Basic D-Wave usage¶

In this notebook you will learn how to:

- Query the D-Wave solvers available to your account
- Embed a QUBO problem, submit it to a solver and inspect the results
- Inspect the qubit connectivity of a QPU
- Submit the same QUBO problem as above, but with manual instead of automatic embedding
- Learn about the five-dimensional Pegasus coordinate system to identify the position of individual qubits on the chip
- Learn about the five-dimensional Zephyr coordinate system (Advantage2) to identify the position of individual qubits on the chip

Initialization¶

In [1]:

import dwave
import dwave.inspector
from dwave.system import DWaveSampler, EmbeddingComposite
from dwave.cloud import Client
import networkx as nx
import dwave_networkx as dnx
import matplotlib as mpl
import matplotlib.pyplot as plt
import pandas as pd
%matplotlib inline

import dwave import dwave.inspector from dwave.system import DWaveSampler, EmbeddingComposite from dwave.cloud import Client import networkx as nx import dwave_networkx as dnx import matplotlib as mpl import matplotlib.pyplot as plt import pandas as pd %matplotlib inline

In [2]:

client = Client.from_config(profile='defaults')
client.get_solvers()

client = Client.from_config(profile='defaults') client.get_solvers()

Out[2]:

[BQMSolver(id='hybrid_binary_quadratic_model_version2'),
 DQMSolver(id='hybrid_discrete_quadratic_model_version1'),
 CQMSolver(id='hybrid_constrained_quadratic_model_version1p'),
 StructuredSolver(id='Advantage_system6.4'),
 StructuredSolver(id='Advantage2_prototype2.3'),
 StructuredSolver(id='Advantage_system4.1')]

In [3]:

client = Client.from_config(profile='defaults', region='eu-central-1')
client.get_solvers()

client = Client.from_config(profile='defaults', region='eu-central-1') client.get_solvers()

Out[3]:

[StructuredSolver(id='Advantage_system5.4')]

Solve a QUBO problem with embedding¶

In [4]:

qubo = {
    (0,0): -1,
    (1,1): -0.5,
    (0,1): 2,
}
sampler = EmbeddingComposite(DWaveSampler(profile='defaults', solver='Advantage_system4.1'))  # can replace solver by any other solver above (need to use region='eu-central-1' for the D-Wave systems in Jülich)
results = sampler.sample_qubo(qubo, num_reads=100)
results.to_pandas_dataframe()

qubo = { (0,0): -1, (1,1): -0.5, (0,1): 2, } sampler = EmbeddingComposite(DWaveSampler(profile='defaults', solver='Advantage_system4.1')) # can replace solver by any other solver above (need to use region='eu-central-1' for the D-Wave systems in Jülich) results = sampler.sample_qubo(qubo, num_reads=100) results.to_pandas_dataframe()

Out[4]:

	0	1	chain_break_fraction	energy	num_occurrences
0	1	0	0.0	-1.0	91
1	0	1	0.0	-0.5	9

In [ ]:

dwave.inspector.show(results)  # to visualize the results on the QPU interactively

dwave.inspector.show(results) # to visualize the results on the QPU interactively

Solve a QUBO problem without embedding¶

In [5]:

plt.figure(figsize=(16,6), dpi=70)
G = dnx.pegasus_graph(16)
dnx.draw_pegasus(G, with_labels=True, crosses=True, node_color="Yellow", node_size=1000)
plt.margins(x=-0.44, y=-0.48)  # zoom into the graph

plt.figure(figsize=(16,6), dpi=70) G = dnx.pegasus_graph(16) dnx.draw_pegasus(G, with_labels=True, crosses=True, node_color="Yellow", node_size=1000) plt.margins(x=-0.44, y=-0.48) # zoom into the graph

In [6]:

qubo = {
    (1387,4327): -1,
    (4327,4327): -0.5,
    (1387,4327): 2,
}
sampler = DWaveSampler(profile='defaults', solver='Advantage_system4.1')  # can replace solver by any other solver above (need to use region='eu-central-1' for the D-Wave systems in Jülich)
results = sampler.sample_qubo(qubo, num_reads=100)
results.to_pandas_dataframe()

qubo = { (1387,4327): -1, (4327,4327): -0.5, (1387,4327): 2, } sampler = DWaveSampler(profile='defaults', solver='Advantage_system4.1') # can replace solver by any other solver above (need to use region='eu-central-1' for the D-Wave systems in Jülich) results = sampler.sample_qubo(qubo, num_reads=100) results.to_pandas_dataframe()

Out[6]:

	1387	4327	energy	num_occurrences
0	0	1	-0.5	94
1	1	0	0.0	3
2	0	0	0.0	3

Pegasus coordinate system¶

Nice coordinates (t,y,x,u,k)¶

In [4]:

pegasus_coords = dnx.pegasus_coordinates(16)  # there are also Chimera coordinates (for DW2000Q: dnx.chimera_coordinates(16,16,4)) or Zephyr coordinates

pegasus_coords = dnx.pegasus_coordinates(16) # there are also Chimera coordinates (for DW2000Q: dnx.chimera_coordinates(16,16,4)) or Zephyr coordinates

