From 91bfb5c1f78ea406106f89c086273a6805399371 Mon Sep 17 00:00:00 2001 From: Ryan LaRose Date: Tue, 14 Sep 2021 13:33:36 -0400 Subject: [PATCH] [Docs] Add calibration FAQ (#4442) This adds FAQ / more information about calibration from @mrwojtek and others. cc @karlunho --- docs/_book.yaml | 2 + docs/google/calibration_faq.md | 316 ++++++++++++++++++ ...chain_with_calibration_example_results.png | Bin 0 -> 39579 bytes ..._echo_with_calibration_example_results.png | Bin 0 -> 38131 bytes docs/google/merge_subsets.png | Bin 0 -> 61139 bytes docs/tutorials/google/calibration_api.ipynb | 4 +- 6 files changed, 321 insertions(+), 1 deletion(-) create mode 100644 docs/google/calibration_faq.md create mode 100644 docs/google/linear_chain_with_calibration_example_results.png create mode 100644 docs/google/loschmidt_echo_with_calibration_example_results.png create mode 100644 docs/google/merge_subsets.png diff --git a/docs/_book.yaml b/docs/_book.yaml index 6a36f7af788..e23c5d650b3 100644 --- a/docs/_book.yaml +++ b/docs/_book.yaml @@ -107,6 +107,8 @@ upper_tabs: path: /cirq/google/specification - title: "Calibration metrics" path: /cirq/google/calibration + - title: "Calibration FAQ" + path: /cirq/google/calibration_faq - title: "Best practices" path: /cirq/google/best_practices diff --git a/docs/google/calibration_faq.md b/docs/google/calibration_faq.md new file mode 100644 index 00000000000..d10b7bca41f --- /dev/null +++ b/docs/google/calibration_faq.md @@ -0,0 +1,316 @@ +# Calibration FAQ + +**Warning:** The circuit-specific calibration API is an advanced alpha feature. Best practices may change in the future. + +## What is calibration? + +Calibration is a technique to reduce systematic errors in quantum circuits. This technique aims to adjust for gate errors +in moments that contain only two-qubit gates. Circuit specific calibrations optimizes gate error for specific circuits. +When executing a circuit with multiple simultaneous two-qubit gates, the actual effect may be different than the intended +effect due to various sorts of errors, such as drift or cross-talk. Though one may request a `cirq.SQRT_ISWAP` gate, the quantum state +may be affected by a unitary effect that is close to, but not exactly, a `cirq.SQRT_ISWAP`. Characterization attempts to identify +the actual effect of the gates using repeated expressions of the two-qubit layer. Once parameters are identified that more +closely resemble the actual effect, some errors can be compensated for by using Z gates to correct phases before and after +each gate. This will improve the accuracy of the overall moment without adding additional duration to the circuit (the newly +added Z gates will be merged with the already existing Z gates after sending circuits to the QCS.) + +The [two supported techniques](../tutorials/google/calibration_api.ipynb) are [Floquet calibration](../tutorials/google/floquet_calibration_example.ipynb) +and [XEB calibration](../tutorials/google/xeb_calibration_example.ipynb), both of which are advanced alpha features. + +## What is the Floquet calibration protocol? + +Floquet calibration protocol allows for determining the parameters of entangling gates rapidly and precisely, which unlocks +the ability to compensate for systematic gate errors caused by drifts and fluctuations. Like XEB, it is robust to state +preparation and measurement errors. Floquet calibration is based on the idea that an entangling gate can be determined by +the eigenvalues of the composite gates consisting of the entangling gate and different single-qubit gates, where each choice +of single-qubit gates provides a snapshot of the entangling gate. There are two stages in Floquet calibration, characterization +and compensation. Currently, only the single-qubit Z phases before and after the two-qubit gate are compensated. The +compensation pulses are combined with the gate pulses; therefore, they do not increase the circuit implementation time. In +structured circuits, two-qubit gates in the same moment should be calibrated simultaneously to combat crosstalks if possible. +Floquet calibration is really fast, which allows one to calibrate multiple moment structures within budgeted time. + +## Which gates are supported by Floquet and XEB calibrations? + +Floquet calibrations specified by `cirq_google.FloquetPhasedFSimCalibrationOptions` supports characterization of four out of +five unitary parameters θ, ζ, γ and φ of the `cirq.FSim(theta=pi / 4, phi=0)` gate (inverse of the `cirq.SQRT_ISWAP` gate) +presently. The Cirq compiler can use Z gates to compensate for the ζ, χ, γ parameters. The compiler can also compile `cirq.SQRT_ISWAP` +gate into its inverse so that it can be used in calibrated circuits and take advantage of the characterization. + +The XEB calibration specified by `cirq_google.LocalXEBPhasedFSimCalibrationOptions` supports `cirq.SQRT_ISWAP` and its inverse. +It characterizes all five unitary parameters and also provides the fidelity