Exploratory notebooks for cross-resonance gate

doc/source/protocols/cross_resonance/cross_resonance.rst

@@ -0,0 +1,188 @@
+Calibration of CNOT gate using Cross-Resonance
+===============================================
+
+It is possible to generate an interaction between two superconducting qubits without requiring
+flux tunability, through a mechanism known as Cross Resonance (CR). This mechanism relies only
+on microwave drive pulses. Moreover, not using flux lines, results in a reduction of the number
+of fridge lines and allows to ignore all problems related to flux noise.
+
+The cross resonance effect was first proposed :cite:p:`CR_First` in and later
+independently discovered in :cite:p:`CR_Righetti, CR_Second`.
+
+The CR effect can be showed by starting with the Hamiltonian of a two-qubit system with
+a drive term on the first qubit :cite:p:`Manenti:2023zzn`
+
+.. math::
+
+    H = b_1^\dagger b_1 \omega_1 + \frac{\alpha_1}{2} b_1^\dagger b_1^\dagger b_1 b_1 +
+        b_2^\dagger b_2 \omega_2 + \frac{\alpha_2}{2} b_2^\dagger b_2^\dagger b_2 b_2 +
+        g (b_1 b_2^\dagger + b_1^\dagger b_2) + \Omega(t) (b_1 + b_1^\dagger)
+
+If we are in a dispersive regime (i.e. :math:`|\omega_1 - \omega_2| \gg g`), through a
+Schrieffer-Wolff transformation we can obtain the effective Hamiltonian:
+
+.. math::
+
+    H_\text{eff} = - \frac{\tilde{\omega_1}}{2} \sigma_1^z - \frac{\tilde{\omega_2}}{2} \sigma_2^z
+    + \frac{\zeta}{4} \sigma_1^z \sigma_2^z
+    + \Omega(t) \Big[ \sigma_1^x + \nu \sigma_2^x + \mu \sigma_1^z \sigma_2^x\Big]
+
+where :math:`\zeta` is the ZZ coupling, :math:`\nu` is quantum crosstalk factor and :math:`\mu` is the
+cross-resonance factor. From the equation above we can see that by driving the first qubit
+at the frequency of the second qubit .
+
+By tuning the amplitude and the duration of this drive pulse it is possible to calibrate a
+:math:`RZX` rotation to rotate exactly by :math:`- \pi/2`. This is done because starting
+from a :math:`ZX_{frac{\pi}{2}}` we can obtain a CNOT gate using single qubit rotations.
+
+.. math::
+
+    \text{CNOT} = \text{R}_\text{ZX}(-\pi/2) \text{R}_\text{IX}(\pi/2) \text{R}_\text{ZI}(\pi/2)
+
+In Qibocal we provide protocols to calibrate CR pulses.
+
+Sweeping the duration of the CR pulse
+-------------------------------------
+
+In a first experiment we can sweep the duration of the CR pulse and measure both the
+target and control qubit. The measurement is performed while preparing the control
+qubit in state :math:`\ket{0}` and :math:`\ket{1}`.
+
+Parameters
+^^^^^^^^^^
+
+.. autoclass:: qibocal.protocols.two_qubit_interaction.cross_resonance.length.CrossResonanceLengthParameters
+  :noindex:
+
+Example
+^^^^^^^
+
+A possible runcard to launch the experiment could be the following:
+
+.. code-block:: yaml
+
+  - id: CR length
+    operation: cross_resonance_length
+    parameters:
+      targets: [[0,1]]
+      pulse_duration_start: 10
+      pulse_duration_end: 200
+      pulse_duration_step: 10
+      flux_pulse_amplitude: 0.1
+      nshots: 2000
+      relaxation_time: 50000
+
+
+The expected output is the following:
