Protocols¶
Generates a 

Generates a 

Generates a 

Generates a 

Generates a 

Generates a 

Generates a 

Generates a 

Generates a 

Computes the quantum capacity (QCAP) bound of the given circuit. 

Randomly compiles the given circuit into many new random circuits which implement the same algorithm. 
Make CB¶

trueq.
make_cb
(cycles, n_random_cycles, n_circuits=30, n_decays=20, targeted_errors=None, twirl=None, propagate_correction=False, compiled_pauli=True)¶ Generates a
CircuitCollection
to estimate the process fidelity of one or more cycles using cycle benchmarking (CB). See the CB guide for more information.import trueq as tq # generate a circuit collection to run CB on the 0th qubit, with 30 circuits, # for each length in [4, 20] and each with 3 randomly chosen Pauli decay strings circuits = tq.make_cb({0: tq.Gate.x}, [4, 20], 30, 3) # draw the first circuit circuits[0].draw()
 Parameters
cycles (
Iterable
Cycle
dict
) – The cycles which specify the subcircuit to benchmark.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[4, 20]
.n_circuits (
int
) – The number of circuits for each number of random cycles.n_decays (
int
) – An integer specifying the total number of randomly chosen Pauli decay strings used to measure the process infidelity or the probability of each error. Warning: Setting this value lower thanmin(20, 4 ** n_qubits  1)
may result in a biased estimate of the process fidelity, and setting this value lower thanmin(40, 4 ** n_qubits  1)
may result in a biased estimate of the probability for nonidentity errors.targeted_errors (
Iterable
) – A list of Pauli strings, e.g.["ZIZIZ", "XYXYX"]
that specify which errors to target. By default, the Pauli"I" * n_qubits
is used to estimate the probability of no error, i.e. the process fidelity.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"P"
) that will be used to automatically instantiate a twirl based on the labels in the given cycles.propagate_correction (
bool
) – Whether to propagate correction gates to the end of the circuit or compile them into neighbouring cycles. Warning: this can result in arbitrary twoqubit gates at the end of the circuit!compiled_pauli (
bool
str
) – Controls whether or not to compile a random Pauli gate onto each qubit in the cycle preceding a measurement operation (default isTrue
). Also accepts a string of Paulis to compile, which will be the same for all circuits returned by this function. A list of compiled Paulis is stored as a string in thekey
attribute, where the order is defined by the sorted labels of the circuit.
 Returns
A collection of CB circuits.
 Return type
Crosstalk Diagnostics¶

trueq.
make_crosstalk_diagnostics
(labels, n_random_cycles, n_circuits=30, subsets=None, include_xrb=True, twirl=None)¶ Generates a
CircuitCollection
to measure the discrepancy between gate quality while applying gates simultaneously versus while applying gates in an isolated way to each individual system. See the CTD guide for more information.This discrepancy is assessed by running SRB simultaneously on the specified systems, as well as running it on each system in turn. Optionally, and
True
by default, the coherence of crosstalk errors is assessed using XRB. Therefore, this function is equivalent to concatenating the circuits from multiple calls tomake_srb()
(and optionallymake_xrb()
) with different label configurations.import trueq as tq # generate a circuit collection to run crosstalk diagnostics in single qubit # mode for qubits 5, 6, 7, and 8 circuits = tq.make_crosstalk_diagnostics([5, 6, 7, 8], [4, 100]) # reduce the number of circuits to perform by excluding XRB circuits # this means we cannot distinguish between coherent errors (due to static # crosstalk) and incoherent errors (due to fluctuating crosstalk) circuits = tq.make_crosstalk_diagnostics( [5, 6, 7, 8], [4, 100], include_xrb=False ) # we can also twirl some pairs of systems using entangling gates circuits = tq.make_crosstalk_diagnostics( [5, [6, 7], 8], [4, 100], include_xrb=False ) # using the subsets option, we can customize exactly which subsets of the full # simultaneous twirl are performed in isolation. Here, the default value would # have resulted in subsets [[5],[6],[[7, 8]]] circuits = tq.make_crosstalk_diagnostics( [5, 6, [7, 8]], [4, 100], include_xrb=False, subsets=[[5], [5, 6], [[7, 8]]] )
 Parameters
labels (
Iterable
) – A list of which sets of system labels are to be twirled together in each circuit, e.g.[3, [1, 2], 4]
.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[6, 20]
.n_circuits (
int
) – The number of circuits for at eachn_random_cycles
for each protocol.subsets (
Iterable
) – A list of subsets of the given labels to be used. The default value ofNone
results in each subset being a member of the given labels. See the last example above.include_xrb (
bool
) – Whether to include XRB circuits in the output.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"C"
) that will be used to automatically instantiate a twirl based on the given labels.
 Returns
A collection of circuits to diagnose crosstalk.
 Return type
Make IRB¶

