`UnitarySynthesis` Outputs Approximated Circuit For `rx` Gate With Non-multiple-of-π Angles

by ADMIN 92 views

Introduction

In quantum computing, the UnitarySynthesis pass is a crucial component of the transpilation process, responsible for decomposing unitary operations into a sequence of primitive gates. However, when dealing with non-multiple-of-π angles, the UnitarySynthesis pass may produce approximated circuits that deviate significantly from the original behavior. This article explores the issue of UnitarySynthesis producing approximated circuits for the rx gate with non-multiple-of-π angles and discusses potential solutions.

Environment

  • Qiskit version: 2.0.0 (latest)
  • Python version: 3.12.9
  • Operating system: Ubuntu 22.04

What is Happening?

The UnitarySynthesis pass produces an approximated circuit for the rx gate when the rotation angle is not a multiple of π. For example, while rx(π/2) is correctly decomposed into hsh, arbitrary angles like rx(1.0) are not accurately synthesized, even when the approximate_degree is 1.0, which is the default parameter value.

In the following program, UnitarySynthesis attempts to approximate the rx operation using only h and s gates. However, this approximation results in a circuit that deviates significantly in behavior from the original, as evidenced by the measurement results. In such cases, wouldn't it be more appropriate to retain the original circuit instead of outputting an imprecise approximation?

Example Program

from qiskit import QuantumCircuit
from qiskit.transpiler.passes import Collect1qRuns, ConsolidateBlocks, UnitarySynthesis
from qiskit_aer import AerSimulator
from qiskit.transpiler import PassManager

qc = QuantumCircuit(1)
qc.rx(1.0, 0)
qc.measure_all()

backend = AerSimulator()
job0 = backend.run(qc, shots=10000)
print("Original circuit:", job0.result().get_counts())

# Consolidate into a unitary
pm0 = PassManager()
pm0.append(Collect1qRuns())
pm0.append(ConsolidateBlocks())
opt_qc = pm0.run(qc)

# Apply UnitarySynthesis using a restricted basis
pm1 = PassManager()
pm1.append(UnitarySynthesis(basis_gates=['h', 's'], method='sk'))
opt_qc = pm1.run(opt_qc)

job1 = backend.run(opt_qc, shots=10000)
print("After UnitarySynthesis:", job1.result().get_counts())

The observed output is:

Original circuit:        {'1': 2352, '0': 7648}
After UnitarySynthesis:  {'1': 4933, '0': 5067}

What Should Happen?

UnitarySynthesis should preserve the semantics of the original circuit. If a unitary cannot be accurately represented within the given basis (e.g., h and s), it may be preferable to avoid decomposition, rather than silently introducing behavioral changes.

Any?

One possible solution is to modify the UnitarySynthesis pass to handle non-multiple-of-π angles more accurately. This could involve using a more sophisticated approximation method or introducing additional parameters to control the approximation process.

Another approach is to use a different transpilation strategy, such as using a more general basis or employing a different decomposition method. This may require significant modifications to the UnitarySynthesis pass and other components of the transpilation pipeline.

Ultimately, the best solution will depend on the specific requirements of the application and the trade-offs between accuracy, complexity, and performance.

Conclusion

The UnitarySynthesis pass is a critical component of the transpilation process in quantum computing. However, when dealing with non-multiple-of-π angles, the pass may produce approximated circuits that deviate significantly from the original behavior. By understanding the limitations of the UnitarySynthesis pass and exploring alternative solutions, we can improve the accuracy and reliability of quantum computing applications.

Future Work

  • Investigate more sophisticated approximation methods for handling non-multiple-of-π angles.
  • Explore alternative transpilation strategies, such as using a more general basis or employing a different decomposition method.
  • Develop a more robust and flexible UnitarySynthesis pass that can handle a wide range of unitary operations and angles.

References

Q: What is the issue with Unitary Synthesis producing approximated circuits for RX gate with non-multiple-of-π angles?

A: The UnitarySynthesis pass produces an approximated circuit for the rx gate when the rotation angle is not a multiple of π. This can result in a circuit that deviates significantly in behavior from the original, as evidenced by the measurement results.

Q: Why is this a problem?

A: In quantum computing, the accuracy of the circuit is crucial. If the approximated circuit deviates significantly from the original, it can lead to incorrect results and undermine the reliability of the application.

Q: What are the consequences of using an approximated circuit?

A: Using an approximated circuit can lead to:

  • Incorrect results
  • Reduced accuracy
  • Increased error rates
  • Decreased reliability

Q: How can we reproduce the issue?

A: The issue can be reproduced by running the following program:

from qiskit import QuantumCircuit
from qiskit.transpiler.passes import Collect1qRuns, ConsolidateBlocks, UnitarySynthesis
from qiskit_aer import AerSimulator
from qiskit.transpiler import PassManager

qc = QuantumCircuit(1)
qc.rx(1.0, 0)
qc.measure_all()

backend = AerSimulator()
job0 = backend.run(qc, shots=10000)
print("Original circuit:", job0.result().get_counts())

# Consolidate into a unitary
pm0 = PassManager()
pm0.append(Collect1qRuns())
pm0.append(ConsolidateBlocks())
opt_qc = pm0.run(qc)

# Apply UnitarySynthesis using a restricted basis
pm1 = PassManager()
pm1.append(UnitarySynthesis(basis_gates=['h', 's'], method='sk'))
opt_qc = pm1.run(opt_qc)

job1 = backend.run(opt_qc, shots=10000)
print("After UnitarySynthesis:", job1.result().get_counts())

Q: What should happen instead?

A: UnitarySynthesis should preserve the semantics of the original circuit. If a unitary cannot be accurately represented within the given basis (e.g., h and s), it may be preferable to avoid decomposition, rather than silently introducing behavioral changes.

Q: Are there any solutions to this issue?

A: Yes, there are several potential solutions:

  • Modify the UnitarySynthesis pass to handle non-multiple-of-π angles more accurately.
  • Use a different transpilation strategy, such as using a more general basis or employing a different decomposition method.
  • Introduce additional parameters to control the approximation process.

Q: What are the implications of this issue?

A: The implications of this issue are significant, as it can lead to incorrect results and undermine the reliability of quantum computing applications. It is essential to address this issue and develop more accurate and reliable transpilation strategies.

Q: What is the next step?

A: The next step is to investigate more sophisticated approximation methods for handling non-multiple-of-π angles and explore alternative transpilation strategies. Additionally, developing a more robust and flexible UnitarySynthesis pass that can handle a wide range of unitary operations and angles is crucial.