estimates for each of the calibrated gates. However, +the compiler can only adjust for three of the five parameters by inserting Z gates. + +This version of XEB is using the client-side Cirq characterization backed by +`cirq.experiments.xeb_fitting.characterize_phased_fsim_parameters_with_xeb_by_pair` and when used directly it can support +arbitrary gates, including composite ones. However, the compiler which adjusts for ζ, χ, γ angles available in cirq_google +package supports only `cirq.SQRT_ISWAP` with its inverse and `cirq_google.SYC`. + +Floquet calibration does not yet support microwave gates, this functionality is planned. + +## How do I calibrate a circuit using Floquet or XEB calibrations? + +Refer to the [Calibration API](../tutorials/google/calibration_api.ipynb) tutorial for an overview, and see the +[Floquet calibration example](../tutorials/google/floquet_calibration_example.ipynb) and [XEB calibration example](../tutorials/google/xeb_calibration_example.ipynb) +for detailed steps on example circuits with benchmarks. + +This is in principle a three-step process which consists of the following three steps: + +1. Analyzing the circuit: To analyze the circuit, use `cirq_google.prepare_characterization_for_moments` with + `cirq_google.FloquetPhasedFSimCalibrationOptions` (for Floquet) or `cirq_google.LocalXEBPhasedFSimCalibrationOptions` + (for XEB). This function will analyze the circuit and figure out which moments will need to be characterized. It will + identify moments with the same two-qubit structure so that they can be characterized together. + +2. Characterizing the layer: The previous step will generate a list of characterization requests (one for each unique layer). + The next step is to call `cirq_google.run_calibrations`. This will invoke the API and send the requests to the device + to be characterized. + +3. Compile the circuit: The final step is to use the results of the characterization to re-compile the circuit to compensate + for ζ, χ and γ angles. This can be done with the help of `cirq_google.make_zeta_chi_gamma_compensation_for_moment` function. + +## When should Floquet or XEB Calibrations be used? + +Both calibrations are primarily focused on decreasing the effects of two sources of errors: calibration drifts and cross-talk +errors. Those errors are not uniform across the chip and vary in magnitude between qubits and device calibrations. The +circuit-specific calibrations should be used in situations when achieving the best performance out of Google’s hardware is more +important than using extra time on the device for the characterizations. + +The ζ, χ and γ parameters of the `cirq.PhasedFSimGate` unitary are subject to drifts that range in frequency from seconds to hours. +They can be automatically compensated by adjusting the single-qubit Z rotations. This functionality is provided for the supported +circuits through the `cirq_google.make_zeta_chi_gamma_compensation_for_moments` or `cirq_google.make_zeta_chi_gamma_compensation_for_operations` +functions. + +The types of cross-talk that are captured by circuit specific calibrations influence the θ, ζ, χ and γ unitary angles the most. Similarly to drift errors; ζ, χ and γ can be compensated by adjusting the single-qubit Z rotations. + +The parameter φ is usually stable in time and is loosely dependent on the user circuit. However, its value might vary between interacting pairs and undergo rapid changes occasionally. + +For reference, the PhaseFSimGate unitary is represented by: + +```text + [[1, 0, 0, 0], + [0, exp(-iγ - iζ) cos(θ), -i exp(-iγ + iχ) sin(θ), 0], + [0, -i exp(-iγ - iχ) sin(θ), exp(-iγ + iζ) cos(θ), 0], + [0, 0, 0, exp(-2iγ-iφ)]]. +``` + +## What is the difference between the user-triggered calibrations (Floquet or XEB) and the maintenance calibration? + +The maintenance or device calibration is performed every few days by the device support team and is focused on low-level +maintenance like adjusting qubit frequencies or profiling the pulse shape of each gate. This maintenance is performed +holistically for the entire chip and is mostly focused on a good performance of the chip in general. This maintenance +benchmarks performance on isolated gates or fully-layered simultaneous gates that may or may not resemble the circuits +specific in your execution. + +The user-triggered calibrations issued through the [Calibration API](../tutorials/google/calibration_api.ipynb) are designed for circuit-specific +execution to capture both drift and cross-talk errors. They can be triggered just before the user circuit execution, in order to +reduce the effect of drift. They can also be triggered on very specific qubits that match the user’s executed circuits in order to +reduce cross-talk errors. The user-triggered calibrations do not change the qubit frequency or pulse shapes at this moment; they +focus only on compensating the gate unitary parameters. + +## What is the difference between