Pub Date : 2024-08-16DOI: 10.1103/prxquantum.5.030335
Simon Hollerith, Valentin Walther, Kritsana Srakaew, David Wei, Daniel Adler, Suchita Agrawal, Pascal Weckesser, Immanuel Bloch, Johannes Zeiher
The coupling of an isolated quantum state to a continuum is typically associated with decoherence and decreased lifetime. For coupling rates larger than the bandwidth of the associated continuum, decoherence can be mitigated, and new stable eigenstates emerge. Here, we laser-couple diatomic molecules of highly excited Rydberg atoms, so-called Rydberg macrodimers, to a continuum of free motional states. Enabled by their small vibrational eigenfrequencies, we achieve the regime of strong continuum couplings and observe the appearance of new resonances. We explain the observed spectroscopic features as molecular states emerging in the presence of the light field using a Fano model. For atoms arranged on a lattice, we predict the strong continuum coupling to even stabilize triatomic molecules and find the first signatures of these by observing three-atom loss correlations using quantum gas microscopy. Our results present a mechanism to control decoherence and bind polyatomic molecules using strong light-matter interactions.
{"title":"Rydberg Molecules Bound by Strong Light Fields","authors":"Simon Hollerith, Valentin Walther, Kritsana Srakaew, David Wei, Daniel Adler, Suchita Agrawal, Pascal Weckesser, Immanuel Bloch, Johannes Zeiher","doi":"10.1103/prxquantum.5.030335","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030335","url":null,"abstract":"The coupling of an isolated quantum state to a continuum is typically associated with decoherence and decreased lifetime. For coupling rates larger than the bandwidth of the associated continuum, decoherence can be mitigated, and new stable eigenstates emerge. Here, we laser-couple diatomic molecules of highly excited Rydberg atoms, so-called Rydberg macrodimers, to a continuum of free motional states. Enabled by their small vibrational eigenfrequencies, we achieve the regime of strong continuum couplings and observe the appearance of new resonances. We explain the observed spectroscopic features as molecular states emerging in the presence of the light field using a Fano model. For atoms arranged on a lattice, we predict the strong continuum coupling to even stabilize triatomic molecules and find the first signatures of these by observing three-atom loss correlations using quantum gas microscopy. Our results present a mechanism to control decoherence and bind polyatomic molecules using strong light-matter interactions.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-15DOI: 10.1103/prxquantum.5.030334
Jordan Hines, Daniel Hothem, Robin Blume-Kohout, Birgitta Whaley, Timothy Proctor
We introduce binary randomized benchmarking (BiRB), a protocol that streamlines traditional RB by using circuits consisting almost entirely of independent identically distributed (IID) layers of gates. BiRB reliably and efficiently extracts the average error rate of a Clifford gate set by sending tensor-product eigenstates of random Pauli operators through random circuits with IID layers. Unlike existing RB methods, BiRB does not use motion reversal circuits—i.e., circuits that implement the identity (or a Pauli) operator—which simplifies both the method and the theory proving its reliability. Furthermore, this simplicity enables scaling BiRB to many more qubits than the most widely used RB methods.
{"title":"Fully Scalable Randomized Benchmarking Without Motion Reversal","authors":"Jordan Hines, Daniel Hothem, Robin Blume-Kohout, Birgitta Whaley, Timothy Proctor","doi":"10.1103/prxquantum.5.030334","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030334","url":null,"abstract":"We introduce <i>binary randomized benchmarking (BiRB)</i>, a protocol that streamlines traditional RB by using circuits consisting almost entirely of independent identically distributed (IID) layers of gates. BiRB reliably and efficiently extracts the average error rate of a Clifford gate set by sending tensor-product eigenstates of random Pauli operators through random circuits with IID layers. Unlike existing RB methods, BiRB does not use motion reversal circuits—i.e., circuits that implement the identity (or a Pauli) operator—which simplifies both the method and the theory proving its reliability. Furthermore, this simplicity enables scaling BiRB to many more qubits than the most widely used RB methods.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-14DOI: 10.1103/prxquantum.5.030333
Teodor Parella-Dilmé, Korbinian Kottmann, Leonardo Zambrano, Luke Mortimer, Jakob S. Kottmann, Antonio Acín
In ab initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step from the problem of fermions into a problem of qubits. This work introduces a physically inspired method for constructing mappings that significantly simplify entanglement requirements when one is simulating states of interest. The presence of electronic excitations drives the construction of our mappings, reducing correlations for target states in the qubit space. To benchmark our method, we simulate ground-states of small molecules and observe an enhanced performance when compared with classical and quantum variational approaches from prior research using conventional mappings. In particular, on the quantum side, our mappings require a reduced number of entangling layers to achieve accuracy for , , , stretching, and benzene’s system using the RY hardware-efficient ansatz. In addition, our mappings also provide an enhanced ground-state simulation performance in the density matrix renormalization group algorithm for the molecule.
