publications
publications & preprints in reverse chronological order.
2024
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Efficiently Cooling Quantum Systems with Finite Resources: Insights from Thermodynamic GeometryPhilip Taranto, Patryk Lipka-Bartosik, Nayeli A. Rodríguez-Briones, Martí Perarnau-Llobet, Nicolai Friis, Marcus Huber, and Pharnam Bakhshinezhad2024Landauer’s universal limit on heat dissipation during information erasure becomes increasingly crucial as computing devices shrink: minimising heat-induced errors demands optimal pure-state preparation. For this, however, Nernst’s third law posits an infinite-resource requirement: either energy, time, or control complexity must diverge. Here, we address the practical challenge of efficiently cooling quantum systems using finite resources. We investigate the ensuing resource trade-offs and present efficient protocols for finite distinct energy gaps in settings pertaining to coherent or incoherent control, corresponding to quantum batteries and heat engines, respectively. Expressing energy bounds through thermodynamic length, our findings illuminate the optimal distribution of energy gaps, detailing the resource limitations of preparing pure states in practical settings.
@misc{arXiv:2404.06649, title = {{Efficiently Cooling Quantum Systems with Finite Resources: Insights from Thermodynamic Geometry}}, author = {Taranto, Philip and Lipka-Bartosik, Patryk and Rodr{\' i}guez-Briones, Nayeli A. and Perarnau-Llobet, Mart{\' i} and Friis, Nicolai and Huber, Marcus and Bakhshinezhad, Pharnam}, year = {2024}, archiveprefix = {arXiv}, eprint = {2404.06649}, } - Robust Error Accumulation SuppressionTatsuki Odake, Philip Taranto, Nobuyuki Yoshioka, Toshinari Itoko, Kunal Sharma, Antonio Mezzacapo, and Mio Murao2024
We present an advanced quantum error suppression technique, which we dub robust error accumulation suppression (REAS). Our method reduces the accumulation of errors in any circuit composed of single- or two-qubit gates expressed as e^I σθ for Pauli operators σ and θ∈[0,\pi); since such gates form a universal gate set, our results apply to a strictly larger class of circuits than those comprising only Clifford gates, thereby generalizing previous results. In the case of coherent errors – which include crosstalk – we demonstrate a reduction of the error scaling in an L-depth circuit from O(L) to O(\sqrtL). Crucially, REAS makes no assumption on the cleanness of the error-suppressing protocol itself and is, therefore, truly robust, applying to situations in which the newly inserted gates have non-negligible coherent noise. Furthermore, we show that REAS can also suppress certain types of decoherence noise by transforming some gates to be robust against such noise, which is verified by the demonstration of the quadratic suppression of error scaling in the numerical simulation. Our results, therefore, present an advanced, robust method of error suppression that can be used in conjunction with error correction as a viable path toward fault-tolerant quantum computation.
@misc{arXiv:2401.16884, title = {{Robust Error Accumulation Suppression}}, author = {Odake, Tatsuki and and Taranto, Philip and Yoshioka, Nobuyuki and Itoko, Toshinari and Sharma, Kunal and Mezzacapo, Antonio and Murao, Mio}, year = {2024}, archiveprefix = {arXiv}, eprint = {2401.16884}, } -
Characterising the Hierarchy of Multi-time Quantum Processes with Classical MemoryPhilip Taranto, Marco Túlio Quintino, Mio Murao, and Simon MilzQuantum, 2024Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise from/are transmitted via interactions between a system and its environment; as such, they can be either classical or quantum. From a practical standpoint, quantum processes with classical memory promise near-term applicability: they are more powerful than their memoryless counterpart, yet at the same time can be controlled over significant timeframes without being spoiled by decoherence. However, despite practical and foundational value, apart from simple two-time scenarios, the distinction between quantum and classical memory remains unexplored. Here, we analyse multi-time quantum processes with memory mechanisms that transmit only classical information forward in time. Complementing this analysis, we also study two related – but simpler to characterise – sets of processes that could also be considered to have classical memory from a structural perspective, and demonstrate that these lead to remarkably distinct phenomena in the multi-time setting. Subsequently, we systematically stratify the full hierarchy of memory effects in quantum mechanics, many levels of which collapse in the two-time setting, making our results genuinely multi-time phenomena.
