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Some Initial Guidelines for Building Reusable Quantum Oracles

Javier Sanchez-Rivero, Daniel Talaván, Jose Garcia-Alonso, Antonio Ruiz-Cortés, Juan Manuel Murillo

arXiv:2303.14959v1quant-phcs.SE

TL;DR

Reusable quantum oracles require deliberate reuse practices and clear documentation. The paper proposes guidelines at three levels and demonstrates them with two range-of-integers oracle implementations. Both are shown to function, and one has lower circuit depth, subject to an input-state condition.

  • Problem

    Quantum oracles are not reusable by themselves, so developers need techniques and practices that support reuse by design.

    Source: §I · p. 1

  • Method

    The paper proposes documentation guidelines for oracle ideas, oracle-building functions, and oracles, demonstrated with two implementations of a range-of-integers oracle.

    Source: §I · p. 1, C. Reuse of the Oracle · p. 6

  • Results

    Implementation B has lower depth than Implementation A and is more suitable for NISQ devices when given a full superposed initial state without relative phases.

    Source: C. Depth comparison of both… · p. 3

  • Takeaways & Limitations

    The paper provides documentation examples for both implementations to foster oracle reuse and identifies input-state requirements as important reuse information.

    Source: C. Reuse of the Oracle · p. 6, §V · p. 7

Abstract

from arXiv · show

The evolution of quantum hardware is highlighting the need for advances in quantum software engineering that help developers create quantum software with good quality attributes. Specifically, reusability has been traditionally considered an important quality attribute in terms of efficiency of cost and effort. Increasing the reusability of quantum software will help developers create more complex solutions, by reusing simpler components, with better quality attributes, as long as the reused components have also these attributes. This work focuses on the reusability of oracles, a well-known pattern of quantum algorithms that can be used to perform functions used as input by other algorithms. In particular, in this work, we present several guidelines for making reusable quantum oracles. These guidelines include three different levels for oracle reuse: the ideas inspiring the oracle, the function which creates the oracle, and the oracle itself. To demonstrate these guidelines, two different implementations of a range of integers oracle have been built by reusing simpler oracles. The quality of these implementations is evaluated in terms of functionality and quantum circuit depth. Then, we provide an example of documentation following the proposed guidelines for both implementations to foster reuse of the provided oracles. This work aims to be a first point of discussion towards quantum software reusability. Additional work is needed to establish more specific criteria for quantum software reusability.

I. INTRODUCTION

Quantum software engineering seeks programs with strong quality attributes, including reusability, which can improve cost and effort efficiency. The paper presents oracle-reuse guidelines and demonstrates them with two range-of-integers oracle implementations.

I. INTRODUCTION

  • Reusable software can improve cost and effort efficiency, and modularity lets smaller assets be reused in other systems or assets.The paper identifies reusability as a quality attribute of maintainability.Source: §I · p. 1
  • Although oracles can serve as function-providing inputs to different algorithms, they are not reusable by themselves and require reuse-oriented techniques and practices.The paper frames an oracle as an isolated component whose internal operation need not concern its consuming algorithm.Source: §I · p. 1
  • The paper proposes documentation guidelines and demonstrates them with two implementations that phase-mark integers in a specified interval.Both implementations mark values from n1 through n2, inclusive, when applied to an integer-encoding superposition.Source: §I · p. 1

II. BACKGROUND AND RELATED WORK

  • Circuit depth matters for reusable quantum software because deeper circuits face greater noise exposure and can reduce result reliability.The paper connects reducing oracle depth with improved quality attributes and reusability.Source: §II · p. 2
  • The paper situates its example within quantum software reuse and argues that well-documented abstract operations help developers use composed operations properly.One range oracle composes less-than and greater-than oracles.Source: §II · p. 2, §I · p. 2

III. ORACLE FOR RANGE OF INTEGERS

The paper demonstrates range-of-integers oracles by composing existing quantum software. Implementation A combines two less-than oracles to mark the target interval.