在 ab initio 电子结构模拟中，费米子到量子比特映射是将费米子问题转化为量子比特问题的初始编码步骤。这项研究介绍了一种受物理启发的映射构建方法，它能在模拟感兴趣的状态时大大简化纠缠要求。电子激发的存在推动了我们映射的构建，降低了量子比特空间中目标状态的相关性。为了对我们的方法进行基准测试，我们模拟了小分子的基态，并观察到与之前研究中使用传统映射的经典和量子变分方法相比，我们的方法具有更强的性能。特别是在量子方面，我们的映射需要减少纠缠层的数量，以达到使用 RY 硬件高效解析法计算 LiH、H2、(H2)2、H4≠拉伸和苯π系统的精度。此外，我们的映射还增强了 N2 分子在密度矩阵重正化群算法中的基态模拟性能。
{"title":"Reducing Entanglement with Physically Inspired Fermion-To-Qubit Mappings","authors":"Teodor Parella-Dilmé, Korbinian Kottmann, Leonardo Zambrano, Luke Mortimer, Jakob S. Kottmann, Antonio Acín","doi":"10.1103/prxquantum.5.030333","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030333","url":null,"abstract":"In <i>ab initio</i> electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step from the problem of fermions into a problem of qubits. This work introduces a physically inspired method for constructing mappings that significantly simplify entanglement requirements when one is simulating states of interest. The presence of electronic excitations drives the construction of our mappings, reducing correlations for target states in the qubit space. To benchmark our method, we simulate ground-states of small molecules and observe an enhanced performance when compared with classical and quantum variational approaches from prior research using conventional mappings. In particular, on the quantum side, our mappings require a reduced number of entangling layers to achieve accuracy for <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>LiH</mi></math>, <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"normal\">H</mi></mrow><mn>2</mn></msub></math>, <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"normal\">H</mi></mrow><mn>2</mn></msub><msub><mo stretchy=\"false\">)</mo><mn>2</mn></msub></math>, <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi mathvariant=\"normal\">H</mi></mrow><mn>4</mn><mo>≠</mo></msubsup></math> stretching, and benzene’s <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>π</mi></math> system using the RY hardware-efficient ansatz. In addition, our mappings also provide an enhanced ground-state simulation performance in the density matrix renormalization group algorithm for the <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"normal\">N</mi></mrow><mn>2</mn></msub></math> molecule.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-13DOI: 10.1103/prxquantum.5.030332
Mircea Bejan, Campbell McLauchlan, Benjamin Béri
The classical simulation of highly entangling quantum dynamics is conjectured to be generically hard. Thus, recently discovered measurement-induced transitions between highly entangling and low-entanglement dynamics are phase transitions in classical simulability. Here, we study simulability transitions beyond entanglement: noting that some highly entangling dynamics (e.g., integrable systems or Clifford circuits) are easy to classically simulate, thus requiring “magic”—a subtle form of quantum resource—to achieve computational hardness, we ask how the dynamics of magic competes with measurements. We study the resulting “dynamical magic transitions” focusing on random monitored Clifford circuits doped by gates (injecting magic). We identify dynamical “stabilizer purification”—the collapse of a superposition of stabilizer states by measurements—as the mechanism driving this transition. We find cases where transitions in magic and entanglement coincide, but also others with a magic and simulability transition in a highly (volume-law) entangled phase. In establishing our results, we use Pauli-based computation, a scheme distilling the quantum essence of the dynamics to a magic state register subject to mutually commuting measurements. We link stabilizer purification to “magic fragmentation” wherein these measurements separate into disjoint, -weight blocks, and relate this to the spread of magic in the original circuit becoming arrested.
