Pub Date : 2024-12-18DOI: 10.22331/q-2024-12-18-1571
Qiushi Liu, Yuxiang Yang
Optimized quantum control can enhance the performance and noise resilience of quantum metrology. However, the optimization quickly becomes intractable when multiple control operations are applied sequentially. In this work, we propose efficient tensor network algorithms for optimizing strategies of quantum metrology enhanced by a long sequence of control operations. Our approach covers a general and practical scenario where the experimenter applies $N-1$ interleaved control operations between $N$ queries of the channel to estimate and uses no or bounded ancilla. Tailored to different experimental capabilities, these control operations can be generic quantum channels or variational unitary gates. Numerical experiments show that our algorithm has a good performance in optimizing the metrological strategy for as many as $N=100$ queries. In particular, our algorithm identifies a strategy that can outperform the state-of-the-art strategy when $N$ is finite but large.
{"title":"Efficient tensor networks for control-enhanced quantum metrology","authors":"Qiushi Liu, Yuxiang Yang","doi":"10.22331/q-2024-12-18-1571","DOIUrl":"https://doi.org/10.22331/q-2024-12-18-1571","url":null,"abstract":"Optimized quantum control can enhance the performance and noise resilience of quantum metrology. However, the optimization quickly becomes intractable when multiple control operations are applied sequentially. In this work, we propose efficient tensor network algorithms for optimizing strategies of quantum metrology enhanced by a long sequence of control operations. Our approach covers a general and practical scenario where the experimenter applies $N-1$ interleaved control operations between $N$ queries of the channel to estimate and uses no or bounded ancilla. Tailored to different experimental capabilities, these control operations can be generic quantum channels or variational unitary gates. Numerical experiments show that our algorithm has a good performance in optimizing the metrological strategy for as many as $N=100$ queries. In particular, our algorithm identifies a strategy that can outperform the state-of-the-art strategy when $N$ is finite but large.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"23 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142840849","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 : 2024-12-18DOI: 10.22331/q-2024-12-18-1572
Seungbeom Chin, Marcin Karczewski, Yong-Su Kim
Non-destructive heralded entanglement with photons is a valuable resource for quantum information processing. However, they generally entail ancillary particles and modes that amplify the circuit intricacy. To address this challenge, a recent work [16] introduced a graph approach for creating multipartite entanglements with boson subtractions. Nonetheless, it remains an essential intermediate step toward practical heralded schemes: the proposition of heralded subtraction operators in bosonic linear quantum networks. This research establishes comprehensive translation rules from subtraction operators to linear optical operators, which provides a seamless path to design heralded schemes with single photons. Our method begets enhanced or previously unreported schemes for the $N$-partite GHZ state with $2N$ photons, $N$-partite W state with $2N+1$ photons and superposition of $N=3$ GHZ and W states with 9 photons. Our streamlined approach can straightforwardly design heralded schemes for multipartite entangled states by assembling the operators according to the guidence of sculpting bigraphs, hence significantly simplifies the quantum circuit design process.