trueq.
make_irb
(cycles, n_random_cycles, n_circuits=30, twirl=None, propagate_correction=False, compiled_pauli=True)¶ Generates a
CircuitCollection
to estimate the process fidelity of specific gates using (simultaneous) interleaved randomized benchmarking (IRB). See the IRB guide for more information.import trueq as tq # generate a circuit collection to run single qubit IRB on an X gate acting on # qubit 0, with 30 random circuits for each circuit length in [5, 40, 60, 100] circuits = tq.make_irb({0: tq.Gate.x}, [5, 40, 60, 100], 30) # next, generate circuits to run IRB on a cycle with an X gate acting on qubit 0 # and a CZ gate on qubits (2, 3), with 20 random circuits at each circuit length circuits = tq.make_irb({0: tq.Gate.x, (2, 3): tq.Gate.cz}, [2, 100], 20) # finding the Pauli matrix compiled into the first circuit print(circuits[0].key.compiled_pauli) # draw the first circuit circuits[0].draw()
XIY
0 2 3 Key: twirl: Cliffords on [0, (2, 3)] cycles: (Cycle((0,): Gate.x, (2, 3): Gate.cz),) protocol: IRB compiled_pauli: XIY n_random_cycles: 2 Labels: (0,) Name: Gate.cliff11 Aliases: Gate.cliff11 Generators: X: 127.28 Y: 127.28 0.71 0.71j 0.71 0.71j 11 Labels: (2, 3) Name: Gate Locally Equivalent: SWAP Generators: ZZ: 60.00 YZ: 60.00 YX: 60.00 XX: 60.00 XY: 60.00 ZY: 60.00 YI: 34.64 ... 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 1 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2, 3) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: IZ: 90.00 ZI: 90.00 ZZ: 90.00 1.00 1.00 1.00 1.00 CZ CZ Labels: (0,) Name: Gate.sx Aliases: Gate.sx Gate.cliff5 Generators: X: 90.00 0.71j 0.71 0.71 0.71j SX Labels: (2, 3) Name: Gate Locally Equivalent: iSWAP Generators: YZ: 73.48 IY: 73.48 YI: 73.48 XZ: 73.48 XI: 73.48 ZX: 73.48 XX: 34.64 ... 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 2 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2, 3) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: IZ: 90.00 ZI: 90.00 ZZ: 90.00 1.00 1.00 1.00 1.00 CZ CZ Labels: (0,) Name: Gate.cliff17 Aliases: Gate.cliff17 Generators: Z: 69.28 X: 69.28 Y: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 17 Labels: (2, 3) Name: Gate Locally Equivalent: CNOT Generators: IX: 90.00 YX: 90.00 0.50j 0.50 0.50 0.50j 0.50 0.50j 0.50j 0.50 0.50 0.50j 0.50j 0.50 0.50j 0.50 0.50 0.50j 3 Labels: (0,) Name: Meas M Labels: (2,) Name: Meas M Labels: (3,) Name: Meas M Note
We invert each random sequence up to an independent random Pauli matrix (accessible as shown in the example above) to diagnose errors to that are missed by always returning to the initial state [4].
Warning
The estimate of the process fidelity obtained by taking the ratio of the process fidelities from IRB and SRB is subject to a large systematic uncertainty that is typically not reported. This systematic uncertainty arises because of the many ways in which the noise in the twirling group can combine with the noise in the interleaved gates. Both the standard interleaved estimate and the systematic uncertainty are automatically computed by
fit
if the circuit collection contains SRB circuits. The systematic uncertainty can be reduced if the circuit collection also contains XRB circuits. Parameters
cycles (
Iterable
Cycle
dict
) – The cycles which specify the subcircuit to benchmark.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[6, 20]
.n_circuits (
int
) – The number of circuits for each number of random cycles.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"C"
) that will be used to automatically instantiate a twirl based on the labels in the given cycles.propagate_correction (
bool
) – Whether to propagate correction gates to the end of the circuit or compile them into neighbouring cycles. Warning: this can result in arbitrary twoqubit gates at the end of the circuit!compiled_pauli (
bool
str
) – Controls whether or not to compile a random Pauli gate onto each qubit in the cycle preceding a measurement operation (default isTrue
). Also accepts a string of Paulis to compile, which will be the same for all circuits returned by this function. A list of compiled Paulis is stored as a string in thekey
attribute, where the order is defined by the sorted labels of the circuit.
 Returns
A collection of IRB circuits.
 Return type
Make KNR¶

