振幅

以下代码示例说明了如何定义张量网络状态，然后计算张量网络状态的振幅切片。 完整代码可以在 NVIDIA/cuQuantum 仓库中找到 (这里)。

头文件和错误处理

 7#include <cstdlib>
 8#include <cstdio>
 9#include <cassert>
10#include <complex>
11#include <vector>
12#include <bitset>
13#include <iostream>
14
15#include <cuda_runtime.h>
16#include <cutensornet.h>
17
18
19#define HANDLE_CUDA_ERROR(x) \
20{ const auto err = x; \
21  if( err != cudaSuccess ) \
22  { printf("CUDA error %s in line %d\n", cudaGetErrorString(err), __LINE__); fflush(stdout); std::abort(); } \
23};
24
25#define HANDLE_CUTN_ERROR(x) \
26{ const auto err = x; \
27  if( err != CUTENSORNET_STATUS_SUCCESS ) \
28  { printf("cuTensorNet error %s in line %d\n", cutensornetGetErrorString(err), __LINE__); fflush(stdout); std::abort(); } \
29};
30
31
32int main()
33{
34  static_assert(sizeof(size_t) == sizeof(int64_t), "Please build this sample on a 64-bit architecture!");
35
36  constexpr std::size_t fp64size = sizeof(double);

定义张量网络状态和所需的状态振幅切片

让我们定义一个对应于 6 量子比特量子电路的张量网络状态，并请求一个状态振幅切片，其中量子比特 0 和 1 固定为值 1。

40  // Quantum state configuration
41  constexpr int32_t numQubits = 6; // number of qubits
42  const std::vector<int64_t> qubitDims(numQubits,2); // qubit dimensions
43  const std::vector<int32_t> fixedModes({0,1}); // fixed modes in the output amplitude tensor (must be in acsending order)
44  const std::vector<int64_t> fixedValues({1,1}); // values of the fixed modes in the output amplitude tensor
45  const int32_t numFixedModes = fixedModes.size(); // number of fixed modes in the output amplitude tensor
46  std::cout << "Quantum circuit: " << numQubits << " qubits\n";

初始化 cuTensorNet 库句柄

50  // Initialize the cuTensorNet library
51  HANDLE_CUDA_ERROR(cudaSetDevice(0));
52  cutensornetHandle_t cutnHandle;
53  HANDLE_CUTN_ERROR(cutensornetCreate(&cutnHandle));
54  std::cout << "Initialized cuTensorNet library on GPU 0\n";

在 GPU 上定义量子门

58  // Define necessary quantum gate tensors in Host memory
59  const double invsq2 = 1.0 / std::sqrt(2.0);
60  //  Hadamard gate
61  const std::vector<std::complex<double>> h_gateH {{invsq2, 0.0},  {invsq2, 0.0},
62                                                   {invsq2, 0.0}, {-invsq2, 0.0}};
63  //  CX gate
64  const std::vector<std::complex<double>> h_gateCX {{1.0, 0.0}, {0.0, 0.0}, {0.0, 0.0}, {0.0, 0.0},
65                                                    {0.0, 0.0}, {1.0, 0.0}, {0.0, 0.0}, {0.0, 0.0},
66                                                    {0.0, 0.0}, {0.0, 0.0}, {0.0, 0.0}, {1.0, 0.0},
67                                                    {0.0, 0.0}, {0.0, 0.0}, {1.0, 0.0}, {0.0, 0.0}};
68
69  // Copy quantum gates to Device memory
70  void *d_gateH{nullptr}, *d_gateCX{nullptr};
71  HANDLE_CUDA_ERROR(cudaMalloc(&d_gateH, 4 * (2 * fp64size)));
72  HANDLE_CUDA_ERROR(cudaMalloc(&d_gateCX, 16 * (2 * fp64size)));
73  std::cout << "Allocated quantum gate memory on GPU\n";
74  HANDLE_CUDA_ERROR(cudaMemcpy(d_gateH, h_gateH.data(), 4 * (2 * fp64size), cudaMemcpyHostToDevice));
75  HANDLE_CUDA_ERROR(cudaMemcpy(d_gateCX, h_gateCX.data(), 16 * (2 * fp64size), cudaMemcpyHostToDevice));
76  std::cout << "Copied quantum gates to GPU memory\n";