据推测，对高度纠缠量子动力学的经典模拟一般很难。因此，最近发现的测量诱导的高纠缠与低纠缠动力学之间的转变是经典可模拟性的相变。在此，我们研究纠缠之外的可模拟性转换：我们注意到一些高度纠缠的动力学（如可积分系统或克利福德电路）易于经典模拟，因此需要 "魔法"--一种微妙的量子资源形式--来实现计算硬度，我们询问魔法动力学如何与测量竞争。我们研究了由此产生的 "动态魔法转换"，重点是通过 T 门（注入魔法）掺杂的随机监控克利福德电路。我们将动态 "稳定器净化"--测量对稳定器叠加态的坍缩--确定为驱动这种转变的机制。我们发现了魔力和纠缠的转变同时发生的情况，也发现了其他在高度（体积律）纠缠阶段发生魔力和可模拟性转变的情况。在建立我们的结果时，我们使用了基于保利的计算，这是一种将动力学的量子本质提炼为受相互换向测量影响的魔态寄存器的方案。我们将稳定器净化与 "魔力碎片化 "联系起来，在 "魔力碎片化 "中，这些测量被分离成不相连的、O(1)重的块，并将此与原始电路中魔力的扩散联系起来。
{"title":"Dynamical Magic Transitions in Monitored Clifford+T Circuits","authors":"Mircea Bejan, Campbell McLauchlan, Benjamin Béri","doi":"10.1103/prxquantum.5.030332","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030332","url":null,"abstract":"The classical simulation of highly entangling quantum dynamics is conjectured to be generically hard. Thus, recently discovered measurement-induced transitions between highly entangling and low-entanglement dynamics are phase transitions in classical simulability. Here, we study simulability transitions beyond entanglement: noting that some highly entangling dynamics (e.g., integrable systems or Clifford circuits) are easy to classically simulate, thus requiring “magic”—a subtle form of quantum resource—to achieve computational hardness, we ask how the dynamics of magic competes with measurements. We study the resulting “dynamical magic transitions” focusing on random monitored Clifford circuits doped by <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> gates (injecting magic). We identify dynamical “stabilizer purification”—the collapse of a superposition of stabilizer states by measurements—as the mechanism driving this transition. We find cases where transitions in magic and entanglement coincide, but also others with a magic and simulability transition in a highly (volume-law) entangled phase. In establishing our results, we use Pauli-based computation, a scheme distilling the quantum essence of the dynamics to a magic state register subject to mutually commuting measurements. We link stabilizer purification to “magic fragmentation” wherein these measurements separate into disjoint, <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"script\">O</mi></mrow><mo stretchy=\"false\">(</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math>-weight blocks, and relate this to the spread of magic in the original circuit becoming arrested.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"785 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/prxquantum.5.030331
Beate E. Asenbeck, Akito Kawasaki, Ambroise Boyer, Tom Darras, Alban Urvoy, Akira Furusawa, Julien Laurat
Optical quantum information processing relies critically on Bell-state measurement, a ubiquitous operation for quantum communication and computing. Its practical realization involves the interference of optical modes and the detection of a single photon in an indistinguishable manner. Yet, in the absence of efficient photon-number-resolution capabilities, errors arise from multiphoton components, decreasing the overall process fidelity. Here, we introduce a hybrid detection scheme for Bell-state measurement, leveraging both on-off single-photon detection and quadrature conditioning via homodyne detection. We derive explicit fidelities for quantum teleportation and entanglement-swapping processes employing this strategy, demonstrating its efficacy. We also compare with photon-number-resolving detectors and find a strong advantage of the hybrid scheme in a wide range of parameters. This work provides a new tool for linear-optics schemes, with applications to quantum state engineering and quantum interconnects.