We can translate the linear physical qubit indices q above into a five-dimensional Pegasus coordinate system (that is compatible with Chimera too):

t, y, x, u, k = pegasus_coords.linear_to_nice(q)

In [5]:

pegasus_coords.linear_to_nice(1387)

pegasus_coords.linear_to_nice(1387)

Out[5]:

(1, 7, 7, 0, 0)

In [6]:

pegasus_coords.linear_to_nice(4327)

pegasus_coords.linear_to_nice(4327)

Out[6]:

(1, 7, 7, 1, 0)

In [7]:

pegasus_coords.linear_to_nice(346)

pegasus_coords.linear_to_nice(346)

Out[7]:

(1, 1, 1, 0, 3)

The "nice" Pegasus coordinates (t,y,x,u,k) enumerate the full Pegasus topology in the following way:

• t: depth index of the three 8-qubit Chimera crosses within one unit cell (t=0,1,2)
• y: vertical unit cell index
• x: horizontal unit cell index
• u: denotes the horizontal (u=0) or vertical (u=1) 4 qubits withing an 8-qubit Chimera cross
• k: enumerates the four qubits within this part of the Chimera cross (k=0,1,2,3)

Note that these coordinates can be easily related to Chimera coordinates (y,x,u,k). In this context, the five-dimensional Pegasus coordinates only have the additional t dimension (t=0,1,2). The corresponding functions chimera_coords.linear_to_chimera(q) and chimera_coords.chimera_to_linear(y,x,u,k) from chimera_coords = dnx.chimera_coordinates(16,16,4) can be used for this purpose.

In [8]:

qubit_labels = {
    pegasus_coords.nice_to_linear((0, 0, 0, 0, 2)): 'x,y=0\nt=0',
    pegasus_coords.nice_to_linear((1, 0, 0, 0, 2)): 't=1',
    pegasus_coords.nice_to_linear((2, 0, 0, 0, 2)): 't=2',
}
qubit_labels.update({
    pegasus_coords.nice_to_linear((0, 0, x, 0, 2)): f'x={x}' for x in range(1,16)
})
qubit_labels.update({
    pegasus_coords.nice_to_linear((0, y, 0, 0, 2)): f'y={y}' for y in range(1,15)
})

fig,ax = plt.subplots(1, 1, figsize=(20,20), dpi=70)
dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=50, node_color='red', edge_color='gray')
dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray')
plt.margins(x=-0.02, y=-0.02)

qubit_labels = { pegasus_coords.nice_to_linear((0, 0, 0, 0, 2)): 'x,y=0\nt=0', pegasus_coords.nice_to_linear((1, 0, 0, 0, 2)): 't=1', pegasus_coords.nice_to_linear((2, 0, 0, 0, 2)): 't=2', } qubit_labels.update({ pegasus_coords.nice_to_linear((0, 0, x, 0, 2)): f'x={x}' for x in range(1,16) }) qubit_labels.update({ pegasus_coords.nice_to_linear((0, y, 0, 0, 2)): f'y={y}' for y in range(1,15) }) fig,ax = plt.subplots(1, 1, figsize=(20,20), dpi=70) dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=50, node_color='red', edge_color='gray') dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray') plt.margins(x=-0.02, y=-0.02)

In [9]:

qubit_labels = {
    pegasus_coords.nice_to_linear((1, 7, 7, 0, 0)): 'u=0\nk=0',
    pegasus_coords.nice_to_linear((1, 7, 7, 0, 1)): '\nk=1',
    pegasus_coords.nice_to_linear((1, 7, 7, 0, 2)): '\nk=2',
    pegasus_coords.nice_to_linear((1, 7, 7, 0, 3)): '\nk=3',
    pegasus_coords.nice_to_linear((2, 7, 7, 1, 0)): 'u=1\nk=0',
    pegasus_coords.nice_to_linear((2, 7, 7, 1, 1)): '\nk=1',
    pegasus_coords.nice_to_linear((2, 7, 7, 1, 2)): '\nk=2',
    pegasus_coords.nice_to_linear((2, 7, 7, 1, 3)): '\nk=3',
}

fig,ax = plt.subplots(figsize=(16,6), dpi=70)
dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=500, node_color='red', edge_color='gray')
dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray')
plt.margins(x=-0.44, y=-0.48)

qubit_labels = { pegasus_coords.nice_to_linear((1, 7, 7, 0, 0)): 'u=0\nk=0', pegasus_coords.nice_to_linear((1, 7, 7, 0, 1)): '\nk=1', pegasus_coords.nice_to_linear((1, 7, 7, 0, 2)): '\nk=2', pegasus_coords.nice_to_linear((1, 7, 7, 0, 3)): '\nk=3', pegasus_coords.nice_to_linear((2, 7, 7, 1, 0)): 'u=1\nk=0', pegasus_coords.nice_to_linear((2, 7, 7, 1, 1)): '\nk=1', pegasus_coords.nice_to_linear((2, 7, 7, 1, 2)): '\nk=2', pegasus_coords.nice_to_linear((2, 7, 7, 1, 3)): '\nk=3', } fig,ax = plt.subplots(figsize=(16,6), dpi=70) dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=500, node_color='red', edge_color='gray') dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray') plt.margins(x=-0.44, y=-0.48)

Pegasus coordinates (u,w,k,z)¶

In addition to the nice coordinates (t,y,x,u,k), there are the four-dimensional Pegasus coordinates (u,w,k,z).