Floquet and XEB calibrations? + +Floquet and XEB have the same purpose of characterizing gates but differ in their specific methods. + +XEB characterization is based on scrambling gates with random single-qubit rotations, which include the microwave X and Y gates. +Based on many different realizations, the unitary parameters which maximize the fidelity of each gate can be learned. Floquet +calibration is more targeted and assumes certain noise characteristics to learn each parameter. The current Floquet calibration +uses only Z gates during the repetition phase of the experiment. + +Because of its nature, XEB is easily adapted to various gates and currently it supports all the angles of √iSWAP gate. Floquet +characterization doesn’t cover all the angles: the angle χ is not supported currently. It also follows that XEB requires more +quantum samples and classical computational resources to estimate the unitary parameters; to reach a comparable precision of +estimation, XEB is about an order of magnitude slower compared to the Floquet calibration. Therefore if you either have limited +time on the processor (e.g. Open-swim time) or the observed fluctuations is longer than the timescale of the calibration, one +may want to use Floquet calibration. + +The other significant difference is concerned with microwave gates. [Physical Z Gate](https://quantumai.google/cirq/google/devices#one_qubit_gates) +(`cirq.PhasedXZGate`) can add additional sources of error that may be captured by XEB characterization. XEB calibration is more applicable to circuits that alternate single-qubit and two-qubit layers due to the similarity between the random XEB circuits and executed circuits. Floquet calibration may be more applicable to the circuits with two-qubit gates and Z gates only. + +Note that, once the gates have been characterized, both methods share the same compilation/compensation method. + +## I have many circuits to calibrate, how do I speed it up? + +If the circuits have a similar structure (compatible moments), then they can probably share the same characterization. To +prepare such a characterization request, it needs to be passed as initial argument to the `cirq_google.prepare_characterization_for_moments` +method: + +```python +circuit_to_compensate = [] +requests = [] +for circuit in circuits: + circuit_to_compensate, requests = prepare_characterization_for_moments( + circuit, options, initial=requests + ) + circuits_to_compensate.append(circuit_to_compensate) +``` + +Alternatively the same result can be achieved by passing a list of circuits to the `cirq_google.prepare_characterization_for_circuits_moments` +helper method: + +```python +circuits_to_compensate, requests = prepare_characterization_for_circuits_moments( + circuits, options +) +``` + +Please note that the software is smart enough to select the minimum number of characterizations for a batch of circuits. + +To control the granularity further, the `cirq_google.prepare_characterization_for_moments` function has a `merge_subsets` +option. This option is by default set to true which indicates that whenever two moments appear, and one of the moments is +a subset of another moment then they will be merged together and characterized as a moment which is the larger of the two. +This choice leads to a smaller number of necessary layers, but some of the issues related to crosstalk are not captured. +For the highest accuracy, it might be desired to characterize each unique moment separately with the merge_subsets option +set to false. + +![Illustration of `merge_subsets` option.](./merge_subsets.png) + +Note that in this image the qubit lines run from top to bottom instead of left to right (the usual in Cirq). + +## What is the difference between moment-oriented and operations-oriented calibrations? + +There are two kinds of calibrations available in `cirq_google.calibrations` module: + +* moment oriented with `cirq_google.prepare_characterization_for_moments` and `cirq_google.make_zeta_chi_gamma_compensation_for_moments` + functions, and +* operations oriented with `cirq_google.prepare_floquet_characterization_for_operations` and `cirq_google.make_zeta_chi_gamma_compensation_for_operations`. + +The moment-oriented characterizations analyse the circuit moment by moment in order to account for cross-talks. When some +gate on a particular set of qubits appears in two different moments, it will be characterized twice in two layers with different +gates acting in parallel. On current devices the cross-talk effects are very strong on certain qubit configurations. + +There is an option to ignore the moment restrictions with the operations based calibration. In this mode, the moment structure +is ignored and the circuit is analyzed on a per-operation basis, a single pair appears in at most one layer being characterized. +With the current planar architecture, this bounds a maximum number of different characterizations for an arbitrary number of