+
+.. image:: length.png
+
+Post-processing
+^^^^^^^^^^^^^^^
+
+The probability of the target qubit is fitted in both cases to a dumped cosine functions.
+It is possible to extract the effective coupling as
+
+.. math::
+
+    \text{J}_\text{eff}/ 2 \pi = \frac{f^{\pi}_\text{Rabi} - f_\text{Rabi}}{2}
+
+
+where :math:`f^{\pi}_\text{Rabi}` and :math:`f_\text{Rabi}` are the frequencies of the
+fitted Rabi oscillations on the target qubit.
+
+Sweeping amplitude of the CR pulse
+----------------------------------
+
+Similarly it is possible to sweep the amplitude of the CR pulse and measure both the
+target and control qubit.
+
+
+Parameters
+^^^^^^^^^^
+
+.. autoclass:: qibocal.protocols.two_qubit_interaction.cross_resonance.length.CrossResonanceLengthParameters
+  :noindex:
+
+Example
+^^^^^^^
+
+A possible runcard to launch the experiment could be the following:
+
+.. code-block:: yaml
+
+  - id: CR amplitude
+    operation: cross_resonance_amplitude
+    parameters:
+      targets: [[0,1]]
+      max_amp: 0.05
+      min_amp: 0.01
+      step_amp: 0.005
+      pulse_duration: 100
+      nshots: 2000
+      relaxation_time: 50000
+
+
+The expected output is the following:
+
+.. image:: amplitude.png
+
+Post-processing
+^^^^^^^^^^^^^^^
+
+The probability of the target qubit is fitted in both cases to a cosine function.
+
+Hamiltonian Tomography measurement
+----------------------------------
+
+Although from the two previous experiments it is possible to perform an initial
+calibration of the CR gate, by performing a state tomography on the target qubit it is
+possible to reconstruct the effective Hamiltonian of the system :cite:p:`CRDrag`:
+
+.. math::
+
+    H_\text{eff} = \frac{\nu_\text{ZX}}{2} \text{ZX} + \frac{\nu_\text{ZY}}{2} \text{ZY} +
+                    \frac{\nu_\text{ZZ}}{2} \text{ZZ} + \frac{\nu_\text{IX}}{2} \text{IX} +
+                    \frac{\nu_\text{IY}}{2} \text{IY} + \frac{\nu_\text{IZ}}{2} \text{IZ}
+
+In particular, by sweeping the duration of the CR pulse and measuring the expectation
+values of the target qubit :math:`\langle X \rangle`, :math:`\langle Y \rangle` and :math:`\langle Z \rangle`
+when the control qubit is prepared in :math:`\ket{0}` and :math:`\ket{1}` we can compute all terms in
+the effective Hamiltonian following the procedure in :cite:p:`CRDrag`.
+
+Parameters
+^^^^^^^^^^
+
+
+.. autoclass:: qibocal.protocols.two_qubit_interaction.cross_resonance.hamiltonian_tomography.length.HamiltonianTomographyCRLengthParameters
+  :noindex:
+
+Example
+^^^^^^^
+
+A possible runcard to launch the experiment could be the following:
+
+.. code-block:: yaml
+
+  - id: Hamiltonian tomography CR
+    operation: cross_resonance_amplitude
+    parameters:
+      targets: [[0,1]]
+      nshots: 2000
+      pulse_amplitude: 0.1
+      pulse_duration_end: 400
+      pulse_duration_start: 10
+      pulse_duration_step: 20
+
+
+The expected output is the following:
+
+.. image:: tomography_length.png
+
+
+
+Requirements
+^^^^^^^^^^^^
+
+To run these experiments single qubit gates for both target and control qubit needs
+to be calibrated.

