# The Rigetti QPU¶

A quantum processor unit (QPU) is a physical device that contains a number of interconnected qubits.
This page presents technical details and average performance of *Acorn*, the 19Q Rigetti QPU device
that is made available for quantum computation through the cloud. This device has been designed,
fabricated and packaged at Rigetti Computing.

## Acorn QPU properties¶

The quantum processor consists of 20 superconducting transmon qubits with fixed capacitive coupling in the planar lattice design shown in Fig. 1. The resonance frequencies of qubits 0–4 and 10–14 are tunable while qubits 5–9 and 15–19 are fixed. The former have two Josephson junctions in an asymmetric SQUID geometry to provide roughly 1 GHz of frequency tunability, and flux-insensitive “sweet spots” near

\(\omega^{\textrm{max}}_{01}/2\pi\approx 4.5 \, \textrm{GHz}\)

and

\(\omega^{\textrm{min}}_{01}/2\pi\approx 3.0 \, \textrm{GHz}\).

These tunable devices are coupled to bias lines for AC and DC flux delivery. Each qubit is capacitively coupled to a quasi-lumped element resonator for dispersive readout of the qubit state. Single-qubit control is effected by applying microwave drives at the resonator ports. Two-qubit gates are activated via RF drives on the flux bias lines.

Due to a fabrication defect, qubit 3 is not tunable, which prohibits operation of the two-qubit
parametric gate described below between qubit 3 and its neighbors. Consequently, we will treat this
as a 19-qubit processor. This also means that **qubit 3 is not accessible** for quantum computation
through Forest.

## 1-Qubit Gate Performance¶

The device is characterized by several parameters:

- \(\omega_\textrm{01}/2\pi\) is the qubit transition frequency
- \(\omega_\textrm{r}/2\pi\) is the resonator frequency
- \(\eta/2\pi\) is the anharmonicity of the qubit
- \(g/2\pi\) is the coupling strength between a qubit and a resonator
- \(\lambda/2\pi\) is the coupling strength between two neighboring qubits

In Rigetti 19Q, each tunable qubit is capacitively coupled to one-to-three fixed-frequency qubits. We use a parametric flux modulation to activate a controlled Z gate between tunable and fixed qubits. The typical time-scale of these entangling gates is in the range 100–250 ns.

Table 1 summarizes the main performance parameters of Rigetti 19Q. The resonator and qubit frequencies are measured with standard spectroscopic techniques. The relaxation time \(T_1\) is extracted from repeated inversion recovery experiments. Similarly, the coherence time \(T^*_2\) is measured with repeated Ramsey fringe experiments. Single-qubit gate fidelities are estimated with randomized benchmarking protocols in which a sequence of \(m\) Clifford gates is applied to the qubit followed by a measurement on the computational basis. The sequence of Clifford gates are such that the first \(m-1\) gates are chosen uniformly at random from the Clifford group, while the last Clifford gate is chosen to bring the state of the system back to the initial state. This protocol is repeated for different values of \(m\in \{2,4,8,16,32,64,128\}\). The reported single-qubit gate fidelity is related to the randomized benchmarking decay constant \(p\) in the following way: \(\mathsf{F}_\textrm{1q} = p +(1-p)/2\). Finally, the readout assignment fidelities are extracted with dispersive readouts combined with a linear classifier trained on \(|0\rangle\) and \(|1\rangle\) state preparation for each qubit. The reported readout assignment fidelity is given by expression \(\mathsf{F}_\textrm{RO} = [p(0|0)+p(1|1)]/2\), where \(p(b|a)\) is the probability of measuring the qubit in state \(b\) when prepared in state \(a\).

\(\omega^{\textrm{max}}_{\textrm{r}}/2\pi\) | \(\omega^{\textrm{max}}_{01}/2\pi\) | \(\eta/2\pi\) | \(T_1\) | \(T^*_2\) | \(\mathsf{F}_{\textrm{1q}}\) | \(\mathsf{F}_{\textrm{RO}}\) | |

\(\textrm{MHz}\) | \(\textrm{MHz}\) | \(\textrm{MHz}\) | \(\mu\textrm{s}\) | \(\mu\textrm{s}\) | |||