在 GPU 上分配振幅切片张量

这里我们在 GPU 内存中为请求的振幅切片张量分配内存。

80  // Allocate Device memory for the specified slice of the quantum circuit amplitudes tensor
81  void *d_amp{nullptr};
82  std::size_t ampSize = 1;
83  for(const auto & qubitDim: qubitDims) ampSize *= qubitDim; // all state modes (full size)
84  for(const auto & fixedMode: fixedModes) ampSize /= qubitDims[fixedMode]; // fixed state modes reduce the slice size
85  HANDLE_CUDA_ERROR(cudaMalloc(&d_amp, ampSize * (2 * fp64size)));
86  std::cout << "Allocated memory for the specified slice of the quantum circuit amplitude tensor of size "
87            << ampSize << " elements\n";

在 GPU 上分配暂存缓冲区

91  // Query the free memory on Device
92  std::size_t freeSize{0}, totalSize{0};
93  HANDLE_CUDA_ERROR(cudaMemGetInfo(&freeSize, &totalSize));
94  const std::size_t scratchSize = (freeSize - (freeSize % 4096)) / 2; // use half of available memory with alignment
95  void *d_scratch{nullptr};
96  HANDLE_CUDA_ERROR(cudaMalloc(&d_scratch, scratchSize));
97  std::cout << "Allocated " << scratchSize << " bytes of scratch memory on GPU\n";

创建纯张量网络状态

现在让我们为 6 量子比特量子电路创建一个纯张量网络状态。

101  // Create the initial quantum state
102  cutensornetState_t quantumState;
103  HANDLE_CUTN_ERROR(cutensornetCreateState(cutnHandle, CUTENSORNET_STATE_PURITY_PURE, numQubits, qubitDims.data(),
104                    CUDA_C_64F, &quantumState));
105  std::cout << "Created the initial quantum state\n";

应用量子门

让我们通过应用相应的量子门来构造 GHZ 量子电路。

109  // Construct the final quantum circuit state (apply quantum gates) for the GHZ circuit
110  int64_t id;
111  HANDLE_CUTN_ERROR(cutensornetStateApplyTensorOperator(cutnHandle, quantumState, 1, std::vector<int32_t>{{0}}.data(),
112                    d_gateH, nullptr, 1, 0, 1, &id));
113  for(int32_t i = 1; i < numQubits; ++i) {
114    HANDLE_CUTN_ERROR(cutensornetStateApplyTensorOperator(cutnHandle, quantumState, 2, std::vector<int32_t>{{i-1,i}}.data(),
115                      d_gateCX, nullptr, 1, 0, 1, &id));
116  }
117  std::cout << "Applied quantum gates\n";

创建状态振幅访问器

一旦量子电路被构造，让我们创建振幅访问器对象，它将计算请求的状态振幅切片。

121  // Specify the quantum circuit amplitudes accessor
122  cutensornetStateAccessor_t accessor;
123  HANDLE_CUTN_ERROR(cutensornetCreateAccessor(cutnHandle, quantumState, numFixedModes, fixedModes.data(),
124                    nullptr, &accessor)); // using default strides
125  std::cout << "Created the specified quantum circuit amplitudes accessor\n";

配置状态振幅访问器

现在我们可以通过设置张量网络收缩路径查找器要使用的超样本数量来配置状态振幅访问器对象。

129  // Configure the computation of the slice of the specified quantum circuit amplitudes tensor
130  const int32_t numHyperSamples = 8; // desired number of hyper samples used in the tensor network contraction path finder
131  HANDLE_CUTN_ERROR(cutensornetAccessorConfigure(cutnHandle, accessor,
132                    CUTENSORNET_ACCESSOR_CONFIG_NUM_HYPER_SAMPLES, &numHyperSamples, sizeof(numHyperSamples)));