trueq.
make_knr
(cycles, n_random_cycles, n_circuits=30, n_bodies=1, twirl=None, propagate_correction=False, compiled_pauli=True)¶ Generates a
CircuitCollection
to estimate the probabilities of all errors acting on all sets of subsystems targeted by a combination of k gates using kbody noise reconstruction (KNR). See the KNR guide for more information.For example, if the input cycle is
{0: tq.Gate.id, (1, 3): tq.Gate.cnot, 2: tq.Gate.x}
andn_bodies=2
, then data will be present to reconstruct any Pauli error rate on the subsystems[0, 1, 3]
,[0, 2]
,[1, 2, 3]
(and any subsystems thereof, e.g.[1, 2]
but not[0, 1, 2]
).import trueq as tq # generate a circuit collection to reconsturct twobody marginal # error distributions # on a 4qubit device using 30 circuits for each length in [6, 20] # and for each Pauli subspace in a set of log2(4) subspaces circuits = tq.make_knr({j: tq.Gate.x for j in range(4)}, [6, 20], 30) # draw the first circuit circuits[0].draw()
0 1 2 3 Key: twirl: Paulis on [0, 1, 2, 3] cycles: (Cycle((0,): Gate.x, (1,): Gate.x, (2,): Gate.x, (3,): Gate.x),) n_bodies: 1 protocol: KNR compiled_pauli: ZXZY n_random_cycles: 6 measurement_basis: YZXX Labels: (0,) Name: Gate.cliff4 Aliases: Gate.cliff4 Generators: X: 90.00 0.71 0.71j 0.71j 0.71 4 Labels: (1,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (2,) Name: Gate.h Aliases: Gate.h Gate.cliff12 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 0.71 H Labels: (3,) Name: Gate.sy Aliases: Gate.sy Gate.cliff7 Generators: Y: 90.00 0.71 0.71 0.71 0.71 SY 1 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (1,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z Labels: (1,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (2,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (3,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z 2 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (1,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (1,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z Labels: (2,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X 3 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (1,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.y Aliases: Gate.y Gate.cliff2 Generators: Y: 180.00 1.00 1.00 Y Labels: (1,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (2,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X 4 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (1,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (1,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z Labels: (2,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (3,) Name: Gate.y Aliases: Gate.y Gate.cliff2 Generators: Y: 180.00 1.00 1.00 Y 5 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (1,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (1,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z Labels: (3,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID 6 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (1,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (2,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (3,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.cliff15 Aliases: Gate.cliff15 Generators: Z: 127.28 Y: 127.28 0.71 0.71j 0.71j 0.71 15 Labels: (1,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID Labels: (2,) Name: Gate.cliff13 Aliases: Gate.cliff13 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 0.71 13 Labels: (3,) Name: Gate.cliff13 Aliases: Gate.cliff13 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 0.71 13 7 Labels: (0,) Name: Meas M Labels: (1,) Name: Meas M Labels: (2,) Name: Meas M Labels: (3,) Name: Meas M Note
The number of returned circuits scales mildly with the number of total systems but exponentially with the value of
n_bodies
.Note
Currently, this function can only benchmark a single cycle.
 Parameters
cycles (
Iterable
Cycle
dict
) – The cycles which specify the subcircuit to benchmark.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[6, 20]
.n_circuits (
int
) – The number of circuits for each number of random cycles.n_bodies (
int
) – A number of gate bodies to reconstruct marginal probability distributions for.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"P"
) that will be used to automatically instantiate a twirl based on the labels in the given cycles.propagate_correction (
bool
) – Whether to propagate correction gates to the end of the circuit or compile them into neighbouring cycles. Warning: this can result in arbitrary twoqubit gates at the end of the circuit!compiled_pauli (
bool
str
) – Controls whether or not to compile a random Pauli gate onto each qubit in the cycle preceding a measurement operation (default isTrue
). Also accepts a string of Paulis to compile, which will be the same for all circuits returned by this function. A list of compiled Paulis is stored as a string in thekey
attribute, where the order is defined by the sorted labels of the circuit.
 Returns
A collection of KNR circuits.
 Return type
Make RCAL¶

trueq.
make_rcal
(labels, stagger=False, independent=True, batch=None)¶ Generates a
CircuitCollection
to measure the readout errors on the provided system labels. These circuits contain \(I\) and \(X\) gates. See RCAL guide for more information. Parameters
labels (
Iterable
) – A list of the system labels whose readout errors are to be estimated.stagger (
bool
) – Whether \(X\) gates should appear in separate marked cycles. If the gates are much worse when applied in parallel, then staggering them will reduce systematic errors, provided that the gate duration multiplied by the number of qubits is much shorter than \(T_1\).independent (
bool
) – Whether it can be assumed that the readout error is independent over qubits. Under this assumption, only two circuits are required, whereas \(2^n\) circuits are required when this assumption does not hold. Note that if you measure the readout calibration matrix in both independent and nonindependent modes, any observed nonindependence could potentially be due to gate crosstalk errors.batch (
int
) – A unique identifier for these calibration circuits. Other circuits which are to be calibrated based on these circuits’ results in particular should set theirtrueq.Circuit.key
batch
attribute to the same value.
 Returns
A circuit collection to measure the readout errors on the provided system labels.
 Return type
Make SC¶