@article{10.22331/q-2024-05-02-1328, title = {{Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory}}, author = {Taranto, Philip and Quintino, Marco T{\' u}lio and Murao, Mio and Milz, Simon}, year = {2024}, url = { https://doi.org/10.22331/q-2024-05-02-1328}, journal = {Quantum}, volume = {8}, pages = {1328}, archiveprefix = {arXiv}, eprint = {2307.11905}, }
2023
- Universal algorithm for transforming Hamiltonian eigenvaluesTatsuki Odake, Hlér Kristjánsson, Philip Taranto, and Mio Murao2023
Manipulating the Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a new way of manipulating Hamiltonians, by transforming their eigenvalues while keeping their eigenvectors fixed. If a classical description of the initial Hamiltonian is known, then one can – in principle – diagonalize it and compute the Hamiltonian transformation on a classical computer. However, this comes with a significant computational cost, and a classical description of the initial Hamiltonian is not always available, in particular for complex systems. In this work, we develop a universal algorithm that deterministically implements any desired (suitably differentiable) function on the eigenvalues of any unknown Hamiltonian, whose dynamics is given as a black box. Our algorithm makes use of correlated randomness to efficiently combine two subroutines – namely controlization and Fourier series simulation – using a general compilation procedure developed in this work. We show that the runtime of our algorithm is significantly reduced using our general compilation framework, compared to a naïve concatenation of the subroutines, and moreover outperforms similar methods based on the quantum singular value transformation.
@misc{arXiv:2312.08848, title = {{Universal algorithm for transforming Hamiltonian eigenvalues}}, author = {Odake, Tatsuki and Kristj{\'a}nsson, Hl{\'e}r and Taranto, Philip and Murao, Mio}, year = {2023}, url = { https://doi.org/10.48550/arXiv.2312.08848}, archiveprefix = {arXiv}, eprint = {2312.08848}, } - Hidden Quantum Memory: Is Memory There When Somebody Looks?Philip Taranto, Thomas J. Elliott, and Simon MilzQuantum, 2023
In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics, first and foremost because quantum measurements are invasive. Going beyond measurement invasiveness, here we derive a novel distinction between classical and quantum processes, namely the possibility of hidden quantum memory. While Markovian statistics of classical processes can always be reproduced by a memoryless dynamical model, our main result shows that this is not true in quantum mechanics: We first provide an example of quantum non-Markovianity whose manifestation depends on whether or not a previous measurement is performed – an impossible phenomenon for memoryless dynamics; we then strengthen this result by demonstrating statistics that are Markovian independent of how they are probed, but are nonetheless still incompatible with memoryless quantum dynamics. Thus, we establish the existence of Markovian statistics gathered by probing a quantum process that nevertheless fundamentally require memory for their creation.
@article{q-2023-04-27-991, title = {{Hidden Quantum Memory: Is Memory There When Somebody Looks?}}, author = {Taranto, Philip and Elliott, Thomas J. and Milz, Simon}, journal = {Quantum}, year = {2023}, volume = {7}, pages = {991}, doi = {10.22331/q-2023-04-27-991}, url = {https://doi.org/10.22331/q-2023-04-27-991}, archiveprefix = {arXiv}, eprint = {2204.08298}, } -
Landauer Versus Nernst: What is the True Cost of Cooling a Quantum System?Philip Taranto, Faraj Bakhshinezhad, Andreas Bluhm, Ralph Silva, Nicolai Friis, Maximilian P.E. Lock, Giuseppe Vitagliano, Felix C. Binder, Tiago Debarba, Emanuel Schwarzhans, Fabien Clivaz, and Marcus HuberPRX Quantum, 2023Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst’s unattainability principle, which states that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilized? And how does this relate to Landauer’s principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure quantum states. We show that perfect cooling is possible with Landauer energy cost given infinite time or control complexity. However, such optimal protocols require complex unitaries generated by an external work source. Restricting to unitaries that can be run solely via a heat engine, we derive a novel Carnot-Landauer limit, along with protocols for its saturation. This generalizes Landauer’s principle to a fully thermodynamic setting, leading to a unification with the third law and emphasizes the importance of control in quantum thermodynamics.
