Deferred timing resolution using stretch

The OpenQASM 3 language specification contains a stretch type with which you can specify relative timing of operations instead of absolute timing. Support for stretch as durations for Delay instructions was added in Qiskit v2.0.0. The concrete value of a stretch duration is resolved at compile time, after the exact duration of calibrated gates are known. The compiler tries to minimize the stretch duration, subject to timing constraints on one or more qubits. You can then express gate designs such as evenly spacing gates (for example, to implement a higher-order echo decoupling sequence), left-aligning a sequence of gates, or applying a gate for the duration of some sub-circuit, without knowing the exact timing.

Examples

Dynamical decoupling

A common use case of stretch is to apply dynamical decoupling to an idling qubit while another qubit is undergoing conditional operations.

For example, we can use stretch to apply an XX dynamical decoupling sequence to qubit 1, for the duration of the conditional block applied to qubit 0, as illustrated by the following diagram:

The corresponding circuit would look like the following. Note that a pair of barriers is needed to define the boundaries of this relative timing.

from qiskit.circuit import QuantumCircuit, QuantumRegister, ClassicalRegister
 
qubits = QuantumRegister(2)
clbits = ClassicalRegister(2)
circuit = QuantumCircuit(qubits, clbits)
(q0, q1) = qubits
(c0, c1) = clbits
 
# Add barriers to define the boundaries
circuit.barrier()
circuit.h(q0)
circuit.measure(q0, c0)
with circuit.if_test((c0, 1)) as else_:
    circuit.h(q0)
with else_:
    circuit.x(q0)
 
# Apply an XX DD sequence with stretch on qubit 1
s = circuit.add_stretch("s")
circuit.delay(s, q1)
circuit.x(q1)
circuit.delay(expr.mul(s, 2), q1)
circuit.x(q1)
circuit.delay(s, q1)
circuit.barrier()

Scheduling alignment

This example uses stretch to ensure a sequence of gates between two barriers are left-aligned, whatever their actual durations are:

from qiskit import QuantumCircuit
from numpy import pi
 
qc = QuantumCircuit(5)
qc.barrier()
qc.cx(0, 1)
qc.u(pi/4, 0, pi/2, 2)
qc.cx(3, 4)
 
a = qc.add_stretch("a")
b = qc.add_stretch("b")
c = qc.add_stretch("c")
 
# Use the stretches as Delay duration.
qc.delay(a, [0, 1])
qc.delay(b, 2)
qc.delay(c, [3, 4])
qc.barrier()

a = circuit.add_stretch("a")
circuit.barrier(q0, q1)
circuit.delay(100, q0)
circuit.delay(a, q1)  # resolve to 26
circuit.x(q1)  # duration: 8
circuit.delay(a, q1)  # resolve to 25
circuit.x(q1)  # duration: 8
circuit.delay(a, q1)  # resolve to 25
circuit.x(q1)  # duration: 8
circuit.barrier(q0, q1)

Qiskit Runtime limitations

Support for stretch in Qiskit Runtime is currently experimental and has the following constraints:

• At most one stretch variable per qubit set between barriers (implicit and explicit). A qubit set is one or more qubits; these sets must be mutually exclusive.

  Invalid

  Valid

  a = circuit.add_stretch("a")
  b = circuit.add_stretch("b")
  circuit.delay(a, (q0, q1))
  circuit.delay(b, q0)  # Invalid because 2 stretches are applied on q0

• The area surrounded by a set of barriers is called a barrier region. A stretch variable cannot be used in multiple barrier regions.

  Invalid

  Valid

  # Stretch a is used in two barrier regions
  a = circuit.add_stretch("a")
  circuit.barrier((q0, q1))
  circuit.delay(a, q0)
  circuit.barrier((q0, q1))
  circuit.delay(a, q0)
  circuit.barrier((q0, q1))

  

• Stretch expressions are limited to those of the form X*stretch + Y where X and Y are floating point or integer constants.

  Invalid

  Valid

  a = circuit.add_stretch("a")
  b = circuit.add_stretch("b")
  c = circuit.add_stretch("c")
   
  # (a /  b) * c is not supported
  circuit.delay(expr.mul(expr.div(a, b), c), q1)

• Stretch expressions can only include a single stretch variable.

  Invalid

  Valid

  a = circuit.add_stretch("a")
  b = circuit.add_stretch("b")
  circuit.delay(expr.add(a, b), 0)

• Stretch expressions cannot resolve to negative delay values. The current solver doesn't infer non-negativity constraints.

  Invalid

  Valid

  from qiskit.circuit import Duration
   
  circuit.barrier((q0, q1))
  circuit.delay(20, q1)
  # The length of this barrier region is 20dt, meaning the
  # equation for solving stretch 'a' is a + 40dt = 20dt, giving a = -20dt.
  circuit.delay(expr.add(a, Duration.dt(40)), q0)
  circuit.barrier((q0, q1))