Pub Date : 2025-12-24DOI: 10.22331/q-2025-12-24-1956
Beatrice Magni, Xhek Turkeshi
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results and perform large-scale simulations in regimes challenging for tensor network and Pauli-based methods. We begin by analyzing generalized stabilizer entropies, computable magic monotones in many-qudit systems, and identify a dynamical phase transition in the doping rate, marking the breakdown of classical simulability and the onset of Haar-random behavior. The critical behavior is governed by the qudit dimension and the magic content of the non-Clifford gate. Using the qudit $T$-gate as a benchmark, we show that higher-dimensional qudits converge faster to Haar-typical stabilizer entropies. For qutrits ($d=3$), analytical predictions match numerics on brickwork circuits, showing that locality plays a limited role in magic spreading. We also examine anticoncentration and entanglement growth, showing that $O(log N)$ non-Clifford gates suffice for approximating Haar expectation values to precision $varepsilon$, and relate antiflatness measures to stabilizer entropies in qutrit systems. Finally, we analyze out-of-time-order correlators and show that a finite density of non-Clifford gates is needed to induce chaos, with a sharp transition fixed by the local dimension, twice that of the magic transition. Altogether, these results establish a unified framework for diagnosing complexity in doped Clifford circuits and deepen our understanding of resource theories in multiqudit systems.
{"title":"Quantum Complexity and Chaos in Many-Qudit Doped Clifford Circuits","authors":"Beatrice Magni, Xhek Turkeshi","doi":"10.22331/q-2025-12-24-1956","DOIUrl":"https://doi.org/10.22331/q-2025-12-24-1956","url":null,"abstract":"We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results and perform large-scale simulations in regimes challenging for tensor network and Pauli-based methods. We begin by analyzing generalized stabilizer entropies, computable magic monotones in many-qudit systems, and identify a dynamical phase transition in the doping rate, marking the breakdown of classical simulability and the onset of Haar-random behavior. The critical behavior is governed by the qudit dimension and the magic content of the non-Clifford gate. Using the qudit $T$-gate as a benchmark, we show that higher-dimensional qudits converge faster to Haar-typical stabilizer entropies. For qutrits ($d=3$), analytical predictions match numerics on brickwork circuits, showing that locality plays a limited role in magic spreading. We also examine anticoncentration and entanglement growth, showing that $O(log N)$ non-Clifford gates suffice for approximating Haar expectation values to precision $varepsilon$, and relate antiflatness measures to stabilizer entropies in qutrit systems. Finally, we analyze out-of-time-order correlators and show that a finite density of non-Clifford gates is needed to induce chaos, with a sharp transition fixed by the local dimension, twice that of the magic transition. Altogether, these results establish a unified framework for diagnosing complexity in doped Clifford circuits and deepen our understanding of resource theories in multiqudit systems.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"20 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.22331/q-2025-12-23-1955
Nhat A. Nghiem, Xianfeng David Gu, Tzu-Chieh Wei
Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be identified. Given a simplex, an important feature is called the Betti numbers, which roughly count the number of `holes' in different dimensions. Calculating Betti numbers exactly can be $#$P-hard, and approximating them can be NP-hard, which rules out the possibility of any generic efficient algorithms and unconditional exponential quantum speedup. Here, we explore the specific setting of a triangulated manifold. In contrast to most known methods to estimate Betti numbers, which rely on homology, we exploit the `dual' approach, namely, cohomology, combining the insight of the Hodge theory and de Rham cohomology. Our proposed algorithm can calculate its $r$-th normalized Betti number $beta_r/|S_r|$ up to some additive error $epsilon$ with running time $mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon^2} log (log |S_r^K|) big( rlog |S_r^K| big) Big)$, where $|S_r|$ is the number of $r$-simplexes in the given complex. For the estimation of $r$-th Betti number $beta_r$ to a chosen multiplicative accuracy $epsilon'$, our algorithm has complexity $ mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon'^2} big( frac{ Gamma}{beta_r}big)^2 (log |S_r^K|) log big( rlog |S_r^K| big) Big)$, where $Gamma leq |S_r^K|$ can be chosen. A detailed analysis is provided, showing that our cohomology framework can even perform exponentially faster than previous homology methods in several regimes. In particular, our method is most effective when $beta_r ll |S_r^K|$, which can offer more flexibility and practicability than existing quantum algorithms that achieve the best performance in the regime $beta_r approx |S_r^K|$.