@article{PRXQuantum.4.010332, title = {Landauer Versus Nernst: What is the True Cost of Cooling a Quantum System?}, author = {Taranto, Philip and Bakhshinezhad, Faraj and Bluhm, Andreas and Silva, Ralph and Friis, Nicolai and Lock, Maximilian P.E. and Vitagliano, Giuseppe and Binder, Felix C. and Debarba, Tiago and Schwarzhans, Emanuel and Clivaz, Fabien and Huber, Marcus}, journal = {PRX Quantum}, volume = {4}, issue = {1}, pages = {010332}, numpages = {61}, year = {2023}, publisher = {American Physical Society}, doi = {10.1103/PRXQuantum.4.010332}, url = {https://link.aps.org/doi/10.1103/PRXQuantum.4.010332}, }
2022
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Quantum Information Processing: Thermodynamics, Complexity, and Multi-Time PhenomenaPhilip TarantoUniversity of Vienna, Austria, 2022The dialectic relationship between physics and information is perhaps best exemplified through thermodynamics: A theory that connects our knowledge of the world to our capability to control and thus manipulate it. Active control over physical processes plays a crucial role regarding our ability to implement desired transformations in practice and therefore should be incorporated to define a meaningful notion of complexity. Such complexity often manifests itself in terms of complicated physical behaviour: Intricate multi-partite correlation structures, difficult-to-model evolution, and layered multi-time phenomena. Generally speaking, what one deems to be a difficult task—either from a physical or information-theoretic standpoint—is largely dictated by the required degree of spatio-temporal control, i.e., control over both multiple degrees of freedom as well as memory effects on different timescales. This cumulative thesis aims to provide a holistic picture regarding the intricate interplay between thermodynamics, complexity, and multi-time phenomena, and lay out the ensuing implications for our ability to control and process quantum information. A core thread running throughout is the following question: What is a complex (quantum) system or process, and how can we describe and exploit control complexity and/or memory effects as a resource for (quantum) information processing? ...
@phdthesis{10.25365/thesis.72003, title = {{Quantum Information Processing: Thermodynamics, Complexity, and Multi-Time Phenomena}}, author = {Taranto, Philip}, year = {2022}, doi = {10.25365/thesis.72003}, url = {https://utheses.univie.ac.at/detail/63340/#}, school = {University of Vienna, Austria}, } - Connecting Commutativity and Classicality for Multi-Time Quantum ProcessesFattah Sakuldee, Philip Taranto, and Simon MilzPhys. Rev. A, 2022
Understanding the demarcation line between classical and quantum is an important issue in modern physics. The development of such an understanding requires a clear picture of the various concurrent notions of “classicality” in quantum theory presently in use. Here we focus on the relationship between Kolmogorov consistency of measurement statistics—the foundational footing of classical stochastic processes in standard probability theory—and the commutativity (or absence thereof) of measurement operators—a concept at the core of quantum theory. Kolmogorov consistency implies that the statistics of sequential measurements on a (possibly quantum) system could be explained entirely by means of a classical stochastic process, thereby providing an operational notion of classicality. On the other hand, commutativity of measurement operators is a structural property that holds in classical physics and its breakdown is the origin of the uncertainty principle, a fundamentally quantum phenomenon. We formalize the connection between these two a priori independent notions of classicality, demonstrate that they are distinct in general and detail their implications for memoryless multitime quantum processes.
@article{PhysRevA.106.022416, title = {{Connecting Commutativity and Classicality for Multi-Time Quantum Processes}}, author = {Sakuldee, Fattah and Taranto, Philip and Milz, Simon}, journal = {Phys. Rev. A}, volume = {106}, pages = {022416}, year = {2022}, doi = {10.1103/PhysRevA.106.022416}, url = {https://link.aps.org/doi/10.1103/PhysRevA.106.022416}, archiveprefix = {arXiv}, eprint = {2204.11698}, }
2021
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Non-Markovian Memory Strength Bounds Quantum Process RecoverabilityPhilip Taranto, Felix A. Pollock, and Kavan Modinpj Quantum Inf., 2021Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovian phenomena, enabling compression and recovery techniques pivotal to near-term technologies. We highlight the implications of our results by analyzing an exactly solvable model to show that memory truncation is possible even in a highly non-Markovian regime.