trueq.
make_sc
(cycles, n_random_cycles, n_circuits=30, pauli_decays=None, twirl=None, propagate_correction=False, compiled_pauli=True)¶ Generates a
CircuitCollection
to optimize the fidelity of one or more cycles using stochastic calibration (SC). See the SC guide for more information.import trueq as tq # generate a circuit collection to run SC on the 0th qubit, with 30 circuits, # for each length in [4, 20] and each with a Pauli decay string "Z" circuits = tq.make_sc({0: tq.Gate.x}, [4, 20], 30, "Z") # draw the first circuit circuits[0].draw()
0 Key: twirl: Paulis on [0] cycles: (Cycle((0,): Gate.x),) protocol: SC analyze_decays: ('Z',) compiled_pauli: X n_random_cycles: 4 measurement_basis: Z Labels: (0,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID 1 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.y Aliases: Gate.y Gate.cliff2 Generators: Y: 180.00 1.00j 1.00j Y 2 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00j 1.00j Z 3 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID 4 Labels: (0,) Name: Gate.x Aliases: Gate.x Gate.cliff1 Generators: X: 180.00 1.00 1.00 X Labels: (0,) Name: Gate.id Aliases: Gate.id Gate.i Gate.cliff0 Locally Equivalent: Identity Generators: I: 0.00 1.00 1.00 ID 5 Labels: (0,) Name: Meas M  Parameters
cycles (
Iterable
Cycle
dict
) – The cycles which specify the subcircuit to benchmark.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[6, 20]
.n_circuits (
int
) – The number of circuits for each number of random cycles.pauli_decays (
Iterable
) – A list of Pauli decay strings, e.g.["ZIZIZ", "XYXYX"]
that specify which elements of the diagonalized channel should be estimated. These should be chosen to anticommute with the Hamiltonian terms of a known noise source to be optimized.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"P"
) that will be used to automatically instantiate a twirl based on the labels in the given cycles.propagate_correction (
bool
) – Whether to propagate correction gates to the end of the circuit or compile them into neighbouring cycles. Warning: this can result in arbitrary twoqubit gates at the end of the circuit!compiled_pauli (
bool
str
) – Controls whether or not to compile a random Pauli gate onto each qubit in the cycle preceding a measurement operation (default isTrue
). Also accepts a string of Paulis to compile, which will be the same for all circuits returned by this function. A list of compiled Paulis is stored as a string in thekey
attribute, where the order is defined by the sorted labels of the circuit.
 Returns
A collection of SC circuits.
 Return type
Make SRB¶