{"title":"Quantum Algorithm for Estimating Betti Numbers Using Cohomology Approach","authors":"Nhat A. Nghiem, Xianfeng David Gu, Tzu-Chieh Wei","doi":"10.22331/q-2025-12-23-1955","DOIUrl":"https://doi.org/10.22331/q-2025-12-23-1955","url":null,"abstract":"Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be identified. Given a simplex, an important feature is called the Betti numbers, which roughly count the number of `holes' in different dimensions. Calculating Betti numbers exactly can be $#$P-hard, and approximating them can be NP-hard, which rules out the possibility of any generic efficient algorithms and unconditional exponential quantum speedup. Here, we explore the specific setting of a triangulated manifold. In contrast to most known methods to estimate Betti numbers, which rely on homology, we exploit the `dual' approach, namely, cohomology, combining the insight of the Hodge theory and de Rham cohomology. Our proposed algorithm can calculate its $r$-th normalized Betti number $beta_r/|S_r|$ up to some additive error $epsilon$ with running time $mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon^2} log (log |S_r^K|) big( rlog |S_r^K| big) Big)$, where $|S_r|$ is the number of $r$-simplexes in the given complex. For the estimation of $r$-th Betti number $beta_r$ to a chosen multiplicative accuracy $epsilon'$, our algorithm has complexity $ mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon'^2} big( frac{ Gamma}{beta_r}big)^2 (log |S_r^K|) log big( rlog |S_r^K| big) Big)$, where $Gamma leq |S_r^K|$ can be chosen. A detailed analysis is provided, showing that our cohomology framework can even perform exponentially faster than previous homology methods in several regimes. In particular, our method is most effective when $beta_r ll |S_r^K|$, which can offer more flexibility and practicability than existing quantum algorithms that achieve the best performance in the regime $beta_r approx |S_r^K|$.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"118 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.22331/q-2025-12-23-1954
Yudai Suzuki, Bi Hong Tiang, Jeongrak Son, Nelly H. Y. Ng, Zoe Holmes, Marek Gluza
Quantum Signal Processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic protocols for implementing QSP rely on post-selection. This can impose prohibitive costs for tasks when amplitude amplification cannot sufficiently improve the success probability. For example, in the context of ground-state preparation, this occurs when using a too poor initial state. In this work, we introduce a new formula for implementing QSP transformations of Hermitian matrices, which requires neither auxiliary qubits nor post-selection. Rather, using approximation to the exact unitary synthesis, we leverage the theory of the double-bracket quantum algorithms to provide a new quantum algorithm for QSP, termed Double-Bracket QSP (DB-QSP). The algorithm requires the energy and energetic variance of the state to be measured at each step and has a recursive structure, which leads to circuit depths that can grow super exponentially with the degree of the polynomial. With these strengths and caveats in mind, DB-QSP should be viewed as complementing the established QSP toolkit. In particular, DB-QSP can deterministically implement low-degree polynomials to ``warm start" QSP methods involving post-selection.