与光子的非破坏性预示纠缠是量子信息处理的宝贵资源。然而，它们通常需要辅助粒子和模式，从而放大了电路的复杂性。为了应对这一挑战，最近的一项研究[16]引入了一种用玻色子减法创建多方纠缠的图方法。尽管如此，它仍然是迈向实用预示方案的重要中间步骤：玻色子线性量子网络中预示减法算子的命题。这项研究建立了从减法算子到线性光学算子的全面转换规则，为设计单光子预示方案提供了一条无缝路径。我们的方法为具有 2N$ 光子的 N$ 部分 GHZ 状态、具有 2N+1$ 光子的 N$ 部分 W 状态以及具有 9 个光子的 N=3$ GHZ 和 W 状态的叠加产生了增强的或以前未报道过的方案。我们的简化方法可以根据雕刻大图的指导组装算子，直接设计多方纠缠态的预示方案，从而大大简化了量子电路的设计过程。
{"title":"Heralded Optical Entanglement Generation via the Graph Picture of Linear Quantum Networks","authors":"Seungbeom Chin, Marcin Karczewski, Yong-Su Kim","doi":"10.22331/q-2024-12-18-1572","DOIUrl":"https://doi.org/10.22331/q-2024-12-18-1572","url":null,"abstract":"Non-destructive heralded entanglement with photons is a valuable resource for quantum information processing. However, they generally entail ancillary particles and modes that amplify the circuit intricacy. To address this challenge, a recent work [16] introduced a graph approach for creating multipartite entanglements with boson subtractions. Nonetheless, it remains an essential intermediate step toward practical heralded schemes: the proposition of heralded subtraction operators in bosonic linear quantum networks. This research establishes comprehensive translation rules from subtraction operators to linear optical operators, which provides a seamless path to design heralded schemes with single photons. Our method begets enhanced or previously unreported schemes for the $N$-partite GHZ state with $2N$ photons, $N$-partite W state with $2N+1$ photons and superposition of $N=3$ GHZ and W states with 9 photons. Our streamlined approach can straightforwardly design heralded schemes for multipartite entangled states by assembling the operators according to the guidence of sculpting bigraphs, hence significantly simplifies the quantum circuit design process.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"13 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841418","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 : 2024-12-17DOI: 10.22331/q-2024-12-17-1568
Frédéric Dupuis, Philippe Lamontagne, Louis Salvail
We explore the cryptographic power of arbitrary shared physical resources. The most general such resource is access to a fresh entangled quantum state at the outset of each protocol execution. We call this the $textit{Common Reference Quantum State (CRQS)}$ model, in analogy to the well-known $textit{Common Reference String (CRS)}$. The CRQS model is a natural generalization of the CRS model but appears to be more powerful: in the two-party setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once by measuring a maximally entangled state in one of many mutually unbiased bases. We formalize this notion as a $textit{Weak One-Time Random Oracle (WOTRO)}$, where we only ask of the $m$-bit output to have some randomness when conditioned on the $n$-bit input. We show that when $n-minomega(lg n)$, any protocol for WOTRO in the CRQS model can be attacked by an (inefficient) adversary. Moreover, our adversary is efficiently simulatable, which rules out the possibility of proving the computational security of a scheme by a fully black-box reduction to a cryptographic game assumption. On the other hand, we introduce a non-game quantum assumption for hash functions that implies WOTRO in the CRQS model (where the CRQS consists only of EPR pairs). We first build a statistically secure WOTRO protocol where $m=n$, then hash the output. The impossibility of WOTRO has the following consequences. First, we show the fully-black-box impossibility of a $quantum$ Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC 2013) to the CRQS model. Second, we show a fully-black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt 2019) where quantum bolts have an additional parameter that cannot be changed without generating new bolts. Our results also apply to $2$-message protocols in the plain model.