trueq.
make_srb
(labels, n_random_cycles, n_circuits=30, twirl=None, compiled_pauli=True)¶ Generates a
CircuitCollection
to estimate the process fidelity of random gates from a group using (simultaneous) streamlined randomized benchmarking (SRB). See the SRB guide for more information.import trueq as tq # generate a circuit collection to run single qubit SRB on qubit 5 circuits = tq.make_srb([5], [4, 200], 30) # generate a circuit collection to run simultaneous onequbit SRB on qubits # 2 and 7 and twoqubit SRB on the pairs [0, 1] and [4, 9] circuits = tq.make_srb([[0, 1], 2, 7, [4, 9]], [4, 200], 30) # finding the Pauli matrix compiled into the first circuit print(circuits[0].key.compiled_pauli) # draw the first circuit circuits[0].draw()
ZYYXZX
0 1 2 4 7 9 Key: twirl: Cliffords on [(0, 1), 2, (4, 9), 7] protocol: SRB compiled_pauli: ZYYXZX n_random_cycles: 4 Labels: (0, 1) Name: Gate Locally Equivalent: CNOT Generators: ZX: 73.48 ZI: 73.48 YX: 73.48 YZ: 73.48 YI: 73.48 ZZ: 73.48 IY: 34.64 ... 0.71j 0.71 0.71j 0.71 0.71 0.71j 0.71 0.71j Labels: (2,) Name: Gate.sx Aliases: Gate.sx Gate.cliff5 Generators: X: 90.00 0.71 0.71j 0.71j 0.71 SX Labels: (4, 9) Name: Gate Locally Equivalent: U(2)⊗U(2) Generators: XZ: 103.92 YZ: 103.92 ZZ: 103.92 ZI: 34.64 XI: 34.64 YI: 34.64 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j Labels: (7,) Name: Gate.sx Aliases: Gate.sx Gate.cliff5 Generators: X: 90.00 0.71 0.71j 0.71j 0.71 SX 1 Labels: (0, 1) Name: Gate Locally Equivalent: iSWAP Generators: YX: 90.00 YI: 69.28 ZY: 69.28 XY: 69.28 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 Labels: (2,) Name: Gate.cliff6 Aliases: Gate.cliff6 Generators: Y: 90.00 0.71 0.71 0.71 0.71 6 Labels: (4, 9) Name: Gate Locally Equivalent: iSWAP Generators: XY: 60.00 XZ: 60.00 ZY: 60.00 YX: 60.00 IZ: 60.00 IY: 60.00 ZI: 60.00 ... 0.50j 0.50 0.50j 0.50 0.50 0.50j 0.50 0.50j 0.50j 0.50 0.50j 0.50 0.50 0.50j 0.50 0.50j Labels: (7,) Name: Gate.cliff11 Aliases: Gate.cliff11 Generators: X: 127.28 Y: 127.28 0.71 0.71j 0.71 0.71j 11 2 Labels: (0, 1) Name: Gate Locally Equivalent: CNOT Generators: ZX: 63.64 IZ: 63.64 YX: 63.64 ZZ: 63.64 IX: 63.64 YZ: 63.64 XZ: 63.64 ... 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j Labels: (2,) Name: Gate.cliff17 Aliases: Gate.cliff17 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 17 Labels: (4, 9) Name: Gate Locally Equivalent: iSWAP Generators: ZX: 60.00 IX: 60.00 XZ: 60.00 ZI: 60.00 ZY: 60.00 YX: 60.00 IZ: 34.64 ... 0.71j 0.71 0.71 0.71j 0.71j 0.71 0.71 0.71j Labels: (7,) Name: Gate.cliff21 Aliases: Gate.cliff21 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 21 3 Labels: (0, 1) Name: Gate Locally Equivalent: iSWAP Generators: XZ: 61.25 ZX: 61.25 ZZ: 61.25 YX: 61.25 ZI: 61.25 YI: 37.85 YZ: 37.85 ... 0.50j 0.50j 0.50j 0.50j 0.50 0.50 0.50 0.50 0.50j 0.50j 0.50j 0.50j 0.50 0.50 0.50 0.50 Labels: (2,) Name: Gate.cliff18 Aliases: Gate.cliff18 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 18 Labels: (4, 9) Name: Gate Locally Equivalent: CNOT Generators: XZ: 60.00 IZ: 60.00 ZX: 60.00 XI: 60.00 IX: 60.00 ZI: 60.00 YI: 34.64 ... 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j Labels: (7,) Name: Gate.cliff19 Aliases: Gate.cliff19 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 19 4 Labels: (0, 1) Name: Gate Locally Equivalent: CNOT Generators: IZ: 61.25 ZI: 61.25 YI: 61.25 YY: 61.25 ZX: 61.25 XI: 37.85 XY: 37.85 ... 0.50j 0.50j 0.50j 0.50j 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50j 0.50j 0.50j 0.50j Labels: (2,) Name: Gate.cliff19 Aliases: Gate.cliff19 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 19 Labels: (4, 9) Name: Gate Locally Equivalent: CNOT Generators: ZY: 99.10 YX: 99.10 YZ: 99.10 ZX: 99.10 IX: 99.10 XI: 23.39 YY: 23.39 ... 0.50 0.50j 0.50j 0.50 0.50j 0.50 0.50 0.50j 0.50 0.50j 0.50j 0.50 0.50j 0.50 0.50 0.50j Labels: (7,) Name: Gate.cliff23 Aliases: Gate.cliff23 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 23 5 Labels: (0,) Name: Meas M Labels: (1,) Name: Meas M Labels: (2,) Name: Meas M Labels: (4,) Name: Meas M Labels: (7,) Name: Meas M Labels: (9,) Name: Meas M Note
We invert each random sequence up to an independent random Pauli matrix (accessible as shown in the example above) to diagnose errors to that are missed by always returning to the initial state [4].
 Parameters
labels (
Iterable
) – A list of which sets of system labels are to be twirled together in each circuit, e.g.[3, [1, 2], 4]
.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[6, 20]
.n_circuits (
int
) – The number of circuits for each number of random cycles.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"C"
) that will be used to automatically instantiate a twirl based on the given labels.compiled_pauli (
bool
str
) – Controls whether or not to compile a random Pauli gate onto each qubit in the cycle preceding a measurement operation (default isTrue
). Also accepts a string of Paulis to compile, which will be the same for all circuits returned by this function. A list of compiled Paulis is stored as a string in thekey
attribute, where the order is defined by the sorted labels of the circuit.
 Returns
A collection of SRB circuits.
 Return type
Make XRB¶