{"title":"Double-bracket algorithm for quantum signal processing without post-selection","authors":"Yudai Suzuki, Bi Hong Tiang, Jeongrak Son, Nelly H. Y. Ng, Zoe Holmes, Marek Gluza","doi":"10.22331/q-2025-12-23-1954","DOIUrl":"https://doi.org/10.22331/q-2025-12-23-1954","url":null,"abstract":"Quantum Signal Processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic protocols for implementing QSP rely on post-selection. This can impose prohibitive costs for tasks when amplitude amplification cannot sufficiently improve the success probability. For example, in the context of ground-state preparation, this occurs when using a too poor initial state. In this work, we introduce a new formula for implementing QSP transformations of Hermitian matrices, which requires neither auxiliary qubits nor post-selection. Rather, using approximation to the exact unitary synthesis, we leverage the theory of the double-bracket quantum algorithms to provide a new quantum algorithm for QSP, termed Double-Bracket QSP (DB-QSP). The algorithm requires the energy and energetic variance of the state to be measured at each step and has a recursive structure, which leads to circuit depths that can grow super exponentially with the degree of the polynomial. With these strengths and caveats in mind, DB-QSP should be viewed as complementing the established QSP toolkit. In particular, DB-QSP can deterministically implement low-degree polynomials to ``warm start\" QSP methods involving post-selection.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"1 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.22331/q-2025-12-22-1953
William A. Simon, Carter M. Gustin, Kamil Serafin, Alexis Ralli, Gary R. Goldstein, Peter J. Love
We describe and analyze LOBE (Ladder Operator Block-Encoding), a framework for block-encoding ladder operators that act upon fermionic and bosonic modes. In this framework, we achieve efficient block-encodings by applying the desired action of the operator onto the quantum state and pushing any undesired effects outside of the encoded subspace. This direct approach avoids any overhead caused by expanding the operators in another basis. We numerically benchmark these constructions using models arising in quantum field theories including the quartic harmonic oscillator, and $phi^4$ and Yukawa Hamiltonians on the light front. These benchmarks show that LOBE often produces block-encodings with fewer non-Clifford operations, fewer block-encoding ancillae and overall number of qubits, and lower rescaling factors for various operators as compared to frameworks that expand the ladder operators in the Pauli basis. LOBE constructions also demonstrate favorable scaling with respect to key parameters, including the maximum occupation of bosonic modes, the total number of fermionic and bosonic modes, and the locality of the operators. LOBE is implemented as an open-source python package to enable further applications.
{"title":"Ladder Operator Block-Encoding","authors":"William A. Simon, Carter M. Gustin, Kamil Serafin, Alexis Ralli, Gary R. Goldstein, Peter J. Love","doi":"10.22331/q-2025-12-22-1953","DOIUrl":"https://doi.org/10.22331/q-2025-12-22-1953","url":null,"abstract":"We describe and analyze LOBE (Ladder Operator Block-Encoding), a framework for block-encoding ladder operators that act upon fermionic and bosonic modes. In this framework, we achieve efficient block-encodings by applying the desired action of the operator onto the quantum state and pushing any undesired effects outside of the encoded subspace. This direct approach avoids any overhead caused by expanding the operators in another basis. We numerically benchmark these constructions using models arising in quantum field theories including the quartic harmonic oscillator, and $phi^4$ and Yukawa Hamiltonians on the light front. These benchmarks show that LOBE often produces block-encodings with fewer non-Clifford operations, fewer block-encoding ancillae and overall number of qubits, and lower rescaling factors for various operators as compared to frameworks that expand the ladder operators in the Pauli basis. LOBE constructions also demonstrate favorable scaling with respect to key parameters, including the maximum occupation of bosonic modes, the total number of fermionic and bosonic modes, and the locality of the operators. LOBE is implemented as an open-source python package to enable further applications.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"93 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145801392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.22331/q-2025-12-18-1951
Kristan Temme, Pawel Wocjan
We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a completely positive and trace preserving map. This quantum map has a unique fixed point, which corresponds to the quantum sample (qsample) of the classical Markov chain's stationary distribution. We show that the convergence time of the quantum map is directly related to the coupling time of the Markov chain coupling.
