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Quantum circuit debugging and sensitivity analysis via local inversions.

F. A. Calderon-Vargas, Timothy J Proctor, Kenneth Rudinger, Mohan Sarovar

Published Oct 1, 2022• 0 citations
Publisher

Abstract

We write a d-layer circuit as:§ We define the i-inverse of the circuit as which we view as a local perturbation of the circuit.§ With the probability distribution over measurement outcomes, ( and is the set of all length-n bitstrings), we assess how such local perturbations affect the circuit outcomes by computing the distance, , between the original and perturbed output distributions.§ We use the total variation distance (TVD) for the distance measure

DOI
10.2172/2005681

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We write a d-layer circuit as:§ We define the i-inverse of the circuit as which we view as a local perturbation of the circuit.§ With the probability distribution over measurement outcomes, ( and is the set of all length-n bitstrings), we assess how such local perturbations affect the circuit outcomes by computing the distance, , between the original and perturbed output distributions.§ We use the total variation distance (TVD) for the distance measure
It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and functions are exponentially hard to approximate [Knill 1995]. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD). TVD is the most relevant metric for the performance of a quantum circuit. In this paper we obtain asymptotically tight bounds for TVD. We show that in a natural sense, almost all states are hard to approximate to within a TVD of 2/e-εeven for exponentially small ε. The quantity 2/e is asymptotically the average distance to the uniform distribution. Almost all states with probability amplitudes concentrated in a small fraction of the space are hard to approximate to within a TVD of 2-ε. These results imply that non-uniform quantum circuit complexity is non-trivial in any reasonable model. They also reinforce the notion that the relative information distance between states (which is based on the difficulty of transforming one state to another) fully reflects the dimensionality of the space of qubits, not the number of qubits.
As the width and depth of quantum circuits implemented by state-of-the-art quantum processors rapidly increase, circuit analysis and assessment via classical simulation are becoming unfeasible. It is crucial, therefore, to develop new methods to identify significant error sources in large and complex quantum circuits. In this work, we present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most and thus helps to identify the most significant sources of error. The technique requires no classical verification of the circuit output and is thus a scalable tool for debugging large quantum programs in the form of circuits. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
Optimization of quantum circuits using an efficient compiler is key to its success for NISQ computers. Several 3rd party compilers are evolving to offer improved performance for large quantum circuits. These 3rd parties, or just a certain release of an otherwise trustworthy compiler, may possibly be untrusted and this could lead to an adversary to Reverse Engineer (RE) the quantum circuit for extracting sensitive aspects e.g., circuit topology, program, and its properties. In this paper, we propose obfuscation of quantum circuits to hide the functionality. Quantum circuits have inherent margin between correct and incorrect outputs. Therefore, obfuscation (i.e., corruption of functionality) by inserting dummy gates is nontrivial. We insert dummy SWAP gates one at a time for maximum corruption of functionality before sending the quantum circuit to an untrusted compiler. If an untrusted party clones the design, they get incorrect functionality. The designer removes the dummy SWAP gate post-compilation to restore the correct functionality. Compared to a classical counterpart, the quantum chip does not reveal the circuit functionality. Therefore, an adversary cannot guess the SWAP gate and location/validate using an oracle model. Evaluation of realistic quantum circuit with/without SWAP insertion is impossible in classical computers. Therefore, we propose a metric-based SWAP gate insertion process. The objective of the metric is to ensure maximum corruption of functionality measured using Total Variation Distance (TVD). The proposed approach is validated using IBM default noisy simulation model. Our metric-based approach predicts the SWAP position to achieve TVD of upto 50%, and performs 7.5% better than average TVD, and performs within 12.3% of the best obtainable TVD for the benchmarks. We obtain an overhead of < 5% for the number of gates and circuit depth after SWAP addition.
We introduce distance measures between quantum states, measurements, and channels based on their statistical distinguishability in generic experiments. Specifically, we analyze the average Total Variation Distance (TVD) between output statistics of protocols in which quantum objects are intertwined with random circuits and measured in standard basis. We show that for circuits forming approximate 4-designs, the average TVDs can be approximated by simple explicit functions of the underlying objects – the average-case distances (ACDs). We apply them to analyze the effects of noise in quantum advantage experiments and for efficient discrimination of high-dimensional states and channels without quantum memory. We argue that ACDs are better suited for assessing the quality of NISQ devices than common distance measures such as trace distance or the diamond norm.
Quantum computing promises to outperform classical systems, yet today’s Noisy Intermediate-Scale Quantum (NISQ) devices remain limited by gate errors, decoherence, and hardware variability. These challenges are compounded by the lack of built-in mechanisms to verify that quantum circuits execute as intended, especially in an untrusted quantum computer. In this work, we define quantum noise as a diagnostic signal rather than a nuisance. We propose a novel authentication method that utilizes Total Variation Distance (TVD) calculated using quantum noise. TVD compares a quantum circuit output distribution with a trusted quantum noise fingerprint. TVD offers a localized, interpretable metric for detecting structural tampering, such as gate reordering or injection. To support fine-grained verification, we introduce the concept of diagnostic ancilla qubits, non-invasive observers embedded in the circuit that store local noise signatures for post-execution analysis. While still a forward-looking concept, this proposal enables circuit-level verification. Our approach combines gate-level noise modeling with lightweight integrity checks, offering a promising path toward secure and tamper-evident quantum computation.