trueq.
make_xrb
(labels, n_random_cycles, n_circuits=30, twirl=None)¶ Generates a
CircuitCollection
to study how coherent the errors in random gates are using (simultaneous) extended randomized benchmarking (XRB). See the XRB guide for more information.import trueq as tq # generate circuit collections to run XRB on a single qubit (qubit 0), with # 30 random circuits for each length in [4, 50, 500] circuits = tq.make_xrb([0], [4, 50, 500], 30) # generate circuit collections to run twoqubit XRB on qubit pair [5, 6], with # 50 random circuits for each length in [3, 150] circuits = tq.make_xrb([[5, 6]], [3, 150], 50) # generate a circuit collection to run simultaneous onequbit XRB on [5, 6, 7] # with 30 random circuits for each length in [5, 10, 100] circuits = tq.make_xrb([5, 6, 7], [5, 10, 100], 30) # generate a circuit collection to run simultaneous onequbit XRB on qubit 5, # and twoqubit XRB on qubits [1, 2], with 15 random circuits for each circuit # length in [4, 30] circuits = tq.make_xrb([[1, 2], 5], [4, 30], 15) # draw the first circuit circuits[0].draw()
1 2 5 Key: twirl: Cliffords on [(1, 2), 5] protocol: XRB seq_label: 4749 n_random_cycles: 4 measurement_basis: YXZ 1 Labels: (1, 2) Name: Gate Locally Equivalent: CNOT Generators: ZX: 63.64 IX: 63.64 XX: 63.64 XZ: 63.64 ZZ: 63.64 IZ: 63.64 YZ: 63.64 ... 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j Labels: (5,) Name: Gate.cliff15 Aliases: Gate.cliff15 Generators: Z: 127.28 Y: 127.28 0.71 0.71j 0.71j 0.71 15 2 Labels: (1, 2) Name: Gate Locally Equivalent: CNOT Generators: IZ: 63.64 YX: 63.64 IX: 63.64 YZ: 63.64 IY: 45.00 YY: 45.00 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j 0.35 0.35j Labels: (5,) Name: Gate.cliff15 Aliases: Gate.cliff15 Generators: Z: 127.28 Y: 127.28 0.71 0.71j 0.71j 0.71 15 3 Labels: (1, 2) Name: Gate Locally Equivalent: iSWAP Generators: XX: 61.25 YZ: 61.25 IZ: 61.25 XZ: 61.25 YY: 61.25 IX: 37.85 XY: 37.85 ... 0.50j 0.50j 0.50j 0.50j 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50j 0.50j 0.50j 0.50j Labels: (5,) Name: Gate.cliff15 Aliases: Gate.cliff15 Generators: Z: 127.28 Y: 127.28 0.71 0.71j 0.71j 0.71 15 4 Labels: (1, 2) Name: Gate Locally Equivalent: CNOT Generators: ZI: 90.00 IZ: 63.64 ZY: 63.64 IY: 63.64 ZZ: 63.64 IX: 45.00 ZX: 45.00 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j Labels: (5,) Name: Gate.cliff19 Aliases: Gate.cliff19 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 19 5 Labels: (1,) Name: Meas M Labels: (2,) Name: Meas M Labels: (5,) Name: Meas M Note
If the circuit collection also contains SRB circuits with the same twirl group, then calling
fit
will also return an estimatee_U
of how much the process fidelity of the twirling groups can be improved by correcting static calibration errors. Parameters
labels (
Iterable
) – A list of which sets of system labels are to be twirled together in each circuit, e.g.[3, [1, 2], 4]
.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[6, 20]
.n_circuits (
int
) – The number of circuits for each number of random cycles.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"C"
) that will be used to automatically instantiate a twirl based on the given labels.
 Returns
A collection of XRB circuits.
 Return type
QCAP (Quantum Capacity)¶

trueq.
make_qcap
(cycles, n_random_cycles, n_circuits=30, n_decays=20)¶ Generates a
CircuitCollection
to measure the quantum capacity (QCAP) bound of any circuit whose marked cycles are contained incycles
. See the QCAP guide for more information.The bound can be obtained by calling
qcap_bound()
on the QCAP circuits once they have been performed and their results have been populated. Note that this function outputs cycle benchmarking circuits, andfit()
will report the individual infidelities of the given cycles.import trueq as tq # make a circuit to assess circuit = tq.Circuit([ {0: tq.Gate.y}, {(0, 1): tq.Gate.cnot}, {0: tq.Gate.h, 1: tq.Gate.h}, {(1, 2): tq.Gate.cnot, (3, 4): tq.Gate.cnot}, {0: tq.Gate.h, 1: tq.Gate.h}, {(1, 2): tq.Gate.cnot, (3, 4): tq.Gate.cnot}, {0: tq.Gate.h, 1: tq.Gate.h}, {(1, 3): tq.Gate.cnot} ]) # generate a circuit collection to measure the QCAP circuits = tq.make_qcap(circuit, [0, 16]) # run the circuits on your hardware or simulator tq.Simulator().add_overrotation(0.05).run(circuits) # generate the QCAP bound tq.qcap_bound(circuit, circuits)
TrueQ formatting will not be loaded without trusting this notebook or rerunning the affected cells. Notebooks can be marked as trusted by clicking "File > Trust Notebook".QCAPQuantum CapacityPaulis (0, 1, 2, 3, 4) Key:

 labels: (0, 1, 2, 3, 4)
 protocol: QCAP
 twirl: Paulis on [0, 1, 2, 3, 4]
${e}_{IU}$The inferred upper bound on the process infidelity of a circuit if it were run under RC.1.1e01 (3.4e03) 0.11008739407202506, 0.003441775318348356Note
This function is a convenience wrapper of
make_cb()
. If, for example, different values ofn_random_cycles
are desired for each cycle, callmake_cb()
manually for each cycle placing all generated circuits in the same collection. However, it is important to set thetwirl
option totq.Twirl("P", labels)
wherelabels
are all the qubit labels involved in the circuit(s) of interest. Parameters
cycles (
Iterable
Circuit
) – An iterable ofCycle
s (note that aCircuit
is an iterable of cycles). Only the nonzero marked cycles will be considered, and duplicate cycles will be ignored.n_random_cycles (
Iterable
) – A list of positive integers specifying how many random cycles will be generated during the protocol, e.g.[6, 20]
.n_circuits (
int
) – The number of circuits for each random cycle.n_decays (
int
) – An integer specifying the total number of randomly chosen pauli decay strings used to measure the process infidelity. Warning: Setting this value lower thanmin(20, 4 ** n_qubits  1)
may result in a biased estimate.
 Returns
A collection of QCAP circuits.
 Return type

trueq.
qcap_bound
(circuit, fit_or_circuits)¶ Computes the quantum capacity (QCAP) bound of the given circuit. This scalar quantity is a bound on the circuit performance when the circuit is executed using
randomly_compile()
. See the QCAP guide for more information. Parameters
circuit (
Circuit
) – The circuit you wish to know the QCAP bound of. This will usually be the original circuit that was given tomake_qcap()
, but can be any circuit whose marked cycles are a subset of the marked cycles present in the CB circuits or fits offit_or_circuits
.fit_or_circuits – A circuit collection output by
make_qcap()
populated with results, or an estimate collection that resulted from callingfit()
on such a circuit collection. For efficiency, use the latter format if computing a bound on multiple circuits.
 Returns
A bound on the circut performance.
 Return type
Randomly Compile¶