{"title":"Quantized Markov Chain Couplings that Prepare Qsamples","authors":"Kristan Temme, Pawel Wocjan","doi":"10.22331/q-2025-12-18-1951","DOIUrl":"https://doi.org/10.22331/q-2025-12-18-1951","url":null,"abstract":"We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a completely positive and trace preserving map. This quantum map has a unique fixed point, which corresponds to the quantum sample (qsample) of the classical Markov chain's stationary distribution. We show that the convergence time of the quantum map is directly related to the coupling time of the Markov chain coupling.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"7 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145771740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.22331/q-2025-12-18-1952
Christina Giarmatzi, Tyler Jones, Alexei Gilchrist, Prasanna Pakkiam, Arkady Fedorov, Fabio Costa
Current quantum technologies are at the cusp of becoming useful, but still face formidable obstacles such as noise. Noise severely limits the ability to scale quantum devices to the point that they would offer an advantage over classical devices. To understand the sources of noise it is necessary to fully characterise the quantum processes occurring across many time steps; only this would reveal any time-correlated noise called non-Markovian. Previous efforts have attempted such a characterisation but obtained only a limited reconstruction of such multi-time processes. In this work, we fully characterise a multi-time quantum process on superconducting hardware using in-house and cloud-based quantum processors. We achieve this by employing sequential measure-and-prepare operations combined with post-processing. Employing a recently developed formalism for multi-time processes, we detect general multi-time correlated noise. We also detect quantum correlated noise which demonstrates that part of the noise originates from quantum sources, such as physically nearby qubits on the chip.
{"title":"Multi-time quantum process tomography on a superconducting qubit","authors":"Christina Giarmatzi, Tyler Jones, Alexei Gilchrist, Prasanna Pakkiam, Arkady Fedorov, Fabio Costa","doi":"10.22331/q-2025-12-18-1952","DOIUrl":"https://doi.org/10.22331/q-2025-12-18-1952","url":null,"abstract":"Current quantum technologies are at the cusp of becoming useful, but still face formidable obstacles such as noise. Noise severely limits the ability to scale quantum devices to the point that they would offer an advantage over classical devices. To understand the sources of noise it is necessary to fully characterise the quantum processes occurring across many time steps; only this would reveal any time-correlated noise called non-Markovian. Previous efforts have attempted such a characterisation but obtained only a limited reconstruction of such multi-time processes. In this work, we fully characterise a multi-time quantum process on superconducting hardware using in-house and cloud-based quantum processors. We achieve this by employing sequential measure-and-prepare operations combined with post-processing. Employing a recently developed formalism for multi-time processes, we detect general multi-time correlated noise. We also detect quantum correlated noise which demonstrates that part of the noise originates from quantum sources, such as physically nearby qubits on the chip.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"9 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145786026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-16DOI: 10.22331/q-2025-12-16-1950
Diego Forlivesi, Lorenzo Valentini, Marco Chiani
We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the undetectable errors based on the quantum MacWilliams identities. The WE is then used to evaluate tight upper bounds on the error rate of CSS quantum codes with minimum weight decoding. For surface codes we also derive a simple closed form expression of the bounds over the depolarizing channel. We introduce a novel approach that combines the knowledge of WE with a logical operator analysis, allowing the derivation of the exact asymptotic error rate for short codes. For example, on a depolarizing channel with physical error rate $rho to 0$, the logical error rate $rho_mathrm{L}$ is asymptotically $rho_mathrm{L} approx 16 rho^2$ for the $[[9,1,3]]$ Shor code, $rho_mathrm{L} approx 16.3 rho^2$ for the $[[7,1,3]]$ Steane code, $rho_mathrm{L} approx 18.7 rho^2$ for the $[[13,1,3]]$ surface code, and $rho_mathrm{L} approx 149.3 rho^3$ for the $[[41,1,5]]$ surface code. For larger codes our bound provides $rho_mathrm{L} approx 1215 rho^4$ and $rho_mathrm{L} approx 663 rho^5$ for the $[[85,1,7]]$ and the $[[181,1,10]]$ surface codes, respectively. Finally, we extend our analysis to include realistic, noisy syndrome extraction circuits by modeling error propagation throughout gadgets. This enables estimation of logical error rates under faulty measurements. The performance analysis serves as a design tool for developing fault-tolerant quantum systems by guiding the selection of quantum codes based on their error correction capability. Additionally, it offers a novel perspective on quantum degeneracy, showing it represents the fraction of non-correctable error patterns shared by multiple logical operators.