Although a bit less intuitive, they can be more easily translated to the future Zephyr coordinates of Advantage2 (see below).

Further information can also be found in this D-Wave example notebook

In [10]:

pegasus_coords = dnx.pegasus_coordinates(16)

pegasus_coords = dnx.pegasus_coordinates(16)

We can translate the linear physical qubit indices q above into four-dimensional Pegasus (m=16) coordinates:

u, w, k, z = pegasus_coords.linear_to_pegasus(q)

The Pegasus coordinates (u,w,k,z) enumerate the Pegasus topology (m=16) in the following way:

• u: qubit orientation (0 = vertical, 1 = horizontal)
• w: orthogonal major offset; 0 <= w <= 15
• k: orthogonal minor offset; 0 <= k <= 11
• z: parallel offset; 0 <= z <= 14

In [11]:

for u in (0,1):
    qubit_labels = { pegasus_coords.pegasus_to_linear((u, 0, 0, 0)): f'w=0\nz=0' }
    qubit_labels.update({ pegasus_coords.pegasus_to_linear((u, w, 0, 0)): f'w={w}' for w in range(1,16) })
    qubit_labels.update({ pegasus_coords.pegasus_to_linear((u, 0, 0, z)): f'z={z}' for z in range(1,15) })
    fig,ax = plt.subplots(1, 1, figsize=(20,20), dpi=70)
    dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=50, node_color='red', edge_color='gray')
    dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray')
    plt.title(f'u = {u}: {("vertical","horizontal")[u]}', fontsize=20, loc='left')
    plt.margins(x=-0.02, y=-0.02)
    plt.show()

for u in (0,1): qubit_labels = { pegasus_coords.pegasus_to_linear((u, 0, 0, 0)): f'w=0\nz=0' } qubit_labels.update({ pegasus_coords.pegasus_to_linear((u, w, 0, 0)): f'w={w}' for w in range(1,16) }) qubit_labels.update({ pegasus_coords.pegasus_to_linear((u, 0, 0, z)): f'z={z}' for z in range(1,15) }) fig,ax = plt.subplots(1, 1, figsize=(20,20), dpi=70) dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=50, node_color='red', edge_color='gray') dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray') plt.title(f'u = {u}: {("vertical","horizontal")[u]}', fontsize=20, loc='left') plt.margins(x=-0.02, y=-0.02) plt.show()

In [12]:

for u in (0,1):
    qubit_labels = { pegasus_coords.pegasus_to_linear((u, 7, k, 7)): f'w=7\nk={k}' if k%4==0 else f'\nk={k}' for k in range(12) }
    qubit_labels_next_w = { pegasus_coords.pegasus_to_linear((u, 8, k, 7)): f'w=8\nk={k}' if k%4==0 else f'\nk={k}' for k in range(12) }
    fig,ax = plt.subplots(figsize=(16,12), dpi=70)
    dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=500, node_color='red', edge_color='gray')
    dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray')
    dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels_next_w), labels=qubit_labels_next_w, ax=ax, crosses=True, node_size=1000, node_color='lightgreen', edge_color='gray')
    plt.title(f'u = {u}:', fontsize=20, loc='left')
    plt.margins(x=-0.44, y=-0.44)
    plt.show()

for u in (0,1): qubit_labels = { pegasus_coords.pegasus_to_linear((u, 7, k, 7)): f'w=7\nk={k}' if k%4==0 else f'\nk={k}' for k in range(12) } qubit_labels_next_w = { pegasus_coords.pegasus_to_linear((u, 8, k, 7)): f'w=8\nk={k}' if k%4==0 else f'\nk={k}' for k in range(12) } fig,ax = plt.subplots(figsize=(16,12), dpi=70) dnx.draw_pegasus(dnx.pegasus_graph(16), ax=ax, crosses=True, node_size=500, node_color='red', edge_color='gray') dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels), labels=qubit_labels, ax=ax, crosses=True, node_size=1000, node_color='yellow', edge_color='gray') dnx.draw_pegasus(dnx.pegasus_graph(16, node_list=qubit_labels_next_w), labels=qubit_labels_next_w, ax=ax, crosses=True, node_size=1000, node_color='lightgreen', edge_color='gray') plt.title(f'u = {u}:', fontsize=20, loc='left') plt.margins(x=-0.44, y=-0.44) plt.show()