We discuss two primitive algorithms to evaluate overlaps and transition matrix time series, which are used to construct a variety of quantum-assisted quantum control algorithms implementable on NISQ devices. Unlike previous approaches, our method bypasses tomographically complete measurements and instead relies solely on single qubit measurements. We analyse circuit complexity of composed algorithms and sources of noise arising from Trotterization and measurement errors.Introduction.-Quantum control is central to the design of quantum technologies [1]. The control problem usually involves optimising a cost function that incorporates conditions such as distance to a target state, bandwidth and fluence restrictions. The problem is then solved by employing gradient search methods [2-6], nongradient search methods [7][8][9][10][11][12][13][14][15][16] or hybrid algorithms [17]. Such solutions typically involve several iterative updates to the controls before convergence to a local optima. Since these methods simulate quantum evolution on a classical computer repeatedly, often the time complexity for many-body quantum control protocols is dominated by the corresponding complexity of the evolution.

We revisit the notion of deniability in quantum key exchange (QKE), a topic that remains largely unexplored. In the only work on this subject by Donald Beaver, it is argued that QKE is not necessarily deniable due to an eavesdropping attack that limits key equivocation. We provide more insight into the nature of this attack and how it extends to other constructions such as QKE obtained from uncloneable encryption. We then adopt the framework for quantum authenticated key exchange, developed by Mosca et al., and extend it to introduce the notion of coercer-deniable QKE, formalized in terms of the indistinguishability of real and fake coercer views. Next, we apply results from a recent work by Arrazola and Scarani on covert quantum communication to establish a connection between covert QKE and deniability. We propose DC-QKE, a simple deniable covert QKE protocol, and prove its deniability via a reduction to the security of covert QKE. Finally, we consider how entanglement distillation can be used to enable information-theoretically deniable protocols for QKE and tasks beyond key exchange. 1 for privacy amplification to get an (n + s)-bit string y ′ . 3: Invert the OTP step to obtain x ′ = y ′ ⊕ e. 4: Parse x ′ as the concatenation m ′ ||µ ′ and use k to verify if MAC(m ′ ) k = µ ′ .

To prove the graph relations such as the connectivity and the isolation for a certified graph, the system of graph signature and proofs have been proposed. In this system, an issuer generates a signature certifying the topology of an undirected graph, and issues a prover the signature. The prover can prove the knowledge of the signature and the graph in the zero-knowledge, i.e., the signature and the signed graph are hidden. In addition, the prover can prove relations on the certified graph such as the connectivity and isolation between two vertexes. In the previous system, using integer commitments on RSA modulus, the graph relations are proved. However, the RSA modulus needs a longer size of each element. Furthermore, the proof size and the verification cost depend on the total numbers of vertexes and edges. In this paper, we propose a graph signature and proof system, where these are computed on bilinear groups without the RSA modulus. Moreover, using a bilinear map accumulator, the prover can prove the connectivity and isolation on a graph, where the proof size and verification cost become independent from the total numbers of vertexes and edges.

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