{"title":"Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities","authors":"Diego Forlivesi, Lorenzo Valentini, Marco Chiani","doi":"10.22331/q-2025-12-16-1950","DOIUrl":"https://doi.org/10.22331/q-2025-12-16-1950","url":null,"abstract":"We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the undetectable errors based on the quantum MacWilliams identities. The WE is then used to evaluate tight upper bounds on the error rate of CSS quantum codes with minimum weight decoding. For surface codes we also derive a simple closed form expression of the bounds over the depolarizing channel. We introduce a novel approach that combines the knowledge of WE with a logical operator analysis, allowing the derivation of the exact asymptotic error rate for short codes. For example, on a depolarizing channel with physical error rate $rho to 0$, the logical error rate $rho_mathrm{L}$ is asymptotically $rho_mathrm{L} approx 16 rho^2$ for the $[[9,1,3]]$ Shor code, $rho_mathrm{L} approx 16.3 rho^2$ for the $[[7,1,3]]$ Steane code, $rho_mathrm{L} approx 18.7 rho^2$ for the $[[13,1,3]]$ surface code, and $rho_mathrm{L} approx 149.3 rho^3$ for the $[[41,1,5]]$ surface code. For larger codes our bound provides $rho_mathrm{L} approx 1215 rho^4$ and $rho_mathrm{L} approx 663 rho^5$ for the $[[85,1,7]]$ and the $[[181,1,10]]$ surface codes, respectively. Finally, we extend our analysis to include realistic, noisy syndrome extraction circuits by modeling error propagation throughout gadgets. This enables estimation of logical error rates under faulty measurements. The performance analysis serves as a design tool for developing fault-tolerant quantum systems by guiding the selection of quantum codes based on their error correction capability. Additionally, it offers a novel perspective on quantum degeneracy, showing it represents the fraction of non-correctable error patterns shared by multiple logical operators.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"43 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-15DOI: 10.22331/q-2025-12-15-1945
Christopher Popp, Tobias C. Sutter, Beatrix C. Hiesmayr
Entanglement distillation, the process of converting weakly entangled states into maximally entangled ones using Local Operations and Classical Communication (LOCC), is pivotal for robust entanglement-assisted quantum information processing in error-prone environments. A construction based on stabilizer codes offers an effective method for designing such protocols. By analytically investigating the effective action of stabilizer protocols for systems of prime dimension $d$, we establish a standard form for the output states of recurrent stabilizer-based distillation. This links the properties of input states, stabilizers, and encodings to the properties of the protocol. Based on those insights, we present a novel two-copy distillation protocol, applicable to all bipartite states in prime dimension, that maximizes the fidelity increase per iteration for Bell-diagonal states. The power of this framework and the protocol is demonstrated through numerical investigations, which provide evidence for superior performance in terms of efficiency and distillability of low-fidelity states compared to other well-established recurrence protocols. By elucidating the interplay between states, errors, and protocols, our contribution advances the systematic development of highly effective distillation protocols, enhancing our understanding of distillability.
{"title":"A Novel Stabilizer-based Entanglement Distillation Protocol for Qudits","authors":"Christopher Popp, Tobias C. Sutter, Beatrix C. Hiesmayr","doi":"10.22331/q-2025-12-15-1945","DOIUrl":"https://doi.org/10.22331/q-2025-12-15-1945","url":null,"abstract":"Entanglement distillation, the process of converting weakly entangled states into maximally entangled ones using Local Operations and Classical Communication (LOCC), is pivotal for robust entanglement-assisted quantum information processing in error-prone environments. A construction based on stabilizer codes offers an effective method for designing such protocols. By analytically investigating the effective action of stabilizer protocols for systems of prime dimension $d$, we establish a standard form for the output states of recurrent stabilizer-based distillation. This links the properties of input states, stabilizers, and encodings to the properties of the protocol. Based on those insights, we present a novel two-copy distillation protocol, applicable to all bipartite states in prime dimension, that maximizes the fidelity increase per iteration for Bell-diagonal states. The power of this framework and the protocol is demonstrated through numerical investigations, which provide evidence for superior performance in terms of efficiency and distillability of low-fidelity states compared to other well-established recurrence protocols. By elucidating the interplay between states, errors, and protocols, our contribution advances the systematic development of highly effective distillation protocols, enhancing our understanding of distillability.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"66 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-15DOI: 10.22331/q-2025-12-15-1948
Xiangyi Meng, Nicolò Lo Piparo, Kae Nemoto, István A. Kovács
Building large-scale quantum communication networks has its unique challenges. Here, we demonstrate that a network-wide synergistic usage of quantum memories distributed in a quantum communication network offers a fundamental advantage. We first map the problem of quantum communication with local usage of memories into a classical continuum percolation model. Then, we show that this mapping can be improved through a cooperation of quantum distillation and relay protocols via remote access to distributed memories. This improved mapping, which we term $alpha$-percolation, can be formulated in terms of graph-merging rules, analogous to the decimation rules of the renormalization group treatment of disordered quantum magnets. These rules can be performed in any order, yielding the same optimal result that is characterized by the emergence of a “positive feedback'' mechanism and the formation of spatially disconnected “hopping'' communication components – both marking significant improvements beyond the traditional point-to-point consideration of quantum communication in networked structures.