trueq.
randomly_compile
(circuit, n_compilations=30, twirl='P', compile_paulis=False)¶ Randomly compiles the given circuit into many new random circuits which implement the same algorithm. Random gates are inserted adjacent to gates in the provided circuit, chosen from the specified twirling group (the Pauli group is used by default). See the RC guide for more information.
Cycles with a marker of
0
in the input circuit will not be changed, while other cycles may have random gates compiled around them.If all cycles in the input circuit have markers of
0
, then all cycles containing multiqubit gates have unique markers assigned automatically. If any cycles have nonzero markers in the circuit, then only those cycles are randomly compiled.import trueq as tq # Define a circuit which applies a nonClifford t gate on the 0th qubit, a # controlledZ gate on qubits 0 and 1 with an rx(10) on 2, then another t gate # on the 0th qubit. cycle1 = tq.Cycle({0: tq.Gate.t}) cycle2 = tq.Cycle({(0, 1): tq.Gate.cz, 2: tq.Gate.rx(15)}); circuit = tq.Circuit((cycle1, cycle2, cycle1)) circuit.measure_all() # run randomized compiling on the circuit compiled_circuit = tq.randomly_compile(circuit) # draw the first circuit compiled_circuit[0].draw()
0 1 2 Key: twirl: Paulis on [0, 1, 2] protocol: RC Labels: (0,) Name: Gate.t Aliases: Gate.t Generators: Z: 45.00 1.00 0.71 0.71j T Labels: (1,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z Labels: (2,) Name: Gate.y Aliases: Gate.y Gate.cliff2 Generators: Y: 180.00 1.00j 1.00j Y 2 Labels: (0, 1) Name: Gate.cz Aliases: Gate.cz Locally Equivalent: CNOT Generators: IZ: 90.00 ZI: 90.00 ZZ: 90.00 1.00 1.00 1.00 1.00 CZ CZ Labels: (2,) Name: Gate Generators: X: 15.00 0.99 0.13j 0.13j 0.99 Labels: (0,) Name: Gate.t Aliases: Gate.t Generators: Z: 45.00 1.00 0.71 0.71j T Labels: (1,) Name: Gate.z Aliases: Gate.z Gate.cliff3 Generators: Z: 180.00 1.00 1.00 Z Labels: (2,) Name: Gate Generators: Y: 173.87 Z: 46.59 0.26 0.97j 0.97j 0.26 1 Labels: (0,) Name: Meas M Labels: (1,) Name: Meas M Labels: (2,) Name: Meas M By default
randomly_compile()
only adds twirling gates around marked cycles when the entangling gates present in the cycles are Clifford (single qubit gates may be arbitrary). If nonClifford multiqubit gates are encountered in the marked cycles, errors will be raised. However, if the target circuit contains nonClifford entangling gates, and the hardware gateset includes Clifford operations such asCNOT
, then these errors can be avoided by compiling the target circuit into the hardware gateset before callingrandomly_compile()
, as in the following example:import trueq as tq # define a config which contains the hardware gates hardware_config = tq.Config.basic(entangler=tq.Gate.cx) # Define a circuit which applies an X gate on the 0th qubit, a ZZ(45) Pauli # gate on qubits 0 and 1, and another X gate on the 0th qubit. cycle1 = tq.Cycle({0: tq.Gate.x}) cycle2 = tq.Cycle({(0, 1): tq.Gate.rp("ZZ", 45)}); circuit = tq.Circuit((cycle1, cycle2, cycle1)) circuit.measure_all() compiler = tq.Compiler.from_config(hardware_config) hardware_compiled_circ = compiler.compile(circuit) # run randomized compiling on the circuit compiled_circuit = tq.randomly_compile(hardware_compiled_circ) # draw the first circuit compiled_circuit[0].draw()
0 1 Key: twirl: Paulis on [0, 1] protocol: RC Labels: (0,) Name: Gate.cliff20 Aliases: Gate.cliff20 Generators: X: 69.28 Y: 69.28 Z: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 20 Labels: (1,) Name: Gate.cliff23 Aliases: Gate.cliff23 Generators: Z: 69.28 X: 69.28 Y: 69.28 0.50 0.50j 0.50 0.50j 0.50 0.50j 0.50 0.50j 23 2 Labels: (0, 1) Name: cx Aliases: Gate.cx Gate.cnot Parameters: Locally Equivalent: CNOT Generators: ZI: 90.00 ZX: 90.00 IX: 90.00 1.00 1.00 1.00 1.00 CX CX Labels: (0,) Name: Gate Generators: Z: 225.71 X: 93.49 Y: 93.49 0.65 0.65j 0.27 0.27j 0.27 0.27j 0.65 0.65j Labels: (1,) Name: Gate.cliff15 Aliases: Gate.cliff15 Generators: Z: 127.28 Y: 127.28 0.71 0.71j 0.71j 0.71 15 3 Labels: (0, 1) Name: cx Aliases: Gate.cx Gate.cnot Parameters: Locally Equivalent: CNOT Generators: ZI: 90.00 ZX: 90.00 IX: 90.00 1.00 1.00 1.00 1.00 CX CX Labels: (0,) Name: Gate.cliff4 Aliases: Gate.cliff4 Generators: X: 90.00 0.71j 0.71 0.71 0.71j 4 Labels: (1,) Name: Gate.cliff13 Aliases: Gate.cliff13 Generators: Z: 127.28 X: 127.28 0.71 0.71 0.71 0.71 13 1 Labels: (0,) Name: Meas M Labels: (1,) Name: Meas M Note
Running randomly_compile() on a circuit several times is likely to return different compiled circuits due to the random nature of the algorithm. The circuit returned will always contain the same number of cycles as the input circuit, and will be logically equivalent, up to a global phase.
Warning
Running randomly_compile() on circuits containing gates acting on multiple systems with a nonClifford gate will typically result in an error because twirling operations cannot be corrected locally.
 Parameters
circuit (
Circuit
) – A circuit to randomly compile.n_compilations (
int
) – The number of random compilations of the input circuit. Each instance will appear as a new circuit in the returned circuit collection.twirl (
Twirl
str
) – TheTwirl
to use in this protocol. You can also specify a twirling group (default is"P"
) that will be used to automatically instantiate a twirl based on the labels in the given circuit. This is for advanced use and in typical use cases should not be changed.compile_paulis (
bool
) – Whether or not to compile a random Pauli gate onto a qubit in the cycle preceding a measurement operation for eachMeas
operation encountered in the circuit. These additional Pauli operations have the effect of removing readout bias, but the final bit strings then need to be flipped as appropriate for each Pauli introduced. The Paulis that were compiled in are stored as a string in thekey
, where the order is first defined by cycle index, and then by sorted labels of each cycle. Seedecompiled_results()
for details on how to undo the addition of these Paulis to the results. (default isFalse
)
 Returns
A circuit collection containing randomly compiled versions of the circuit.
 Return type
py:class:~trueq.CircuitCollection