Equivalence Checking of Sequential Quantum Circuits

We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopted is a quantum state machine, which is a natural quantum generalisation of Mealy machines. A major difficulty in checking quantum circuits (but not present in checking classical circuits) is that the state spaces of quantum circuits are continuums. This difficulty is resolved by our main theorem showing that equivalence checking of two quantum Mealy machines can be done with input sequences that are taken from some chosen basis (which are finite) and have a length quadratic in the dimensions of the state Hilbert spaces of the machines. Based on this theoretical result, we develop an (and to the best of our knowledge, the first) algorithm for checking equivalence of sequential quantum circuits. A case study and experiments are presented

Sync+Sync: A Covert Channel Built on fsync with Storage

Scientists have built a variety of covert channels for secretive information transmission with CPU cache and main memory. In this paper, we turn to a lower level in the memory hierarchy, i.e., persistent storage. Most programs store intermediate or eventual results in the form of files and some of them call fsync to synchronously persist a file with storage device for orderly persistence. Our quantitative study shows that one program would undergo significantly longer response time for fsync call if the other program is concurrently calling fsync, although they do not share any data. We further find that, concurrent fsync calls contend at multiple levels of storage stack due to sharing software structures (e.g., Ext4's journal) and hardware resources (e.g., disk's I/O dispatch queue). We accordingly build a covert channel named Sync+Sync. Sync+Sync delivers a transmission bandwidth of 20,000 bits per second at an error rate of about 0.40% with an ordinary solid-state drive. Sync+Sync can be conducted in cross-disk partition, cross-file system, cross-container, cross-virtual machine, and even cross-disk drive fashions, without sharing data between programs. Next, we launch side-channel attacks with Sync+Sync and manage to precisely detect operations of a victim database (e.g., insert/update and B-Tree node split). We also leverage Sync+Sync to distinguish applications and websites with high accuracy by detecting and analyzing their fsync frequencies and flushed data volumes. These attacks are useful to support further fine-grained information leakage.Comment: A full version for the paper with the same title accepted by the 33rd USENIX Security Symposium (USENIX Security 2024

Fast Quantum Algorithms for Trace Distance Estimation

In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient quantum algorithms for estimating the trace distance within additive error $\varepsilon$ between mixed quantum states of rank $r$. Specifically, we first provide a quantum algorithm using $r \cdot \widetilde O(1/\varepsilon^2)$ queries to the quantum circuits that prepare the purifications of quantum states. Then, we modify this quantum algorithm to obtain another algorithm using $\widetilde O(r^2/\varepsilon^5)$ samples of quantum states, which can be applied to quantum state certification. These algorithms have query/sample complexities that are independent of the dimension $N$ of quantum states, and their time complexities only incur an extra $O(\log (N))$ factor. In addition, we show that the decision version of low-rank trace distance estimation is $\mathsf{BQP}$-complete.Comment: Final version. Improve proof details, add BQP-completeness. 31 pages, 2 algorithms, 2 tables, 2 figure

Oscillation and asymptotic behavior for a class of delay parabolic differential

AbstractSome comparative theorems are given for the oscillation and asymptotic behavior for a class of high order delay parabolic differential equations of the form ∂n(u(x,t)−p(t)u(x,t−τ))∂tn−a(t)△u+c(x,t,u)+∫abq(x,t,ξ)f(u(x,g1(t,ξ)),…,u(x,gl(t,ξ)))dσ(ξ)=0,(x,t)∈Ω×R+≡G, where n is an odd integer, Ω is a bounded domain in Rm with a smooth boundary ∂Ω, and △ is the Laplacian operation with three boundary value conditions. Our results extend some of those of [P. Wang, Oscillatory criteria of nonlinear hyperbolic equations with continuous deviating arguments, Appl. Math. Comput. 106 (1999), 163–169] substantially

Calliffusion: Chinese Calligraphy Generation and Style Transfer with Diffusion Modeling

In this paper, we propose Calliffusion, a system for generating high-quality Chinese calligraphy using diffusion models. Our model architecture is based on DDPM (Denoising Diffusion Probabilistic Models), and it is capable of generating common characters in five different scripts and mimicking the styles of famous calligraphers. Experiments demonstrate that our model can generate calligraphy that is difficult to distinguish from real artworks and that our controls for characters, scripts, and styles are effective. Moreover, we demonstrate one-shot transfer learning, using LoRA (Low-Rank Adaptation) to transfer Chinese calligraphy art styles to unseen characters and even out-of-domain symbols such as English letters and digits.Comment: 5pages, International Conference on Computational Creativity, ICC

Succinct quantum testers for closeness and kk-wise uniformity of probability distributions

We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. \textit{Closeness testing} is the problem of distinguishing whether two $n$-dimensional distributions are identical or at least $\varepsilon$-far in $\ell^1$- or $\ell^2$-distance. We show that the quantum query complexities for $\ell^1$- and $\ell^2$-closeness testing are O\rbra{\sqrt{n}/\varepsilon} and O\rbra{1/\varepsilon}, respectively, both of which achieve optimal dependence on $\varepsilon$, improving the prior best results of \hyperlink{cite.gilyen2019distributional}{Gily{\'e}n and Li~(2019)}. \textit{$k$-wise uniformity testing} is the problem of distinguishing whether a distribution over \cbra{0, 1}^n is uniform when restricted to any $k$ coordinates or $\varepsilon$-far from any such distributions. We propose the first quantum algorithm for this problem with query complexity O\rbra{\sqrt{n^k}/\varepsilon}, achieving a quadratic speedup over the state-of-the-art classical algorithm with sample complexity O\rbra{n^k/\varepsilon^2} by \hyperlink{cite.o2018closeness}{O'Donnell and Zhao (2018)}. Moreover, when $k = 2$ our quantum algorithm outperforms any classical one because of the classical lower bound \Omega\rbra{n/\varepsilon^2}. All our quantum algorithms are fairly simple and time-efficient, using only basic quantum subroutines such as amplitude estimation.Comment: We have added the proof of lower bounds and have polished the languag

Parallel Quantum Algorithm for Hamiltonian Simulation

We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including various Hamiltonians of practical interest like local Hamiltonians and Pauli sums. Given the oracle access to the target sparse Hamiltonian, in both query and gate complexity, the running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence $\operatorname{polylog}\log(1/\epsilon)$ on the simulation precision $\epsilon$. This presents an exponential improvement over the dependence $\operatorname{polylog}(1/\epsilon)$ of previous optimal sparse Hamiltonian simulation algorithm without parallelism. To obtain this result, we introduce a novel notion of parallel quantum walk, based on Childs' quantum walk. The target evolution unitary is approximated by a truncated Taylor series, which is obtained by combining these quantum walks in a parallel way. A lower bound $\Omega(\log \log (1/\epsilon))$ is established, showing that the $\epsilon$-dependence of the gate depth achieved in this work cannot be significantly improved. Our algorithm is applied to simulating three physical models: the Heisenberg model, the Sachdev-Ye-Kitaev model and a quantum chemistry model in second quantization. By explicitly calculating the gate complexity for implementing the oracles, we show that on all these models, the total gate depth of our algorithm has a $\operatorname{polylog}\log(1/\epsilon)$ dependence in the parallel setting.Comment: Minor revision. 55 pages, 6 figures, 1 tabl