{"title":"Hybrid Approach to Mitigate Errors in Linear Photonic Bell-State Measurement for Quantum Interconnects","authors":"Beate E. Asenbeck, Akito Kawasaki, Ambroise Boyer, Tom Darras, Alban Urvoy, Akira Furusawa, Julien Laurat","doi":"10.1103/prxquantum.5.030331","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030331","url":null,"abstract":"Optical quantum information processing relies critically on Bell-state measurement, a ubiquitous operation for quantum communication and computing. Its practical realization involves the interference of optical modes and the detection of a single photon in an indistinguishable manner. Yet, in the absence of efficient photon-number-resolution capabilities, errors arise from multiphoton components, decreasing the overall process fidelity. Here, we introduce a hybrid detection scheme for Bell-state measurement, leveraging both on-off single-photon detection and quadrature conditioning via homodyne detection. We derive explicit fidelities for quantum teleportation and entanglement-swapping processes employing this strategy, demonstrating its efficacy. We also compare with photon-number-resolving detectors and find a strong advantage of the hybrid scheme in a wide range of parameters. This work provides a new tool for linear-optics schemes, with applications to quantum state engineering and quantum interconnects.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"290 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-09DOI: 10.1103/prxquantum.5.030330
A. Craddock, Anne Lazenby, Gabriel Bello Portmann, Rourke Sekelsky, Mael Flament, M. Namazi
The distribution of high-fidelity high-rate entanglement over telecommunication infrastructure is one of the main paths toward large-scale quantum networks, enabling applications such as quantum encryption and network protection, blind quantum computing, distributed quantum computing, and distributed quantum sensing. However, the fragile nature of entangled photons operating in real-world fiber infrastructure has historically limited continuous operation of such networks. Here, we present a fully automated system capable of distributing polarization-entangled photons over a 34-km deployed fiber in New York City, achieving high rates of nearly 5×105 pairs/s. Separately, we demonstrate a high fidelity of approximately 99% for rates up to 2×104 pairs/s. Lastly, we achieve 15 days of continuous distribution, with a network up-time of 99.84%. Our work paves the way for practical deployment of always-on entanglement-based networks with rates and fidelity adequate for many current and future use cases. Published by the American Physical Society 2024
{"title":"Automated Distribution of Polarization-Entangled Photons Using Deployed New York City Fibers","authors":"A. Craddock, Anne Lazenby, Gabriel Bello Portmann, Rourke Sekelsky, Mael Flament, M. Namazi","doi":"10.1103/prxquantum.5.030330","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030330","url":null,"abstract":"The distribution of high-fidelity high-rate entanglement over telecommunication infrastructure is one of the main paths toward large-scale quantum networks, enabling applications such as quantum encryption and network protection, blind quantum computing, distributed quantum computing, and distributed quantum sensing. However, the fragile nature of entangled photons operating in real-world fiber infrastructure has historically limited continuous operation of such networks. Here, we present a fully automated system capable of distributing polarization-entangled photons over a 34-km deployed fiber in New York City, achieving high rates of nearly 5×105 pairs/s. Separately, we demonstrate a high fidelity of approximately 99% for rates up to 2×104 pairs/s. Lastly, we achieve 15 days of continuous distribution, with a network up-time of 99.84%. Our work paves the way for practical deployment of always-on entanglement-based networks with rates and fidelity adequate for many current and future use cases.\u0000 \u0000 \u0000 \u0000 \u0000 Published by the American Physical Society\u0000 2024\u0000 \u0000 \u0000","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"48 44","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141923961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-08DOI: 10.1103/prxquantum.5.030329
Youenn Le Gal, Xhek Turkeshi, Marco Schirò
Monitored quantum many-body systems display a rich pattern of entanglement dynamics, which is unique to this nonunitary setting. This work studies the effect of quantum jumps on the entanglement dynamics beyond the no-click limit corresponding to a deterministic non-Hermitian evolution. To this aim, we introduce a new tool that looks at the statistics of entanglement-entropy gain and loss after and in between quantum jumps. This insight allows us to build a simple stochastic model of a random walk with partial resetting, which reproduces the entanglement dynamics, and to dissect the mutual role of jumps and non-Hermitian evolution on the entanglement scaling. We apply these ideas to the study of measurement-induced transitions in monitored fermions. We demonstrate that significant deviations from the no-click limit arise whenever quantum jumps strongly renormalize the non-Hermitian dynamics, as in the case of models with symmetry at weak monitoring. On the other hand, we show that the weak-monitoring phase of the Ising chain leads to a robust subvolume logarithmic phase due to weakly renormalized non-Hermitian dynamics.
{"title":"Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps","authors":"Youenn Le Gal, Xhek Turkeshi, Marco Schirò","doi":"10.1103/prxquantum.5.030329","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030329","url":null,"abstract":"Monitored quantum many-body systems display a rich pattern of entanglement dynamics, which is unique to this nonunitary setting. This work studies the effect of quantum jumps on the entanglement dynamics beyond the no-click limit corresponding to a deterministic non-Hermitian evolution. To this aim, we introduce a new tool that looks at the statistics of entanglement-entropy gain and loss after and in between quantum jumps. This insight allows us to build a simple stochastic model of a random walk with partial resetting, which reproduces the entanglement dynamics, and to dissect the mutual role of jumps and non-Hermitian evolution on the entanglement scaling. We apply these ideas to the study of measurement-induced transitions in monitored fermions. We demonstrate that significant deviations from the no-click limit arise whenever quantum jumps strongly renormalize the non-Hermitian dynamics, as in the case of models with <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>U</mi><mo stretchy=\"false\">(</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math> symmetry at weak monitoring. On the other hand, we show that the weak-monitoring phase of the Ising chain leads to a robust subvolume logarithmic phase due to weakly renormalized non-Hermitian dynamics.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-08DOI: 10.1103/prxquantum.5.030328
Zijian Liang (梁子健), Yijia Xu (许逸葭), Joseph T. Iosue, Yu-An Chen (陳昱安)
In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to qudits, including instances where is a nonprime number. This capability allows the identification of topological orders that differ from the toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for qudits (with being a prime) are equivalent to finite copies of toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order.