doc/source/protocols/index.rst

@@ -40,6 +40,7 @@ In this section we introduce the basics of all protocols supported by ``qibocal`
     chevron
     virtual_z
     state_tomographies
+    cross_resonance/cross_resonance
     coherence/index
     chsh
     twpa_calibration/twpa

doc/source/refs.bib

@@ -262,6 +262,69 @@ @misc{reed2013entanglementquantumerrorcorrection
       url={https://arxiv.org/abs/1311.6759},
 }
 
+@article{CR_First,
+  title = {Microwave-induced coupling of superconducting qubits},
+  author = {Paraoanu, G. S.},
+  journal = {Phys. Rev. B},
+  volume = {74},
+  issue = {14},
+  pages = {140504},
+  numpages = {4},
+  year = {2006},
+  month = {Oct},
+  publisher = {American Physical Society},
+  doi = {10.1103/PhysRevB.74.140504},
+  url = {https://link.aps.org/doi/10.1103/PhysRevB.74.140504}
+}
+
+@article{CR_Righetti,
+  title = {Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies},
+  author = {Rigetti, Chad and Devoret, Michel},
+  journal = {Phys. Rev. B},
+  volume = {81},
+  issue = {13},
+  pages = {134507},
+  numpages = {7},
+  year = {2010},
+  month = {Apr},
+  publisher = {American Physical Society},
+  doi = {10.1103/PhysRevB.81.134507},
+  url = {https://link.aps.org/doi/10.1103/PhysRevB.81.134507}
+}
+
+@article{CR_Second,
+author = {Groot, P. and Lisenfeld, Jürgen and Schouten, R. and Ashhab, S. and Lupascu, Adrian and Harmans, Kees and Mooij, Hans},
+year = {2010},
+month = {08},
+pages = {},
+title = {Selective darkening of degenerate transitions demonstrated with two
+superconducting quantum bits},
+volume = {6},
+journal = {Nature Physics},
+doi = {10.1038/nphys1733}
+}
+
+@book{Manenti:2023zzn,
+    author = "Manenti, Riccardo and Motta, Mario",
+    title = "{Quantum Information Science}",
+    isbn = "978-0-19-878748-8",
+    publisher = "Oxford University Press",
+    month = "8",
+    year = "2023"
+}
+
+@article{CRDrag,
+author = {Li, Boxi and Calarco, Tommaso and Motzoi, Felix},
+year = {2024},
+month = {07},
+pages = {},
+title = {Experimental error suppression in Cross-Resonance gates via multi-derivative pulse shaping},
+volume = {10},
+journal = {npj Quantum Information},
+doi = {10.1038/s41534-024-00863-4}
+}
+
+
 @article{Klimov_2018,
    title={Fluctuations of Energy-Relaxation Times in Superconducting Qubits},
    volume={121},

platforms/qubit/parameters.json

@@ -12,7 +12,7 @@
   },
   "hamiltonian":{
     "transmon_levels": 2,
-    "single_qubit": {
+    "qubits": {
       "0": {
         "frequency": 5e9,
         "anharmonicity": -200e6,

platforms/qutrit/parameters.json

@@ -12,7 +12,7 @@
     },
     "hamiltonian":{
       "transmon_levels": 3,
-      "single_qubit": {
+      "qubits": {
         "0": {
           "frequency": 5e9,
           "anharmonicity": -200e6,

platforms/qutrits/calibration.json

@@ -0,0 +1,75 @@
+{
+    "single_qubits": {
+        "0": {
+            "resonator": {
+                "bare_frequency": 0.0,
+                "dressed_frequency": 0.0,
+                "depletion_time": 0,
+                "bare_frequency_amplitude": null
+            },
+            "qubit": {
+                "frequency_01": 5114000000.0,
+                "frequency_12": 4784000000.0,
+                "maximum_frequency": 5114000000.0,
+                "asymmetry": 0.0,
+                "sweetspot": 0.0,
+                "flux_coefficients": null
+            },
+            "readout": {
+                "fidelity": 0.0,
+                "coupling": null,
+                "effective_temperature": null,
+                "ground_state": [
+                    0.0,
+                    1.0
+                ],
+                "excited_state": [
+                    1.0,
+                    0.0
+                ],
+                "qudits_frequency": {}
+            },
+            "t1": null,
+            "t2": null,
+            "t2_spin_echo": null,
+            "rb_fidelity": null
+        },
+        "1": {
+            "resonator": {
+                "bare_frequency": 0.0,
+                "dressed_frequency": 0.0,
+                "depletion_time": 0,
+                "bare_frequency_amplitude": null
+            },
+            "qubit": {
+                "frequency_01": 4914000000.0,
+                "frequency_12": 4584000000.0,
+                "maximum_frequency": 4914000000.0,
+                "asymmetry": 0.0,
+                "sweetspot": 0.0,
+                "flux_coefficients": null
+            },
+            "readout": {
+                "fidelity": 0.0,
+                "coupling": null,
+                "effective_temperature": null,
+                "ground_state": [
+                    0.0,
+                    1.0
+                ],
+                "excited_state": [
+                    1.0,
+                    0.0
+                ],
+                "qudits_frequency": {}
+            },
+            "t1": null,
+            "t2": null,
+            "t2_spin_echo": null,
+            "rb_fidelity": null
+        }
+    },
+    "two_qubits": {},
+    "readout_mitigation_matrix": null,
+    "flux_crosstalk_matrix": null
+}