III. ORACLE FOR RANGE OF INTEGERS

  • Both range-oracle implementations reuse existing quantum software, including a linear-depth multi-controlled Z-gate and a less-than oracle.Implementation B also uses quantum addition; the paper reports polynomial depth for the composed pieces.Source: §III · p. 2

A. Implementation A: two less-than oracles

  • Implementation A combines less-than n2 + 1 and less-than n1 oracles to mark the close interval [n1, n2], regardless of their order.Values below n1 are marked twice, returning them to 0-phase.Source: A. Implementation A: two less-than… · p. 2
  • The paper states that Implementation A performs the intended function for any input state.Its unitary has the indicated -1 entries at positions (n1, n1) and (n2, n2).Source: A. Implementation A: two less-than… · p. 2
  • The paper illustrates Implementation A with a circuit and state diagrams showing the target-range states marked after applying the less-than oracles.The figure distinguishes 0-phase states from π-phase states.Source: A. Implementation A: two less-than… · p. 3

B. Implementation B: less-than oracle and displacement

Implementation B applies a less-than oracle and then uses quantum addition to displace the marked states into the target range. Unlike Implementation A, it requires a particular input state.

B. Implementation B: less-than oracle and displacement

C. Depth comparison of both implementations

The depth comparison finds that Implementation B is shallower than Implementation A, with its suitability for NISQ devices conditional on a particular input state.

C. Depth comparison of both implementations

  • The comparison transpiled circuits to the gate set of IBM Washington using a fake provider and tested intervals across 3 to 12 qubits.Circuits were generated for each interval satisfying 0 < n1 < n2 < N −1.Source: C. Depth comparison of both… · p. 3
  • Implementation B has lower depth than Implementation A and is more suitable for NISQ devices with a full superposed initial state without relative phases.Both implementations have polynomial depth; Implementation A works on any input state.Source: C. Depth comparison of both… · p. 3

IV. GUIDELINES FOR MAKING REUSABLE ORACLES

The paper proposes reusable-oracle guidelines based on experience with two range-of-integers implementations. The guidelines distinguish reuse of the ideas behind an oracle, its circuit-generating function, and the oracle itself.

IV. GUIDELINES FOR MAKING REUSABLE ORACLES

  • For the current implementations, B is preferred for its lower circuit depth, though a more efficient less-than oracle could change that choice.Developers should know aspects of an oracle that may affect its impact in their software.Source: §IV · p. 3
  • Reusable-oracle guidance spans the ideas inspiring an oracle, the function that creates its circuit, and the oracle itself.These three levels organize the proposed guidelines.Source: §IV · pp. 3–4
  • The first reuse level aims to make the fundamental ideas inspiring an oracle easier to reuse.The guidelines are based on experience creating two implementations of the range-of-integers oracle.Source: §IV · p. 3
  • Oracle-level documentation should explain composition, effects on the quantum state, circuit impact, and other elements needed for effective reuse.The oracle itself is the final software component that can be composed with others to create more complex functions.Source: §IV · p. 4

A. Reuse of the Ideas Inspiring the Oracle

Reusing the ideas behind an oracle requires documenting more than its function: developers need to understand its underlying components and their behavior. This information can help them reason about and adapt those ideas, while implementation choice may depend on hardware and software context.

A. Reuse of the Ideas Inspiring the Oracle

  • Hardware diversity or advances in algorithms and transpilers could change which implementation performs better.A more efficient oracle may perform worse on a particular quantum computer.Source: A. Reuse of the Ideas Inspiring the… · p. 5
  • Reuse requires documenting an oracle's underlying components, not only its function, so developers can compare and select implementations for their situation.Treating an oracle as a black-box function may explain how to use it but is insufficient for comparing alternatives.Source: A. Reuse of the Ideas Inspiring the… · pp. 4–5
  • Implementation A uses double marking: a state marked by both less-than oracles returns to 0-phase, an idea that may inspire new software.This behavior is not obvious from the less-than oracle alone.Source: A. Reuse of the Ideas Inspiring the… · p. 5
  • Document the ideas inspiring an oracle alongside it so developers can reason about them and draw inspiration for other oracles.Implementation B illustrates reuse of quantum addition to shift marked states to the desired ones.Source: A. Reuse of the Ideas Inspiring the… · p. 5

B. Reuse of the Algorithm that Creates the Oracle

The circuit-generating function is a distinct reuse target: document its interface and distinguish its parameters from those used by the oracle itself.

