Onsager's Scars in Disordered Spin Chains

We propose a class of non-integrable quantum spin chain models that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct such scarred models for arbitrary spin quantum number $S$. There are two types of scar states, namely, coherent states associated to an Onsager-algebra element and one-magnon scar states. While both of them are highly-excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also investigate the dynamics of the fidelity and entanglement entropy for several initial states. The results clearly show that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly. To our knowledge, our model is the first explicit example of disordered quantum many-body scarred model.Comment: 5+7 pages, 4+5 figure

Handbook for Efficiently Quantifying Robustness of Magic

The nonstabilizerness, or magic, is an essential quantum resource to perform universal quantum computation. Robustness of magic (RoM) in particular characterizes the degree of usefulness of a given quantum state for non-Clifford operation. While the mathematical formalism of RoM can be given in a concise manner, it is extremely challenging to determine the RoM in practice, since it involves superexponentially many pure stabilizer states. In this work, we present efficient novel algorithms to compute the RoM. The crucial technique is a subroutine that achieves the remarkable features in calculation of overlaps between pure stabilizer states: (i) the time complexity per each stabilizer is reduced exponentially, (ii) the space complexity is reduced superexponentially. Based on this subroutine, we present algorithms to compute the RoM for arbitrary states up to $n=7$ qubits on a laptop, while brute-force methods require a memory size of 86 TiB. As a byproduct, the proposed subroutine allows us to simulate the stabilizer fidelity up to $n=8$ qubits, for which naive methods require memory size of 86 PiB so that any state-of-the-art classical computer cannot execute the computation. We further propose novel algorithms that utilize the preknowledge on the structure of target quantum state such as the permutation symmetry of disentanglement, and numerically demonstrate our state-of-the-art results for copies of magic states and partially disentangled quantum states. The series of algorithms constitute a comprehensive ``handbook'' to scale up the computation of the RoM, and we envision that the proposed technique applies to the computation of other quantum resource measures as well.Comment: 16+12 pages, 8+1 figure

Universal cost bound of quantum error mitigation based on quantum estimation theory

We present a unified approach to analyzing the cost of various quantum error mitigation methods on the basis of quantum estimation theory. By analyzing the quantum Fisher information matrix of a virtual quantum circuit that effectively represents the operations of quantum error mitigation methods, we derive for a generic layered quantum circuit under a wide class of Markovian noise that, unbiased estimation of an observable encounters an exponential growth with the circuit depth in the lower bound on the measurement cost. Under the global depolarizing noise, we in particular find that the bound can be asymptotically saturated by merely rescaling the measurement results. Moreover, we prove for random circuits with local noise that the cost grows exponentially also with the qubit count. Our numerical simulations support the observation that, even if the circuit has only linear connectivity, such as the brick-wall structure, each noise channel converges to the global depolarizing channel with its strength growing exponentially with the qubit count. This not only implies the exponential growth of cost both with the depth and qubit count, but also validates the rescaling technique for sufficiently deep quantum circuits. Our results contribute to the understanding of the physical limitations of quantum error mitigation and offer a new criterion for evaluating the performance of quantum error mitigation techniques.Comment: 7 + 14 pages, 10 figures. See also a related work by Takagi et al., which appears in the same arXiv posting as arXiv:2208.0917

Target-selective homologous recombination cloning for high-throughput generation of monoclonal antibodies from single plasma cells

<p>Abstract</p> <p>Background</p> <p>Molecular cloning of functional immunoglobulin genes from single plasma cells is one of the most promising technologies for the rapid development of monoclonal antibody drugs. However, the proper insertion of PCR-amplified immunoglobulin genes into expression vectors remains an obstacle to the high-throughput production of recombinant monoclonal antibodies.</p> <p>Results</p> <p>We developed a single-step cloning method, target-selective homologous recombination (TS-HR), in which PCR-amplified immunoglobulin variable genes were selectively inserted into vectors, even in the presence of nonspecifically amplified DNA. TS-HR utilizes Red/ET-mediated homologous recombination with a target-selective vector (TS-vector) with unique homology arms on its termini. Using TS-HR, immunoglobulin variable genes were cloned directly into expression vectors by co-transforming unpurified PCR products and the TS-vector into <it>E. coli</it>. Furthermore, the high cloning specificity of TS-HR allowed plasmids to be extracted from pools of transformed bacteria without screening single colonies for correct clones. We present a one-week protocol for the production of recombinant mouse monoclonal antibodies from large numbers of single plasma cells.</p> <p>Conclusion</p> <p>The time requirements and limitations of traditional cloning procedures for the production of recombinant immunoglobulins have been significantly reduced with the development of the TS-HR cloning technique.</p

Adaptive measurement strategy for quantum subspace methods

Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum computation, in particular, existing studies have mainly focused on holistic state tomography or estimation on specific observables with known classical descriptions, while this lacks the important class of problems where the estimation target itself relies on the measurement outcome. In this work, we propose an adaptive measurement optimization method that is useful for the quantum subspace methods, namely the variational simulation methods that utilize classical postprocessing on measurement outcomes. The proposed method first determines the measurement protocol based on QSE calculation for classically simulatable states, and then adaptively updates the protocol according to the quantum measurement result. As a numerical demonstration, we have shown for excited-state simulation of molecules that (i) we are able to reduce the number of measurements by an order of magnitude by constructing an appropriate measurement strategy (ii) the adaptive iteration converges successfully even for strongly correlated molecule of H$_4$. Our work reveals that the potential of the QSE method can be empowered by elaborated measurement protocols, and opens a path to further pursue efficient quantum measurement techniques in practical computations.Comment: 9 pages, 4 figure