Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by ${\cal L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.
Robustness of non-abelian holonomic quantum gates against parametric noise
本文对一类非阿贝尔完整量子门的鲁棒性进行了数值研究。我们考虑到由于控制场的随机波动的参数噪声驱动的时间相关的哈密顿沿绝热环。所用的性能估计器是无噪声和有噪声完整门之间的状态保真度。我们进行了我们的分析与不同的相关时间，我们发现，有噪声的完整门似乎是接近无噪声的“短”和“长”噪声相关时间。这个结果可以解释为完整算子的几何性质的结果。我们的模拟是通过使用与激子方案有关的参数来实现完整量子计算的[P.Solinas et al.Phys.Rev.B67，121307（2003）]
Quantum-Classical Hybrid Computation of Electron Transfer in a Cryptochrome Protein via VQE-PDFT and Multiscale Modeling
State Key Laboratory of Genome and Multi-omics Technologies, BGI Research（华大基因组技术国家重点实验室）；School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）；BGI Research（华大基因研究院）；Guangdong Bigdata Engineering Technology Research Center for Life Sciences, BGI Research（华大基因广东省生命科学大数据工程技术研究中心）
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly. Here, we develop a tensor network formalism to simulate the time-dynamics and the Fourier spectrum of noisy quantum circuits. We prove that under general conditions most of the quantum circuits at any constant level of noise per gate can be efficiently simulated classically with the cost increasing only polynomially with the size of the circuits. The result…
The quantum states representing classical phase space are given, and these are used to formulate quantum statistical mechanics as a formally exact double perturbation expansion about classical statistical mechanics. One series of quantum contributions arises from the non-commutativity of the position and momentum operators. Although the formulation of the quantum states differs, the present results for separate averages of position operators and of momentum operators agree with Wigner (1932) and Kirkwood (1933). The second series arises from wave function symmetrization, and is given in terms …
Noiseless subsystems were proved to be an efficient and faithful approach to preserve fragile information against decoherence in quantum information processing and quantum computation. They were employed to design a general (hybrid) quantum memory cell model that can store both quantum and classical information. In this paper, we find an interesting new phenomenon that the purely classical memory cell can be super-activated to preserve quantum states, whereas the null memory cell can only be super-activated to encode classical information. Furthermore, necessary and sufficient conditions for t…
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general …
We present an accreditation protocol for the outputs of noisy intermediate-scale quantum devices. By testing entire circuits rather than individual gates, our accreditation protocol can provide an upper-bound on the variation distance between noisy and noiseless probability distribution of the outputs of the target circuit of interest. Our accreditation protocol requires implementation of quantum circuits no larger than the target circuit, therefore it is practical in the near term and scalable in the long term. Inspired by trap-based protocols for the verification of quantum computations, our…
High-connectivity circuits are a major roadblock for current quantum hardware. We propose a hybrid classical-quantum algorithm to simulate such circuits without swap-gate ladders. As main technical tool, we introduce quantum-classical-quantum interfaces. These replace an experimentally problematic gate (e.g. a long-range one) by single-qubit random measurements followed by state-preparations sampled according to a classical quasi-probability simulation of the noiseless gate. Each interface introduces a multiplicative statistical overhead which is remarkably independent of the on-chip qubit dis…
In classical two-party computation, a trusted initializer who prepares certain initial correlations, known as one-time tables, can help make the inputs of both parties information-theoretically secure. We propose some bipartite quantum protocols with possible aborts for approximately generating such bipartite classical correlations with varying degrees of privacy, without introducing a third party. Under some weak requirements for the parties, the security level is nontrivial for use in bipartite computation. We show that the security is sometimes dependent on the noise level, but we propose a…
The single excitation subspace (SES) method for universal quantum simulation is investigated for a number of diatomic molecular collision complexes. Assuming a system of $n$ tunably-coupled, and fully-connected superconducting qubits, computations are performed in the $n$-dimensional SES which maps directly to an $n$-channel collision problem within a diabatic molecular wave function representation. Here we outline the approach on a classical computer to solve the time-dependent Schrödinger equation in an $n$-dimensional molecular basis - the so-called semiclassical molecular-orbital close-cou…
Quantum Differential Privacy: An Information Theory Perspective
Technical University of Munich（慕尼黑工业大学）；National University of Singapore（新加坡国立大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；University of Copenhagen（哥本哈根大学）