circuits +by four. This option might be useful to quickly check for the state of a device or benchmark particular qubit configurations before +doing the actual experiment. + +For example, if you have a circuit on a line of 5 qubits, there are 4 unique two-qubit gates and 7 unique moments with different +combinations of two-qubit gates. If you use `cirq_google.prepare_floquet_characterization_for_operations`, this will result +in 2 characterizations (since 2 unique gates can be put into a single moment) . If you use `cirq_google.prepare_characterization_for_moments` +with `merge_subsets=False` this will result in 7 characterizations. + +## What if the compensation based on single-qubit phases is not enough? + +The provided compilation `cirq_google.make_zeta_chi_gamma_compensation_for_moments` uses Z gates to compensate for errors. +For the `cirq.SQRT_ISWAP` gate this does not affect duration of a circuit because the added Z gates are merged with the +already-existing Z gate pulses after submitting circuits to server. This compilation method that uses just Z gates can only +compensate for 3 angles: ζ, χ and γ. + +Compensation for the remaining two parameters θ and φ can’t be realized in a simple way. Some experiments can be modified +to adjust to these errors by modifying circuit construction, compilation, or problem statement, but this must be handled by the +user and cannot be done automatically. + +For these advanced use cases, the `cirq_google.run_calibration` method can be called directly with a list of +`cirq_google.PhasedFSimCalibrationRequest` objects. This will allow you to call the Calibration API directly to specify +customized layers for characterizations. + +```python +@dataclasses.dataclass(frozen=True) +class PhasedFSimCalibrationRequest(abc.ABC): + pairs: Tuple[Tuple[Qid, Qid], ...] # a list of pairs of in a single moment to characterize + gate: Gate # desired gate (must be cirq.ISWAP ** -0.5 for Floquet) + options: PhasedFSimCalibrationOptions # detailed adjustments + # either FloquetPhasedFSimCalibrationOptions or LocalXEBPhasedFSimCalibrationOptions +``` + +After triggering this calibration with the `cirq_google.run_calibrations` method, the `PhasedFSimCalibrationResult` is returned +with a parameters field that contains the unitary parameters of all the requested gates. The object also contains additional +execution metadata which might be useful. + +See also ["How to compensate for the parasitic c-phase φ angle?"](#how-to-compensate-for-the-parasitic-c-phase-φ-angle) below. + +## Floquet calibration fails with a message: Readout errors above the tolerance for qubit pairs (...), what can be done? + +This is an automated check performed before the actual Floquet calibration on QCS used to detect if a particular gate did not +drift too much outside of reasonable error levels. When the check fails, the following exception is reported: + +```python +PhasedFSimCalibrationError: Readout errors above the tolerance for qubit pairs ((8, 3), (8, 4)) +``` + +Probably the most desired action would be to try to avoid this particular pair. For many qubits, this might be a temporary +effect and repeating the experiment at a later time might help. + +The automated check can also be relaxed by setting the `readout_error_tolerance` parameter to a value higher than `0.4` in +`cirq_google.FloquetPhasedFSimCalibrationOptions`. (A value of `1.0` disables the readout checks entirely). + +## How should I validate that Floquet or XEB calibration is working? + +One mechanism for determining if your circuit performance is improving would be to run Floquet / XEB calibration on your +actual circuit and compare the results to your noiseless simulation. This however could be difficult and expensive as your +circuit size increases. + +Alternatively, one can run a Loschmidt echo with random circuits using Floquet calibration, and see that the overall return +probability is higher than before. Even though the Loschmidt Echo random circuit may look very different from the actual circuit +you are running, the gate compensations should result in a decent improvement in the return probabilities. + +See [this tutorial for an example of using Loschmidt echo](../tutorials/google/echoes.ipynb). Here is an example of applying Floquet and XEB +corrections to a 16-site Loschmidt echo circuit (higher is better): + +![Calibration benchmark with Loscmidt echoes](./loschmidt_echo_with_calibration_example_results.png) + +Here is another example of applying calibrations to a linear chain circuit that contains only Z gates and `cirq.SQRT_ISWAP` gates +(lower is better): + +![Calibration benchmark with linear chain circuit](./linear_chain_with_calibration_example_results.png) + +## How should I test Floquet / XEB Calibration on my circuit? + +* First, you should have a circuit whose performance needs to be improved. Defining a metric of success is important to + clarify whether the procedure was successful. (E.g., for