我们探索了任意共享物理资源的加密能力。最常用的资源是在每个协议执行开始时访问一个新的纠缠量子态。我们称之为$textit{Common Reference Quantum State (CRQS)}$模型，类似于众所周知的$textit{Common Reference String (CRS)}$模型。CRQS模型是CRS模型的自然泛化，但似乎更强大：在双方设置中，CRQS有时可以通过测量许多相互无偏的基中的一个的最大纠缠状态来显示与一次查询的随机Oracle相关的属性。我们将这个概念形式化为$textit{Weak One-Time Random Oracle (WOTRO)}$，其中我们只要求$m$位输出在$n$位输入的条件下具有一些随机性。我们表明，当$n-minomega(lg n)$时，CRQS模型中用于WOTRO的任何协议都可能被（低效的）对手攻击。此外，我们的对手是可有效模拟的，这排除了通过对加密游戏假设的完全黑盒还原来证明方案的计算安全性的可能性。另一方面，我们为哈希函数引入了一个非博弈量子假设，这意味着CRQS模型中的WOTRO（其中CRQS仅由EPR对组成）。我们首先构建一个统计安全的WOTRO协议，其中$m=n$，然后对输出进行散列。WOTRO的不可能性有以下后果。首先，我们展示了$quantum$菲亚特-沙米尔变换的全黑盒不可能性，将Bitansky等人（TCC 2013）的不可能性结果推广到CRQS模型。其次，我们展示了一个强化版量子闪电的完全黑盒不可能结果（Zhandry, Eurocrypt 2019），其中量子闪电有一个额外的参数，在不产生新闪电的情况下无法改变。我们的结果也适用于普通模型中的$2$ -消息协议。
{"title":"Fiat-Shamir for Proofs Lacks a Proof Even in the Presence of Shared Entanglement","authors":"Frédéric Dupuis, Philippe Lamontagne, Louis Salvail","doi":"10.22331/q-2024-12-17-1568","DOIUrl":"https://doi.org/10.22331/q-2024-12-17-1568","url":null,"abstract":"We explore the cryptographic power of arbitrary shared physical resources. The most general such resource is access to a fresh entangled quantum state at the outset of each protocol execution. We call this the $textit{Common Reference Quantum State (CRQS)}$ model, in analogy to the well-known $textit{Common Reference String (CRS)}$. The CRQS model is a natural generalization of the CRS model but appears to be more powerful: in the two-party setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once by measuring a maximally entangled state in one of many mutually unbiased bases. We formalize this notion as a $textit{Weak One-Time Random Oracle (WOTRO)}$, where we only ask of the $m$-bit output to have some randomness when conditioned on the $n$-bit input.<br/> We show that when $n-minomega(lg n)$, any protocol for WOTRO in the CRQS model can be attacked by an (inefficient) adversary. Moreover, our adversary is efficiently simulatable, which rules out the possibility of proving the computational security of a scheme by a fully black-box reduction to a cryptographic game assumption. On the other hand, we introduce a non-game quantum assumption for hash functions that implies WOTRO in the CRQS model (where the CRQS consists only of EPR pairs). We first build a statistically secure WOTRO protocol where $m=n$, then hash the output.<br/> The impossibility of WOTRO has the following consequences. First, we show the fully-black-box impossibility of a $quantum$ Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC 2013) to the CRQS model. Second, we show a fully-black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt 2019) where quantum bolts have an additional parameter that cannot be changed without generating new bolts. Our results also apply to $2$-message protocols in the plain model.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"9 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142831986","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 : 2024-12-17DOI: 10.22331/q-2024-12-17-1567
Pablo Antonio Moreno Casares, Modjtaba Shokrian Zini, Juan Miguel Arrazola
Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.
{"title":"Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators","authors":"Pablo Antonio Moreno Casares, Modjtaba Shokrian Zini, Juan Miguel Arrazola","doi":"10.22331/q-2024-12-17-1567","DOIUrl":"https://doi.org/10.22331/q-2024-12-17-1567","url":null,"abstract":"Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"11 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142832036","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 : 2024-12-17DOI: 10.22331/q-2024-12-17-1570
Laura J. Henderson, Rishi Goel, Sally Shrapnel
The popular qubit framework has dominated recent work on quantum kernel machine learning, with results characterising expressivity, learnability and generalisation. As yet, there is no comparative framework to understand these concepts for continuous variable (CV) quantum computing platforms. In this paper we represent CV quantum kernels as closed form functions and use this representation to provide several important theoretical insights. We derive a general closed form solution for all CV quantum kernels and show every such kernel can be expressed as the product of a Gaussian and an algebraic function of the parameters of the feature map. Furthermore, in the multi-mode case, we present quantification of a quantum-classical separation for all quantum kernels via a hierarchical notion of the “stellar rank" of the quantum kernel feature map. We then prove kernels defined by feature maps of infinite stellar rank, such as GKP-state encodings, can be approximated arbitrarily well by kernels defined by feature maps of finite stellar rank. Finally, we simulate learning with a single-mode displaced Fock state encoding and show that (i) accuracy on our specific task (an annular data set) increases with stellar rank, (ii) for underfit models, accuracy can be improved by increasing a bandwidth hyperparameter, and (iii) for noisy data that is overfit, decreasing the bandwidth will improve generalisation but does so at the cost of effective stellar rank.
