TopQAD Documentation

Noise Profiler

This page uses the terminology and concepts discussed in the Quantum Architecture Basics section.

The Noise Profiler automates the process of profiling logical performance of FTQC protocols, such as quantum memory or teleportation, based on hardware noise characteristics. This enables you to quickly run simulation experiments to guide the design and evaluation of your quantum computer towards FTQC. The Noise Profiler includes methods for estimating performance at scales and for parameter values beyond those directly accessible via simulation.

For example, the Noise Profiler can help answer the following questions:

Quantum Processing Unit (QPU) and Controller

What error rates will a hardware noise model result in when executing an FTQC protocol?
Which hardware noise model parameters are most important to focus on and/or improve? How do they trade off?
How does a given variability in the fabrication process affect the performance of an FTQC protocol?

Decoder

What error rates does a particular decoder generate when integrated with certain target hardware?

Portal Specifications

Noise Profiler Portal Access Specifications

Inputs

Code

Users must select a QECC from the drop-down menu. Options are described in the table below. A description of the selected option is given in the table below. The table will be updated as additional QECCs become available.

Code	Description
Rotated surface code	A CSS stabilizer code that can be embedded on a square lattice. Each stabilizer addresses only the nearest neighbour data qubits.

Protocol

Users must select a protocol from a drop-down menu. The parameters that they must enter vary based on the protocol selected, and are described below. For details on each protocol please see the TopQAD's Tools >> Noise Profiler section.

Protocol	Parameters	Descriptions
Memory	Distance	The code distance. The value must be odd.
	Rounds	The number of stabilization rounds.
	Basis	The logical basis state to preserve.
Magic state preparation rep code	Distances	The distances of the stages of the protocol. They are comma-separated and there are at least two.
	Rounds	The number of stabilization rounds of the stages of the protocol. They are comma-separated and there are at least two.
	Inject state	The basis state to create, as magic states cannot be created in a Clifford simulation.
Magic state preparation hook injection	d_1	The distance of the first stage.
	d_2	The distance of the second stage.
	r_2	The number of stabilization rounds of the second stage.
	Inject state	The basis state to create, as magic states cannot be created in a Clifford simulation. Only the basis state "X" is allowed.
Stability	Rounds	The number of stabilization rounds.
Stability	Diameter	The length of the patch. The value must be even.

Noise Model

Users must select a noise model from a drop-down menu. The parameters that they must enter vary based on the noise model selected, and are described below. For details on each protocol please see the TopQAD's Tools >> Noise Profiler section.

Physical Depolarizing

Parameter	Description	Presets
Parameter	Description	Baseline	Target	Desired
Measurement time	The time taken to measure a qubit.	200 ns	100 ns	100 ns
Preparation time	The time taken to prepare a qubit in a zero or one state at the start of a protocol.	1 µs	1 µs	1 µs
Reset time	The time taken to reset a qubit to the zero state mid-protocol.	200 ns	100 ns	100 ns
One-qubit gate time	The time taken to implement one-qubit gates (e.g., the Hadamard gate).	25 ns	25 ns	25 ns
Two-qubit gate time	The time taken to implement two-qubit gates (e.g., the controlled-NOT, or CNOT, gate).	25 ns	25 ns	25 ns
$T_1$ longitudinal relaxation time	The relaxation time for a qubit.	100 µs	200 µs	340 µs
$T_2$ transverse relaxation time	The dephasing time for a qubit. When $T_2\neq T_1$ , idling noise is modelled as a general one-qubit Pauli channel. If $T_2=T_1$ , idling noise reduces to a one-qubit depolarizing channel.	100 µs	200 µs	340 µs
Measurement error	The infidelity of measuring a physical qubit, that is, the average probability of an output of 0 when measuring the one state and an output of 1 when measuring the zero state.	0.01	0.005	0.00294
Preparation error	The infidelity of preparing a qubit at the start of the protocol, that is, the average probability of preparing the zero state when trying to prepare the one state, and preparing the one state when trying to prepare the zero state.	0.02	0.01	0.00588
Reset error	The infidelity of resetting a qubit mid-protocol, that is, one minus the probability of correctly resetting to the zero state regardless of the outcome of the preceding measurement.	0.01	0.005	0.00294
One-qubit gate error	The infidelity of implementing one-qubit gates (e.g., the Hadamard gate).	0.0004	0.0002	0.00012
Two-qubit gate error	The infidelity of implementing two-qubit gates (e.g., the CNOT gate).	0.003	0.0005	0.00029

Uniform Depolarizing

Parameter	Description
$p$	The strength of all noise channels.
Stabilization time	The time required to execute one stabilization round. It is only used for QRE.

Decoder

Users must select a decoder from the drop-down menu. A description of the selected option is given in the table below. The table will be updated as additional decoders become available.

Decoder	Description
PyMatching	A minimum-weight perfect matching decoder.

Simulation Parameters

Parameter	Description
Max N samples	The maximum number of samples to collect for each row in the simulation table.
Signal to noise	If the signal-to-noise ratio (SNR) is achieved before "Max N samples" is reached, no additional data is collected for the row. The number of errors required to achieve the desired SNR is equal to (SNR) $^2$ .

Outputs

Simulation Results

Parameter	Description
Elapsed time	The time taken to run the noise profiling.
Simulation specifications	The specifications for simulation are output for reference. They are primarily user inputs, which are described above under "Inputs". The parameters Category and Name are determined based on the protocol's specifier. The Category parameter describes the function the protocol performs (e.g., memory, magic state preparation, lattice surgery).
Shots	The number of samples collected. The result appears under the simulation results tab.
Errors	The number of logical errors observed. The result appears under the simulation results tab.
Discards	This field only exists for protocols with post-selection. It is the number of samples discarded after post-selection. The result appears under the simulation results tab.
Logical error rate per shot	The logical error rate (LER) computed by $\text{Errors}/\text{Shots}$ . The result appears under the simulation results tab.
ΔLER	The satistical error in the LER due to finite sampling. Computed by $\sqrt{\text{LER} \cdot (1-\text{LER}) / \text{Shots}}$ . The result appears under the simulation results tab.
Discard rate per shot	This field only exists for protocols with post-selection. It is the discard rate (DR) computed by $\text{Discards}/\text{Shots}$ . The result appears under the simulation results tab.
ΔDR	This field only exists for protocols with post-selection. It is the statistical error in the DR due to finite sampling, computed by $\sqrt{\text{DR} \cdot (1-\text{DR}) / \text{Shots}}$ . The result appears under the simulation results tab.
Noise model	All input specifications for the chosen noise model. The result appears under the noise model tab.
Stabilization time	The time taken to perform one cycle of stabilizer measurements (i.e., parity checks on QEC codes). The result appears under the code characteristics tab.

The Noise Profiler simulator uses a heuristic to avoid simulations that are unlikely to yield good statistics. It first collects $10\%$ of the samples. If no errors are observed, then the remaining samples are not collected. In this case, the output statistical parameters will have the value "F" (indicating failure).