{"title":"Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions","authors":"Zijian Liang (梁子健), Yijia Xu (许逸葭), Joseph T. Iosue, Yu-An Chen (陳昱安)","doi":"10.1103/prxquantum.5.030328","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030328","url":null,"abstract":"In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"double-struck\">Z</mi></mrow><mi>d</mi></msub></math> qudits, including instances where <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi></math> is a nonprime number. This capability allows the identification of topological orders that differ from the <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"double-struck\">Z</mi></mrow><mi>d</mi></msub></math> toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"double-struck\">Z</mi></mrow><mi>p</mi></msub></math> qudits (with <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math> being a prime) are equivalent to finite copies of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"double-struck\">Z</mi></mrow><mi>p</mi></msub></math> toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-07DOI: 10.1103/prxquantum.5.030326
Lukas Postler, Friederike Butt, Ivan Pogorelov, Christian D. Marciniak, Sascha Heußen, Rainer Blatt, Philipp Schindler, Manuel Rispler, Markus Müller, Thomas Monz
Encoding information redundantly using quantum error-correcting (QEC) codes allows one to overcome the inherent sensitivity to noise in quantum computers to ultimately achieve large-scale quantum computation. The Steane QEC method involves preparing an auxiliary logical qubit of the same QEC code as used for the data register. The data and auxiliary registers are then coupled with a logical controlled-not (cnot) gate, enabling a measurement of the auxiliary register to reveal the error syndrome. This study presents the implementation of multiple rounds of fault-tolerant (FT) Steane QEC on a trapped-ion quantum computer. Various QEC codes are employed and the results are compared to a previous experimental approach utilizing flag qubits. Our experimental findings show improved logical fidelities for Steane QEC and accompanying numerical simulations indicate an even larger performance advantage for quantum processors limited by entangling-gate errors. This establishes experimental Steane QEC as a competitive paradigm for FT quantum computing.
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Pub Date : 2024-08-07DOI: 10.1103/prxquantum.5.030327
Izabella Lovas, Utkarsh Agrawal, Sagar Vijay
We investigate phase transitions in the encoding of quantum information in a quantum many-body system due to the competing effects of unitary scrambling and boundary dissipation. Specifically, we study the fate of quantum information in a one-dimensional qudit chain, subject to local unitary quantum circuit evolution in the presence of depolarizing noise at the boundary. If the qudit chain initially contains a finite amount of locally accessible quantum information, unitary evolution in the presence of boundary dissipation allows this information to remain partially protected when the dissipation is sufficiently weak, and up to timescales growing linearly in the system size . In contrast, for strong enough dissipation, this information is completely lost to the dissipative environment. We analytically investigate this “quantum coding transition” by considering dynamics involving Haar-random, local unitary gates, and confirm our predictions in numerical simulations of Clifford quantum circuits. Scrambling the quantum information in the qudit chain with a unitary circuit of depth before the onset of dissipation can perfectly protect the information until late times. The nature of the coding transition changes when the dynamics extend for times much longer than . We further show that at weak dissipation, it is possible to code at a finite rate, i.e., a fraction of the many-body Hilbert space of the qudit chain can be used to encode quantum information.
我们研究了量子多体系统中量子信息编码的相变，这种相变是由单元扰动和边界耗散的竞争效应引起的。具体来说，我们研究了量子信息在一维量子链中的命运，该量子链在边界存在去极化噪声的情况下受到局部单元量子回路演化的影响。如果量子链最初包含有限数量的局部可访问量子信息，那么当耗散足够弱时，存在边界耗散的单元演化允许这些信息保持部分保护，其时间尺度与系统大小 L 呈线性增长。通过考虑涉及哈尔随机、局部单元门的动力学，我们对这种 "量子编码转换 "进行了分析研究，并在克利福德量子电路的数值模拟中证实了我们的预测。在耗散开始之前，用深度为 O(logL)的单元电路扰乱量子链中的量子信息，可以完美地保护信息直到后期。我们进一步证明，在弱耗散情况下，有可能以有限速率进行编码，也就是说，魁拔链的多体希尔伯特空间的一部分可以用来编码量子信息。
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