Related papers: Non-Identity Check Remains QMA-Complete for Short …
Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…
Quantum circuits constitute Intellectual Property (IP) of the quantum developers and users, which needs to be protected from theft by adversarial agents, e.g., the quantum cloud provider or a rogue adversary present in the cloud. This…
We examine two quantum operations, the Permutation Test and the Circle Test, which test the identity of n quantum states. These operations naturally extend the well-studied Swap Test on two quantum states. We first show the optimality of…
Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…
Quantum computing has proven to be capable of accelerating many algorithms by performing tasks that classical computers cannot. Currently, Noisy Intermediate Scale Quantum (NISQ) machines struggle from scalability and noise issues to render…
This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit…
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the…
The depth of quantum circuits is a critical factor when running them on state-of-the-art quantum devices due to their limited coherence times. Reducing circuit depth decreases noise in near-term quantum computations and reduces overall…
The optimization of quantum circuit depth is crucial for practical quantum computing, as limited coherence times and error-prone operations constrain executable algorithms. Measurement and feedback operations are fundamental in quantum…
A $\Sigma\Pi\Sigma\Pi(k)$ circuit $C=\sum_{i=1}^kF_i=\sum_{i=1}^k\prod_{j=1}^{d_i}f_{ij}$ is unmixed if for each $i\in[k]$, $F_i=f_{i1}(x_1)... f_{in}(x_n)$, where each $f_{ij}$ is a univariate polynomial given in the sparse representation.…
The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. Unfortunately, the implemented schemes can be totally insecure. We provide a thorough investigation of security…
Complementarity is an essential feature of quantum mechanics. The preparation of an eigenstate of one observable implies complete randomness in its complementary observable. In quantum cryptography, complementarity allows us to formulate…
Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any…
Fault-tolerant quantum computers compose elements of a discrete gate set in order to approximate a target unitary. The problem of minimising the number of gates is known as gate-synthesis. The approximation error is a form of coherent…
The conventional approach to understanding the characteristics of an unknown quantum state involves having numerous identical independent copies of the system in that state. However, we demonstrate that gleaning insights into specific…
We introduce Quantum Spectral Authentication (QSA), a primitive for verifying that a remote quantum endpoint still possesses a previously installed secret quantum resource, such as a hidden state or state-preparation capability, without…
The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not…
Accurate and robust quantum process tomography (QPT) is crucial for verifying quantum gates and diagnosing implementation faults in experiments aimed at building universal quantum computers. However, the reliability of QPT protocols is…
We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage…
Device-independent (DI) certification allows the verification of quantum systems based solely on observed statistics, without assumptions about their internal structure. While self-testing, the strongest DI certification, of a wide range of…