B. Reuse of the Algorithm that Creates the Oracle

  • Document the circuit-generating algorithm with reuse metrics such as input/output parameter ratio and comment ratio.For most oracles, a classical algorithm generates a quantum circuit for a given input size.Source: B. Reuse of the Algorithm that Creates… · p. 6
  • Distinguish parameters used only to generate the circuit from parameters that are inputs to the resulting oracle.This distinction is a quantum-specific guideline for documenting an oracle-generating algorithm.Source: B. Reuse of the Algorithm that Creates… · p. 6
  • Clearly document generator parameters that are not oracle inputs, since developers may otherwise misunderstand how the function's parameters work.The function's interface comprises properties that interact with other artifacts.Source: B. Reuse of the Algorithm that Creates… · p. 6
  • Target qubits are oracle inputs, not generator parameters; the [4, 7] circuit is unchanged when applied to different qubits.The range limits, in contrast, are used to generate the circuit.Source: B. Reuse of the Algorithm that Creates… · p. 6

C. Reuse of the Oracle

Reusable oracle documentation should specify the quantum states an oracle expects and guarantees, as well as circuit properties that affect reuse. The paper identifies input-state preconditions and circuit depth as especially important.

C. Reuse of the Oracle

  • Implementation A marks states regardless of amplitude, whereas implementation B expects a full superposition with no relative phase.Implementation B may not behave as expected if its input-state precondition is unmet.Source: C. Reuse of the Oracle · p. 6
  • Document the oracle’s input-state preconditions and output-state postconditions so users know what states it accepts and what state it returns.For the range oracle, states in the selected range receive a π-phase without other changes, provided the input meets the preconditions.Source: C. Reuse of the Oracle · pp. 6–7
  • Document circuit depth because it helps developers assess whether an oracle can run successfully on NISQ-era hardware.Measure depth after transpiling to a specific device, since chip architectures can affect the resulting depth.Source: C. Reuse of the Oracle · p. 7
  • Document gate requirements and qubit-connectivity assumptions because they can affect circuit performance and depth.Unavailable gates may require alternative circuits, and entangling connections may affect circuit properties.Source: C. Reuse of the Oracle · p. 7

D. Documentation of the range of integer oracles following the proposed guidelines

The paper points readers to documentation cards for both range-of-integers oracle implementations.

D. Documentation of the range of integer oracles following the proposed guidelines

V. CONCLUSIONS AND FUTURE WORK

The paper demonstrates oracle reuse with two range-of-integers implementations and proposes reuse guidelines. It presents this work as an initial discussion, noting that more specific criteria remain to be established.

V. Conclusions and Future Work

  • Both range-of-integers implementations were shown to function, and one showed an improvement in circuit depth.The implementations reuse simpler oracles, including less-than and addition oracles.Source: §V · p. 7
  • The proposed guidelines address reuse of the ideas inspiring an oracle, the function that creates it, and the oracle itself.The paper provides example documentation following the guidelines for both implementations.Source: §V · p. 7
  • The work is an initial discussion, and more specific criteria for quantum software reusability remain to be established.The authors note that quantum software is at an early development stage and suggest further guidelines could cover software beyond oracles.Source: §V · p. 7

Documentation of Implementation A

The documentation examples describe two range-of-integers oracle constructions, their parameters and state conditions, and backend-related assumptions.

Documentation of Implementation A

  • The other construction applies less-than a and less-than b + 1, giving the desired states a π-phase and other states a 2π-phase.The 2π-phase returns the other states to their initial state.Source: Documentation of Implementation A · p. 9
  • The documentation lists the oracle parameters as the range boundaries a and b, the qubit count n, and the qubits to which the oracle is applied.For the first implementation, it states there are no hard preconditions and that states within [a, b] receive a π-phase.Source: Documentation of Implementation A · p. 9
  • The documentation’s circuit details are tied to FakeWashingtonV2 and state universal gate-set and all-to-all qubit-connection assumptions.The listed backend gates are CX, RZ, S, and X.Source: Documentation of Implementation A · pp. 9–10
  • One construction applies a less-than oracle for b − a + 1, then an addition oracle for +a, to mark the interval [a, b].The documentation describes this as reusing the less-than and addition oracles.Source: Documentation of Implementation A · p. 10
  • The second implementation requires a full superposed input state with relative 0-phase and returns that state with a π-phase on states in [a, b].Its documentation also lists the range boundaries, qubit count, and target qubits as parameters.Source: Documentation of Implementation A · p. 10
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