{"title":"Quantum Kernel Machine Learning With Continuous Variables","authors":"Laura J. Henderson, Rishi Goel, Sally Shrapnel","doi":"10.22331/q-2024-12-17-1570","DOIUrl":"https://doi.org/10.22331/q-2024-12-17-1570","url":null,"abstract":"The popular qubit framework has dominated recent work on quantum kernel machine learning, with results characterising expressivity, learnability and generalisation. As yet, there is no comparative framework to understand these concepts for continuous variable (CV) quantum computing platforms. In this paper we represent CV quantum kernels as closed form functions and use this representation to provide several important theoretical insights. We derive a general closed form solution for all CV quantum kernels and show every such kernel can be expressed as the product of a Gaussian and an algebraic function of the parameters of the feature map. Furthermore, in the multi-mode case, we present quantification of a quantum-classical separation for all quantum kernels via a hierarchical notion of the “stellar rank\" of the quantum kernel feature map. We then prove kernels defined by feature maps of infinite stellar rank, such as GKP-state encodings, can be approximated arbitrarily well by kernels defined by feature maps of finite stellar rank. Finally, we simulate learning with a single-mode displaced Fock state encoding and show that (i) accuracy on our specific task (an annular data set) increases with stellar rank, (ii) for underfit models, accuracy can be improved by increasing a bandwidth hyperparameter, and (iii) for noisy data that is overfit, decreasing the bandwidth will improve generalisation but does so at the cost of effective stellar rank.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"3 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142831988","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 : 2024-12-17DOI: 10.22331/q-2024-12-17-1569
Wayne Lin, Georgios Piliouras, Ryann Sim, Antonios Varvitsiotis
As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as solution concepts of strategic quantum interactions, but these approaches did not directly connect to decentralized adaptive setups where agents possess limited information. This paper delves into the dynamics of quantum-enabled agents within decentralized systems that employ no-regret algorithms to update their behaviors over time. Specifically, we investigate two-player quantum zero-sum games and polymatrix quantum zero-sum games, showing that no-regret algorithms converge to separable quantum Nash equilibria in time-average. In the case of general multi-player quantum games, our work leads to a novel solution concept, that of the separable quantum coarse correlated equilibria (QCCE), as the convergent outcome of the time-averaged behavior no-regret algorithms, offering a natural solution concept for decentralized quantum systems. Finally, we show that computing QCCEs can be formulated as a semidefinite program and establish the existence of entangled (i.e., non-separable) QCCEs, which are unlearnable via the current paradigm of no-regret learning.