the case of the Fermi-Hubbard experiment, calculating the + spin-charge density of each site). + +* Make sure you get a reservation budget and then + [reserve a block of time using the cloud console](https://console.cloud.google.com/quantum/processors/) to test various + permutations of your circuit. Expect that each calibration would take about 1.6s per qubit and 28s per moment of additional + time to your regular circuit runs. + +* Run the circuit against both a perfect simulator and a coherent noise simulator to get valid baselines for performance. + +* Using [this tutorial for Floquet calibration](../tutorials/google/floquet_calibration_example.ipynb) as a guide, introduce Floquet characterization + and resulting compensating Z phase gates into your circuit, and compare the results with Floquet calibration turned on and turned off. + +In order to ensure an apt comparison, it is important to keep the following points in mind: + +* Make sure you pick your qubits wisely. + - Use parallel readout heatmap to avoid any obviously broken qubits. + - Use two-qubit error heatmaps to choose various patches of qubits with good two-qubit gate performance. + - Use a mini-benchmark circuit to sanity check both qubit choice and basic circuit design. + - If in doubt, [use parallel XEB to check for issues like drift / TLS](../tutorials/google/compare_to_calibration.ipynb). + +* Start small with a low number of qubits (e.g. 2 qubits, with 5-10 layers of 2 qubit gates), and increase the number of qubits + and gate depth. +* Do not increase the gate depth past the T1 time of the qubits. +* Use out of the box re-compilation first. If that doesn’t work, then try custom recompilation. + +For a complete set of best practices, check the following [guide](./best_practices.md). + +## How to compensate for the parasitic c-phase φ angle? + +The `cirq_google.SQRT_ISWAP` gate ideally should have a zero value of the φ angle. In practice the ZZ interaction always +happen during the gate execution and all the two-qubit gates attain some unwanted parasitic c-phase angle φ. The typical +values for √iSWAP gate are about 0.13 which might be significant amount for certain applications, especially when circuits +of large depth are executed that accumulate errors caused by this term. + +Compensating for this parameter can be achieved in certain situations although in most cases the compensation adds more gates +which can cause the increase in the circuit runtime. Thus, the compensation itself might introduce even more noise during +execution, so it’s feasibility should be chosen on a case-by-case basis. + +The following references might provide some help on dealing with this issue but none of them is a complete solution to the problem: + +* The cirq-google package has a numerical [GateTabulation compiler](https://github.com/quantumlib/Cirq/blob/eb72fb547eec8377f24287aa5d03a2b66eaedff4/cirq-google/cirq_google/optimizers/two_qubit_gates/example.py) + that decomposes arbitrary gate into arbitrary two-qubit base gate. This code was not designed for the case where each base + gate is different and might not be practical to use for actual applications. + +* [arXiv:2106.15490](https://arxiv.org/abs/2106.15490) proposes a numerical optimization routine for approximate gate + compilation and discusses tradeoffs of using approximate gate compilation (higher decomposition error) to reduce circuit + depth (lower hardware error) in an attempt to maximize overall circuit fidelity. + +* [arXiv:2010.07965](https://arxiv.org/abs/2010.07965) in Supplementary Information A describes analytical decomposition + of arbitrary FSimGate(0, 𝜙), under the assumption that |𝜙| is larger than twice the parasitic c-phase φ of the base gate. + An implementation of this decomposition is included in ReCirq. + +* There is also a helper method in Cirq `cirq.two_qubit_matrix_to_sqrt_iswap_operations` that is based on + [arXiv:2105.06074](https://arxiv.org/abs/2105.06074). However, it only allows to decompose into ideal `cirq.SQRT_ISWAP` + gates and thus is not useful for dealing with parasitic c-phase. + +* This is an active topic of research and we welcome more references. diff --git a/docs/google/linear_chain_with_calibration_example_results.png b/docs/google/linear_chain_with_calibration_example_results.png new file mode 100644 index 0000000000000000000000000000000000000000..20bce8bc5092045a07a5c0f59002b397e2c3d809 GIT binary patch literal 39579 zcmce;cR1F6{6BglTXslf%icnS5JGmcGPC#2yvfQYdnGFg*(-ZQR%Z6hOjanH^Yr_uX}-$Xn)B4x{Bef4H<)Rx*;g8u!CCL`9jA^v4{HS_={vFdBdHN|QTlyJoQjHyOvGX3Xr3FPG=3>! zo)z)&qm$*PzCJ$T;o;F#B7DZ}L6MP>1meewx7le#-M4H?o0#K!ZeSW$k${mB7G;~V!pr9Gxx=9rUluOpU-3{Y%^YrOU|X=;J!U|=T^j5lk(%K z-*kENLnUfbctySZ?SGcL^|ZBTo4k+mlMO1$${ZaXQ$#)NSH0hI^o4|m*4j)cb0v$4 zh&)XbVCCjkx!U>sqT%u&>#FX{m)@6r+}x%4ipg5dH7Z%+gAb2pzebRIAMKQAveC>m z={3IM?cmX?u^qN}WU&4{vpa^yuzsasxA|ay|83997hhaOke7|k=e>#S%iS>!KRzYu 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