{"title":"Quantum Communication Networks Enhanced by Distributed Quantum Memories","authors":"Xiangyi Meng, Nicolò Lo Piparo, Kae Nemoto, István A. Kovács","doi":"10.22331/q-2025-12-15-1948","DOIUrl":"https://doi.org/10.22331/q-2025-12-15-1948","url":null,"abstract":"Building large-scale quantum communication networks has its unique challenges. Here, we demonstrate that a network-wide synergistic usage of quantum memories distributed in a quantum communication network offers a fundamental advantage. We first map the problem of quantum communication with local usage of memories into a classical continuum percolation model. Then, we show that this mapping can be improved through a cooperation of quantum distillation and relay protocols via remote access to distributed memories. This improved mapping, which we term $alpha$-percolation, can be formulated in terms of graph-merging rules, analogous to the decimation rules of the renormalization group treatment of disordered quantum magnets. These rules can be performed in any order, yielding the same optimal result that is characterized by the emergence of a “positive feedback'' mechanism and the formation of spatially disconnected “hopping'' communication components – both marking significant improvements beyond the traditional point-to-point consideration of quantum communication in networked structures.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"162 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-15DOI: 10.22331/q-2025-12-15-1944
Shishir Khandelwal, Gianmichele Blasi
Recent years have seen a surge of interest in exceptional points in open quantum systems. The natural approach in this area has been the use of Markovian master equations. While the resulting Liouvillian EPs have been seen in a variety of systems and have been associated to numerous exotic effects, it is an open question whether such degeneracies and their peculiarities can persist beyond the validity of master equations. In this work, taking the example of a dissipative double-quantum-dot system, we show that exact Heisenberg equations governing system and bath dynamics exhibit the same EPs as the corresponding master equations. To highlight the importance of this finding, we prove that the paradigmatic property associated to EPs – critical damping, persists well beyond the validity of master equations. Our results demonstrate that Liouvillian EPs can arise from underlying fundamental exact principles, rather than merely as a consequence of approximations involved in deriving master equations.
{"title":"Emergent Liouvillian exceptional points from exact principles","authors":"Shishir Khandelwal, Gianmichele Blasi","doi":"10.22331/q-2025-12-15-1944","DOIUrl":"https://doi.org/10.22331/q-2025-12-15-1944","url":null,"abstract":"Recent years have seen a surge of interest in exceptional points in open quantum systems. The natural approach in this area has been the use of Markovian master equations. While the resulting Liouvillian EPs have been seen in a variety of systems and have been associated to numerous exotic effects, it is an open question whether such degeneracies and their peculiarities can persist beyond the validity of master equations. In this work, taking the example of a dissipative double-quantum-dot system, we show that exact Heisenberg equations governing system and bath dynamics exhibit the same EPs as the corresponding master equations. To highlight the importance of this finding, we prove that the paradigmatic property associated to EPs – critical damping, persists well beyond the validity of master equations. Our results demonstrate that Liouvillian EPs can arise from underlying fundamental exact principles, rather than merely as a consequence of approximations involved in deriving master equations.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"12 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145753238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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