Basic Usage#
This chapter provides a brief overview of the basic usage of Qurrium.
1. Entanglement Entropy#
This part will introduce several methods to compute the entanglement entropy of a quantum system. The methods include:
All three methods calculate the entropy of a quantum state, but their calculation techniques and post-processing procedures are entirely different.
2. WaveFuction Overlap#
This part will introduce several methods to compute the wavefuction overlap between 2 quantum system. The methods include:
3. Magnetization Square#
This part will introduce several methods to compute the magnetization square of a quantum system. The methods include:
Extra. Workflow Tools#
Workflow Tools
Reference#
Randomized Measurement#
Probing Rényi entanglement entropy via randomized measurements - Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoît Vermersch, Christine Maier, Ben P. Lanyon, Peter Zoller, Rainer Blatt ,and Christian F. Roos doi:10.1126/science.aau4963
@article{ doi:10.1126/science.aau4963, author = {Tiff Brydges and Andreas Elben and Petar Jurcevic and Benoît Vermersch and Christine Maier and Ben P. Lanyon and Peter Zoller and Rainer Blatt and Christian F. Roos }, title = {Probing Rényi entanglement entropy via randomized measurements}, journal = {Science}, volume = {364}, number = {6437}, pages = {260-263}, year = {2019}, doi = {10.1126/science.aau4963}, URL = {https://www.science.org/doi/abs/10.1126/science.aau4963}, eprint = {https://www.science.org/doi/pdf/10.1126/science.aau4963}, abstract = {Quantum systems are predicted to be better at information processing than their classical counterparts, and quantum entanglement is key to this superior performance. But how does one gauge the degree of entanglement in a system? Brydges et al. monitored the build-up of the so-called Rényi entropy in a chain of up to 10 trapped calcium ions, each of which encoded a qubit. As the system evolved, interactions caused entanglement between the chain and the rest of the system to grow, which was reflected in the growth of the Rényi entropy. Science, this issue p. 260 The buildup of entropy in an ion chain reflects a growing entanglement between the chain and its complement. Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.}}
Error Mitigation on Randomized Measurement#
Simple mitigation of global depolarizing errors in quantum simulations - Vovrosh, Joseph and Khosla, Kiran E. and Greenaway, Sean and Self, Christopher and Kim, M. S. and Knolle, Johannes PhysRevE.104.035309
@article{PhysRevE.104.035309, title = {Simple mitigation of global depolarizing errors in quantum simulations}, author = {Vovrosh, Joseph and Khosla, Kiran E. and Greenaway, Sean and Self, Christopher and Kim, M. S. and Knolle, Johannes}, journal = {Phys. Rev. E}, volume = {104}, issue = {3}, pages = {035309}, numpages = {8}, year = {2021}, month = {Sep}, publisher = {American Physical Society}, doi = {10.1103/PhysRevE.104.035309}, url = {https://link.aps.org/doi/10.1103/PhysRevE.104.035309} }
Classical Shadow#
Predicting many properties of a quantum system from very few measurements - Huang, Hsin-Yuan and Kueng, Richard and Preskill, John doi:10.1038/s41567-020-0932-7
@article{Huang2020-xg, title = "Predicting many properties of a quantum system from very few measurements", author = "Huang, Hsin-Yuan and Kueng, Richard and Preskill, John", abstract = "Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a `classical shadow', can be used to predict many different properties; order $$\{\textbackslashmathrm\{log\}\}\textbackslash,(M)$$measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.", journal = "Nature Physics", volume = 16, number = 10, pages = "1050--1057", month = oct, year = 2020 }
The randomized measurement toolbox - Elben, Andreas and Flammia, Steven T. and Huang, Hsin-Yuan and Kueng, Richard and Preskill, John and Vermersch, Benoît and Zoller, Peter doi:10.1038/s42254-022-00535-2
@article{Elben2023-bk, title = "The randomized measurement toolbox", author = "Elben, Andreas and Flammia, Steven T and Huang, Hsin-Yuan and Kueng, Richard and Preskill, John and Vermersch, Beno{\^\i}t and Zoller, Peter", abstract = "Programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of computational power but also makes them difficult to control precisely or characterize accurately using measured classical data. We review protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis; then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages. For example, a single data set can be used multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of non-local order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world.", journal = "Nature Reviews Physics", volume = 5, number = 1, pages = "9--24", month = jan, year = 2023 }
String Operator#
Crossing a topological phase transition with a quantum computer - Smith, Adam and Jobst, Bernhard and Green, Andrew G. and Pollmann, Frank PhysRevResearch.4.L022020
@article{PhysRevResearch.4.L022020, title = {Crossing a topological phase transition with a quantum computer}, author = {Smith, Adam and Jobst, Bernhard and Green, Andrew G. and Pollmann, Frank}, journal = {Phys. Rev. Research}, volume = {4}, issue = {2}, pages = {L022020}, numpages = {8}, year = {2022}, month = {Apr}, publisher = {American Physical Society}, doi = {10.1103/PhysRevResearch.4.L022020}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.4.L022020} }