准备状态振幅切片张量的计算

让我们创建一个工作区描述符并准备状态振幅切片张量的计算。

136  // Prepare the computation of the specified slice of the quantum circuit amplitudes tensor
137  cutensornetWorkspaceDescriptor_t workDesc;
138  HANDLE_CUTN_ERROR(cutensornetCreateWorkspaceDescriptor(cutnHandle, &workDesc));
139  std::cout << "Created the workspace descriptor\n";
140  HANDLE_CUTN_ERROR(cutensornetAccessorPrepare(cutnHandle, accessor, scratchSize, workDesc, 0x0));
141  std::cout << "Prepared the computation of the specified slice of the quantum circuit amplitudes tensor\n";
142  double flops {0.0};
143  HANDLE_CUTN_ERROR(cutensornetAccessorGetInfo(cutnHandle, accessor,
144                    CUTENSORNET_ACCESSOR_INFO_FLOPS, &flops, sizeof(flops)));
145  std::cout << "Total flop count = " << (flops/1e9) << " GFlop\n";

设置工作区

现在我们可以设置所需的工作区缓冲区。

149  // Attach the workspace buffer
150  int64_t worksize {0};
151  HANDLE_CUTN_ERROR(cutensornetWorkspaceGetMemorySize(cutnHandle,
152                                                      workDesc,
153                                                      CUTENSORNET_WORKSIZE_PREF_RECOMMENDED,
154                                                      CUTENSORNET_MEMSPACE_DEVICE,
155                                                      CUTENSORNET_WORKSPACE_SCRATCH,
156                                                      &worksize));
157  std::cout << "Required scratch GPU workspace size (bytes) = " << worksize << std::endl;
158  if(worksize <= scratchSize) {
159    HANDLE_CUTN_ERROR(cutensornetWorkspaceSetMemory(cutnHandle, workDesc, CUTENSORNET_MEMSPACE_DEVICE,
160                      CUTENSORNET_WORKSPACE_SCRATCH, d_scratch, worksize));
161  }else{
162    std::cout << "ERROR: Insufficient workspace size on Device!\n";
163    std::abort();
164  }
165  std::cout << "Set the workspace buffer\n";

计算指定的状态振幅切片

一旦一切都设置好，我们计算请求的状态振幅切片，将其复制回主机内存，并打印出来。

169  // Compute the specified slice of the quantum circuit amplitudes tensor
170  std::complex<double> stateNorm2{0.0,0.0};
171  HANDLE_CUTN_ERROR(cutensornetAccessorCompute(cutnHandle, accessor, fixedValues.data(),
172                    workDesc, d_amp, static_cast<void*>(&stateNorm2), 0x0));
173  std::cout << "Computed the specified slice of the quantum circuit amplitudes tensor\n";
174  std::vector<std::complex<double>> h_amp(ampSize);
175  HANDLE_CUDA_ERROR(cudaMemcpy(h_amp.data(), d_amp, ampSize * (2 * fp64size), cudaMemcpyDeviceToHost));
176  std::cout << "Amplitudes slice for " << (numQubits - numFixedModes) << " qubits:\n";
177  for(std::size_t i = 0; i < ampSize; ++i) {
178    std::cout << " " << h_amp[i] << std::endl;
179  }
180  std::cout << "Squared 2-norm of the state = (" << stateNorm2.real() << ", " << stateNorm2.imag() << ")\n";

释放资源

184  // Destroy the workspace descriptor
185  HANDLE_CUTN_ERROR(cutensornetDestroyWorkspaceDescriptor(workDesc));
186  std::cout << "Destroyed the workspace descriptor\n";
187
188  // Destroy the quantum circuit amplitudes accessor
189  HANDLE_CUTN_ERROR(cutensornetDestroyAccessor(accessor));
190  std::cout << "Destroyed the quantum circuit amplitudes accessor\n";
191
192  // Destroy the quantum circuit state
193  HANDLE_CUTN_ERROR(cutensornetDestroyState(quantumState));
194  std::cout << "Destroyed the quantum circuit state\n";
195
196  HANDLE_CUDA_ERROR(cudaFree(d_scratch));
197  HANDLE_CUDA_ERROR(cudaFree(d_amp));
198  HANDLE_CUDA_ERROR(cudaFree(d_gateCX));
199  HANDLE_CUDA_ERROR(cudaFree(d_gateH));
200  std::cout << "Freed memory on GPU\n";
201
202  // Finalize the cuTensorNet library
203  HANDLE_CUTN_ERROR(cutensornetDestroy(cutnHandle));
204  std::cout << "Finalized the cuTensorNet library\n";
205
206  return 0;
207}