{"title":"No-Regret Learning and Equilibrium Computation in Quantum Games","authors":"Wayne Lin, Georgios Piliouras, Ryann Sim, Antonios Varvitsiotis","doi":"10.22331/q-2024-12-17-1569","DOIUrl":"https://doi.org/10.22331/q-2024-12-17-1569","url":null,"abstract":"As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as solution concepts of strategic quantum interactions, but these approaches did not directly connect to decentralized adaptive setups where agents possess limited information. This paper delves into the dynamics of quantum-enabled agents within decentralized systems that employ no-regret algorithms to update their behaviors over time. Specifically, we investigate two-player quantum zero-sum games and polymatrix quantum zero-sum games, showing that no-regret algorithms converge to separable quantum Nash equilibria in time-average. In the case of general multi-player quantum games, our work leads to a novel solution concept, that of the separable quantum coarse correlated equilibria (QCCE), as the convergent outcome of the time-averaged behavior no-regret algorithms, offering a natural solution concept for decentralized quantum systems. Finally, we show that computing QCCEs can be formulated as a semidefinite program and establish the existence of entangled (i.e., non-separable) QCCEs, which are unlearnable via the current paradigm of no-regret learning.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"47 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142831990","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 : 2024-12-17DOI: 10.22331/q-2024-12-17-1566
Michal Kolář, Radim Filip
Bosonic systems with negative Wigner function superposition states are fundamentally witnessing nonlinear quantum dynamics beyond linearized systems and, recently, have become essential resources of quantum technology with many applications. Typically, they appear due to sophisticated combination of external drives, nonlinear control, measurements or strong nonlinear dissipation of subsystems to an environment. Here, we propose a conceptually different and more autonomous way to obtain such states, avoiding these ingredients, using purely sudden interaction decay in the paradigmatic interacting qubit-oscillator system weakly coupled to bath at thermal equilibrium in a low-temperature limit. We demonstrate simultaneously detectable unconditional negative Wigner function and quantum coherence and their qualitative enhancement employing more qubits.
{"title":"Negative Wigner function by decaying interaction from equilibrium","authors":"Michal Kolář, Radim Filip","doi":"10.22331/q-2024-12-17-1566","DOIUrl":"https://doi.org/10.22331/q-2024-12-17-1566","url":null,"abstract":"Bosonic systems with negative Wigner function superposition states are fundamentally witnessing nonlinear quantum dynamics beyond linearized systems and, recently, have become essential resources of quantum technology with many applications. Typically, they appear due to sophisticated combination of external drives, nonlinear control, measurements or strong nonlinear dissipation of subsystems to an environment. Here, we propose a conceptually different and more autonomous way to obtain such states, avoiding these ingredients, using purely sudden interaction decay in the paradigmatic interacting qubit-oscillator system weakly coupled to bath at thermal equilibrium in a low-temperature limit. We demonstrate simultaneously detectable unconditional negative Wigner function and quantum coherence and their qualitative enhancement employing more qubits.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"11 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142831985","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 : 2024-12-16DOI: 10.22331/q-2024-12-16-1565
Isaac Layton, Jonathan Oppenheim, Zachary Weller-Davies
We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider an unravelling approach, describing the system in terms of a classical-quantum trajectory. We derive the general form of the dynamics under the assumptions that the classical trajectories are continuous and the evolution is autonomous, and the requirement that the dynamics is linear and completely positive in the combined classical-quantum state. This requirement is necessary in order to consistently describe probabilities, and forces the dynamics to be stochastic when the back-reaction is non-zero. The resulting equations of motion are natural generalisations of the standard semi-classical equations of motion, but since the resulting dynamics is linear in the combined classical-quantum state, it does not lead to the pathologies which usually follow from evolution laws based on expectation values. In particular, the evolution laws we present account for correlations between the classical and quantum system, which resolves issues associated with other semi-classical approaches. In addition, despite a breakdown of predictability in the classical degrees of freedom, the quantum state evolves deterministically conditioned on the classical trajectory, provided a trade-off between decoherence and diffusion is saturated. As a result, the quantum state remains pure when conditioned on the classical trajectory. To illustrate these points, we numerically simulate a number of semi-classical toy models, including one of vacuum fluctuations as a source driving the expansion of the universe. Finally, we discuss the application of these results to semi-classical gravity, and the black-hole information problem.