0 | 5592 | 4386 | -208 | 15.2 \(\pm\) 2.5 |
7.2 \(\pm\) 0.7 |
0.9815 | 0.938 |

1 | 5703 | 4292 | -210 | 17.6 \(\pm\) 1.7 |
7.7 \(\pm\) 1.4 |
0.9907 | 0.958 |

2 | 5599 | 4221 | -142 | 18.2 \(\pm\) 1.1 |
10.8 \(\pm\) 0.6 |
0.9813 | 0.97 |

3 | 5708 | 3829 | -224 | 31.0 \(\pm\) 2.6 |
16.8 \(\pm\) 0.8 |
0.9908 | 0.886 |

4 | 5633 | 4372 | -220 | 23.0 \(\pm\) 0.5 |
5.2 \(\pm\) 0.2 |
0.9887 | 0.953 |

5 | 5178 | 3690 | -224 | 22.2 \(\pm\) 2.1 |
11.1 \(\pm\) 1.0 |
0.9645 | 0.965 |

6 | 5356 | 3809 | -208 | 26.8 \(\pm\) 2.5 |
26.8 \(\pm\) 2.5 |
0.9905 | 0.84 |

7 | 5164 | 3531 | -216 | 29.4 \(\pm\) 3.8 |
13.0 \(\pm\) 1.2 |
0.9916 | 0.925 |

8 | 5367 | 3707 | -208 | 24.5 \(\pm\) 2.8 |
13.8 \(\pm\) 0.4 |
0.9869 | 0.947 |

9 | 5201 | 3690 | -214 | 20.8 \(\pm\) 6.2 |
11.1 \(\pm\) 0.7 |
0.9934 | 0.927 |

10 | 5801 | 4595 | -194 | 17.1 \(\pm\) 1.2 |
10.6 \(\pm\) 0.5 |
0.9916 | 0.942 |

11 | 5511 | 4275 | -204 | 16.9 \(\pm\) 2.0 |
4.9 \(\pm\) 1.0 |
0.9901 | 0.900 |

12 | 5825 | 4600 | -194 | 8.2 \(\pm\) 0.9 |
10.9 \(\pm\) 1.4 |
0.9902 | 0.942 |

13 | 5523 | 4434 | -196 | 18.7 \(\pm\) 2.0 |
12.7 \(\pm\) 0.4 |
0.9933 | 0.921 |

14 | 5848 | 4552 | -204 | 13.9 \(\pm\) 2.2 |
9.4 \(\pm\) 0.7 |
0.9916 | 0.947 |

15 | 5093 | 3733 | -230 | 20.8 \(\pm\) 3.1 |
7.3 \(\pm\) 0.4 |
0.9852 | 0.970 |

16 | 5298 | 3854 | -218 | 16.7 \(\pm\) 1.2 |
7.5 \(\pm\) 0.5 |
0.9906 | 0.948 |

17 | 5097 | 3574 | -226 | 24.0 \(\pm\) 4.2 |
8.4 \(\pm\) 0.4 |
0.9895 | 0.921 |

18 | 5301 | 3877 | -216 | 16.9 \(\pm\) 2.9 |
12.9 \(\pm\) 1.3 |
0.9496 | 0.930 |

19 | 5108 | 3574 | -228 | 24.7 \(\pm\) 2.8 |
9.8 \(\pm\) 0.8 |
0.9942 | 0.930 |

## Qubit-Qubit Coupling¶

The coupling strength between two qubits can be extracted from a precise measurement of the shift in qubit frequency after the neighboring qubit is in the excited state. This protocol consists of two steps: a \(\pi\) pulse is applied to the first qubit, followed by a Ramsey fringe experiment on the second qubit which precisely determines its transition frequency (see Fig. 2a). The effective shift is denoted by \(\chi_\textrm{qq}\) and typical values are in the range \(\approx 100 \, \textrm{kHz}\). The coupling strength \(\lambda\) between the two qubits can be calculated in the following way:

\[\lambda^{(1,2)} = \sqrt{\left|\frac{\chi^{(1,2)}_\textrm{qq} \left[\,f^\textrm{(1)}_{01}-f^\textrm{(2)}_{12}\right]\left[\,f^\textrm{(1)}_{12}-f^\textrm{(2)}_{01}\right]}{2(\eta_1+\eta_2)}\right|}\]

Figure 2b shows the coupling strength for our device. This quantity is crucial to predict the gate time of our parametric entangling gates.

## 2-Qubit Gate Performance¶

Table 2 shows the two-qubit gate performance of Rigetti 19Q. These parameters refer to parametric CZ gates performed on one pair at a time. We analyze these CZ gates through quantum process tomography (QPT). This procedure starts by applying local rotations to the two qubits taken from the set \(\{I,R_x(\pi/2),R_y(\pi/2),R_x(\pi)\}\), followed by a CZ gate and post-rotations that bring the qubit states back to the computational basis. QPT involves the analysis of \(16\times16 =256\) different experiments, each of which we repeat \(500\) times. The reported process tomography fidelity \(\mathsf{F}^\textrm{cptp}_\textrm{PT}\) is the fidelity of the measured process compared with the ideal process, computed imposing complete positivity (cp) and trace preservation (tp) constraints.

\(A_0\) | \(f_\textrm{m}\) | \(t_\textrm{CZ}\) | \(\mathsf{F}^\textrm{cptp}_{\textrm{PT}}\) | |

\(\Phi/\Phi_0\) | \(\textrm{MHz}\) | ns | ||

0 - 5 | 0.27 | 94.5 | 168 | 0.936 |

0 - 6 | 0.36 | 123.9 | 197 | 0.889 |

1 - 6 | 0.37 | 137.1 | 173 | 0.888 |

1 - 7 | 0.59 | 137.9 | 179 | 0.919 |

2 - 7 | 0.62 | 87.4 | 160 | 0.817 |

2 - 8 | 0.23 | 55.6 | 189 | 0.906 |

4 - 9 | 0.43 | 183.6 | 122 | 0.854 |

5 - 10 | 0.60 | 152.9 | 145 | 0.870 |

6 - 11 | 0.38 | 142.4 | 180 | 0.838 |

7 - 12 | 0.60 | 241.9 | 214 | 0.87 |

8 - 13 | 0.40 | 152.0 | 185 | 0.881 |

9 - 14 | 0.62 | 130.8 | 139 | 0.872 |

10 - 15 | 0.53 | 142.1 | 154 | 0.854 |

10 - 16 | 0.43 | 170.3 | 180 | 0.838 |

11 - 16 | 0.38 | 160.6 | 155 | 0.891 |

11 - 17 | 0.29 | 85.7 | 207 | 0.844 |

12 - 17 | 0.36 | 177.1 | 184 | 0.876 |

12 - 18 | 0.28 | 113.9 | 203 | 0.886 |

13 - 18 | 0.24 | 66.2 | 152 | 0.936 |

13 - 19 | 0.62 | 109.6 | 181 | 0.921 |

14 - 19 | 0.59 | 188.1 | 142 | 0.797 |

## Using the QPU¶

To maintain above performance levels, Rigetti Forest periodically takes the QPU offline to retune single-qubit and two-qubit gates. To access Acorn for running quantum algorithms, see Using the QPU-based stack for a tutorial.