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Quantum Circuits for Dynamic Runtime Assertions in Quantum Computation
Huiyang Zhou, Gregory Byrd
TL;DR
Dynamic assertions are difficult because qubits cannot be copied and direct measurement collapses superpositions, while prior statistical checks stop execution. The paper proposes ancilla-based circuits for classical, superposition, and entanglement assertions; on IBM Q, filtering assertion errors reduced expected-entanglement-state error from 18.4% to 12.6%.
Problem
Method
The paper uses ancilla qubits to indirectly check classical, superposition, and entanglement assertions without directly measuring the qubits under test.
Source: §1 · p. 1, §3.3 · p. 3Results
The circuits are proven and simulator-verified; on IBM Q, filtering assertion errors reduced expected-entanglement-state error from 18.4% to 12.6%, a 31.5% improvement.
Source: §7 · p. 4, §4.2 · p. 4Takeaways & Limitations
Assertion logic can filter erroneous results in NISQ systems and may force tested qubits into a desired state.
Source: §7 · p. 4
Abstract
from arXiv · showhide
In this paper, we propose quantum circuits for runtime assertions, which can be used for both software debugging and error detection. Runtime assertion is challenging in quantum computing for two key reasons. First, a quantum bit (qubit) cannot be copied, which is known as the non-cloning theorem. Second, when a qubit is measured, its superposition state collapses into a classical state, losing the inherent parallel information. In this paper, we overcome these challenges with runtime computation through ancilla qubits, which are used to indirectly collect the information of the qubits of interest. We design quantum circuits to assert classical states, entanglement, and superposition states.
1 INTRODUCTION
Runtime assertions could help debug quantum programs, but qubits cannot be copied and measuring a superposition collapses it. The paper proposes ancilla-based circuits for assertions about classical, superposition, and entanglement states.
1 INTRODUCTION
- Ancilla qubits indirectly check conditions on qubits of interest, avoiding direct measurement and using simpler assertion circuits than quantum error correction.The design is inspired by error correction, but its circuits check assertions rather than correct corrupted qubits.Source: §1 · p. 1
- Huang et al. proposed statistical assertions based on multiple measurement results, but each measurement stops execution and prevents assertions during collection of computation results.The paper presents its circuits as a way to overcome that limitation.Source: §1 · p. 1
- “Classical states” means computational-basis states |0⟩ and |1⟩ in this paper.Measurements are assumed to be performed with respect to the computational basis.Source: §1 · p. 1
- The proposed circuits cover classical-state, superposition, and entanglement assertions, and are proved, simulator-verified, and exercised on IBM Q.Classical assertions check values, superposition assertions check a desired superposition, and entanglement assertions check the desired correlation.Source: §1 · p. 1
2 BACKGROUND AND RELATED WORK
The section introduces qubit states and gates, then explains why quantum-program assertions are difficult: prior statistical checks rely on measurements that collapse states and stop execution.
2 BACKGROUND AND RELATED WORK
- Superposition supports quantum parallelism, while entangled qubits have correlated measurement results; measuring one can collapse the others.A qubit's superposition is a linear combination of computational-basis states, and measurement projects it to a classical state.Source: §2 · p. 1
- Figure 1 presents the logic functions of the Hadamard and CNOT gates; H is a single-qubit gate, whereas CNOT is a multi-qubit gate.The paper uses H and CNOT gates extensively.Source: Figure 1 · p. 2, §2 · p. 2
- Huang et al. proposed repeated-measurement assertions for classical values, superposition, and entanglement, but those measurements collapse states and stop program execution.Consequently, intermediate assertions cannot be enforced while computation results are being collected.Source: §2 · p. 2
3 QUANTUM CIRCUITS FOR DYNAMIC ASSERTIONS
The proposed circuits use ancillas to check classical values, entanglement, and superposition while aiming to preserve the qubits under test. Their measurement outcomes signal assertion errors and can reveal information about the input state.
3.1 Dynamic Assertion for Classical Values
- For a classical-value check, one ancilla and a CNOT test whether the qubit is |0⟩; initializing the ancilla to |1⟩ instead tests for |1⟩.The measurement can project the tested qubit into the expected classical state or report an error, and repeated outcomes can estimate its original amplitudes.Source: §3.1 · p. 2, Figure 2 · p. 2
3.2 Dynamic Assertion for Entanglement
- A parity circuit checks whether two qubits have the form a|00⟩+b|11⟩ or a|01⟩+b|10⟩, with the ancilla initialized to |0⟩ or |1⟩, respectively.For the first entangled form, the ancilla separates from the tested pair and the pair's state is preserved; the three-qubit case uses an even number of CNOT gates to avoid leaving the ancilla entangled.Source: §3.2 · pp. 2–3, Figure 4 · p. 3
3.3 Dynamic Assertion for Superposition
- For |ψ⟩ = |+⟩, the superposition circuit leaves the ancilla in |0⟩ and unentangled, so measuring it does not affect subsequent computation.For |ψ⟩ = |-⟩, the ancilla instead remains in |1⟩ and unentangled; inputs other than |+⟩ or |-⟩ are forced into an equal superposition after the check.Source: §3.3 · p. 3
- For inputs other than |+⟩ or |-⟩, the superposition check leaves the ancilla entangled with the tested qubit, and its outcome probabilities can estimate the original coefficients.An equal probability of ancilla outcomes indicates the input is likely in a classical state.Source: §3.3 · p. 3
4 EXPERIMENTS
Experiments used QUIRK to check circuit derivations and IBM Q to test assertion-based filtering of erroneous results. Simulations and hardware results cover classical, entanglement, and superposition assertions.
4 EXPERIMENTS
- QUIRK simulations checked the mathematical derivations, while IBM Q experiments assessed whether assertions filter erroneous results.The experiments used the simulator and the IBM Q ibmqx4 quantum computer.Source: §4 · pp. 3–4
4.1 Classical Assertions
- 2.5% classical-assertion error after discarding assertion-error results, down from 3.5%—a 28.5% reduction.The 5-qubit IBM Q experiment tested q1 == |0⟩ using q2 as the ancilla.Source: Table 1 · p. 4, Figure 6 · p. 4
4.2 Entanglement Assertions
- 12.6% entanglement-state error after filtering assertion-error shots, versus 18.4% without filtering, an improvement of 31.5%.The 5-qubit IBM Q experiment asserted the correlation between q1 and q2 prepared in (|00⟩+|11⟩).Source: Table 2 · p. 4, §4.2 · p. 4
4.3 Superposition Assertions
- 50% assertion error in QUIRK confirmed the superposition-circuit derivation, while IBM Q reported assertion errors in 15.6% of measurements.The QUIRK test began with a classical input; Figure 7 reports the hardware result.Source: §4.3 · p. 4, Figure 7 · p. 4
7 CONCLUSIONS
The paper proposes dynamic assertion circuits for classical values, entanglement, and superposition. It proves and simulates the circuits, and reports that assertion logic can force tested qubits into desired states and filter erroneous NISQ results.
- The proposed quantum circuits provide dynamic assertions for classical values, entanglement, and superposition.Source: §7 · p. 4
- The paper proves the circuits’ functions and verifies them with a quantum simulator.Source: §7 · p. 4
- Assertion logic may force tested qubits into desired states and can filter erroneous results in NISQ systems, as demonstrated on a 5-qubit IBM Q computer.Source: §7 · p. 4