{"title":"A healthier semi-classical dynamics","authors":"Isaac Layton, Jonathan Oppenheim, Zachary Weller-Davies","doi":"10.22331/q-2024-12-16-1565","DOIUrl":"https://doi.org/10.22331/q-2024-12-16-1565","url":null,"abstract":"We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider an unravelling approach, describing the system in terms of a classical-quantum trajectory. We derive the general form of the dynamics under the assumptions that the classical trajectories are continuous and the evolution is autonomous, and the requirement that the dynamics is linear and completely positive in the combined classical-quantum state. This requirement is necessary in order to consistently describe probabilities, and forces the dynamics to be stochastic when the back-reaction is non-zero. The resulting equations of motion are natural generalisations of the standard semi-classical equations of motion, but since the resulting dynamics is linear in the combined classical-quantum state, it does not lead to the pathologies which usually follow from evolution laws based on expectation values. In particular, the evolution laws we present account for correlations between the classical and quantum system, which resolves issues associated with other semi-classical approaches. In addition, despite a breakdown of predictability in the classical degrees of freedom, the quantum state evolves deterministically conditioned on the classical trajectory, provided a trade-off between decoherence and diffusion is saturated. As a result, the quantum state remains pure when conditioned on the classical trajectory. To illustrate these points, we numerically simulate a number of semi-classical toy models, including one of vacuum fluctuations as a source driving the expansion of the universe. Finally, we discuss the application of these results to semi-classical gravity, and the black-hole information problem.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"38 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142831984","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 : 2024-12-12DOI: 10.22331/q-2024-12-12-1563
Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian simulation, which is directly applicable only to Schrödinger-type equations. To address this limitation, Schrödingerisation techniques have been developed, employing the warped transformation to convert general linear PDEs into Schrödinger-type equations. However, despite the development of Schrödingerisation techniques, the explicit implementation of the corresponding quantum circuit for solving general PDEs remains to be designed. In this paper, we present detailed implementation of a quantum algorithm for general PDEs using Schrödingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme, to demonstrate the effectiveness of our approach. Complexity analysis is also carried out to demonstrate the quantum advantages of these algorithms in high dimensions over their classical counterparts.
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Pub Date : 2024-12-12DOI: 10.22331/q-2024-12-12-1564
Jinzhao Wang, Shunyu Yao
Quantum energy teleportation (QET) is the phenomenon in which locally inaccessible energy is activated as extractable work through collaborative local operations and classical communication (LOCC) with an entangled partner. It closely resembles the more well-known quantum information teleportation (QIT) where quantum information can be sent through an entangled pair with LOCC. It is tempting to ask how QET is related to QIT. Here we report a first study of this connection. Despite the apparent similarity, we show that these two phenomena are not only distinct but moreover are mutually competitive. We show a perturbative trade-off relation between their performance in a thermal entangled chaotic many-body system, in which both QET and QIT are simultaneously implemented through a traversable wormhole in an emergent spacetime. Motivated by this example, we study a generic setup of two entangled qudits and prove a universal non-perturbative trade-off bound. It shows that for any teleportation protocol, the overall performance of QET and QIT together is constrained by the entanglement resource. We discuss some explanations of our results.
{"title":"Quantum Energy Teleportation versus Information Teleportation","authors":"Jinzhao Wang, Shunyu Yao","doi":"10.22331/q-2024-12-12-1564","DOIUrl":"https://doi.org/10.22331/q-2024-12-12-1564","url":null,"abstract":"Quantum energy teleportation (QET) is the phenomenon in which locally inaccessible energy is activated as extractable work through collaborative local operations and classical communication (LOCC) with an entangled partner. It closely resembles the more well-known quantum information teleportation (QIT) where quantum information can be sent through an entangled pair with LOCC. It is tempting to ask how QET is related to QIT. Here we report a first study of this connection. Despite the apparent similarity, we show that these two phenomena are not only distinct but moreover are mutually competitive. We show a perturbative trade-off relation between their performance in a thermal entangled chaotic many-body system, in which both QET and QIT are simultaneously implemented through a traversable wormhole in an emergent spacetime. Motivated by this example, we study a generic setup of two entangled qudits and prove a universal non-perturbative trade-off bound. It shows that for any teleportation protocol, the overall performance of QET and QIT together is constrained by the entanglement resource. We discuss some explanations of our results.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"113 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142809197","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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