@article{npjqi.s41534-021-00481-4, author = {Taranto, Philip and Pollock, Felix A. and Modi, Kavan}, doi = {10.1038/s41534-021-00481-4}, journal = {npj Quantum Inf.}, pages = {149}, title = {{Non-Markovian Memory Strength Bounds Quantum Process Recoverability}}, volume = {7}, year = {2021}, archiveprefix = {arXiv}, eprint = {1907.12583}, } - Experimental Demonstration of Instrument-Specific Quantum Memory Effects and Non-Markovian Process Recovery for Common-Cause ProcessesYu Guo, Philip Taranto, Bi-Heng Liu, Xiao-Min Hu, Yun-Feng Huang, Chuan-Feng Li, and Guang-Can GuoPhys. Rev. Lett., 2021
The duration, strength, and structure of memory effects are crucial properties of physical evolution. Because of the invasive nature of quantum measurement, such properties must be defined with respect to the probing instruments employed. Here, using a photonic platform, we experimentally demonstrate this necessity via two paradigmatic processes: future-history correlations in the first process can be erased by an intermediate quantum measurement; for the second process, a noisy classical measurement blocks the effect of history. We then apply memory truncation techniques to recover an efficient description that approximates expectation values for multitime observables. Our proof-of-principle analysis paves the way for experiments concerning more general non-Markovian quantum processes and highlights where standard open systems techniques break down.
@article{PhysRevLett.126.230401, title = {{Experimental Demonstration of Instrument-Specific Quantum Memory Effects and Non-Markovian Process Recovery for Common-Cause Processes}}, author = {Guo, Yu and Taranto, Philip and Liu, Bi-Heng and Hu, Xiao-Min and Huang, Yun-Feng and Li, Chuan-Feng and Guo, Guang-Can}, journal = {Phys. Rev. Lett.}, volume = {126}, pages = {230401}, year = {2021}, doi = {10.1103/PhysRevLett.126.230401}, archiveprefix = {arXiv}, eprint = {2003.14045}, }
2020
- When Is a Non-Markovian Quantum Process Classical?Simon Milz, Dario Egloff, Philip Taranto, Thomas Theurer, Martin B. Plenio, Andrea Smirne, and Susana F. HuelgaPhys. Rev. X, 2020
More than a century after the inception of quantum theory, the question of which traits and phenomena are fundamentally quantum remains under debate. Here, we give an answer to this question for temporal processes that are probed sequentially by means of projective measurements of the same observable. Defining classical processes as those that can, in principle, be simulated by means of classical resources only, we fully characterize the set of such processes. Based on this characterization, we show that for non-Markovian processes (i.e., processes with memory), the absence of coherence does not guarantee the classicality of observed phenomena; furthermore, we derive an experimentally and computationally accessible measure for nonclassicality in the presence of memory. We then provide a direct connection between classicality and the vanishing of quantum discord between the evolving system and its environment. Finally, we demonstrate that—in contrast to the memoryless setting—in the non-Markovian case, there exist processes that are genuinely quantum; i.e., they display nonclassical statistics independent of the measurement scheme that is employed to probe them.
@article{PhysRevX.10.041049, title = {{When Is a Non-Markovian Quantum Process Classical?}}, author = {Milz, Simon and Egloff, Dario and Taranto, Philip and Theurer, Thomas and Plenio, Martin B. and Smirne, Andrea and Huelga, Susana F.}, journal = {Phys. Rev. X}, volume = {10}, pages = {041049}, year = {2020}, doi = {10.1103/PhysRevX.10.041049}, archiveprefix = {arXiv}, eprint = {1907.05807}, } - Exponential Improvement for Quantum Cooling Through Finite-Memory EffectsPhilip Taranto, Faraj Bakhshinezhad, Philipp Schüttelkopf, Fabien Clivaz, and Marcus HuberPhys. Rev. Appl., 2020
Practical implementations of quantum technologies require preparation of states with a high degree of purity—or, in thermodynamic terms, very low temperatures. Given finite resources, the third law of thermodynamics prohibits perfect cooling; nonetheless, attainable upper bounds for the asymptotic ground-state population of a system repeatedly interacting with quantum thermal machines have been derived. These bounds apply within a memoryless (Markovian) setting, in which each refrigeration step proceeds independently of those previous. Here, we expand this framework to study the effects of memory on quantum cooling. By introducing a memory mechanism through a generalized collision model that permits a Markovian embedding, we derive achievable bounds that provide an exponential advantage over the memoryless case. For qubits, our bound coincides with that of heat-bath algorithmic cooling, which our framework generalizes to arbitrary dimensions. We lastly describe the adaptive stepwise optimal protocol that outperforms all standard procedures.
@article{PhysRevApplied.14.054005, title = {{Exponential Improvement for Quantum Cooling Through Finite-Memory Effects}}, author = {Taranto, Philip and Bakhshinezhad, Faraj and Sch\"uttelkopf, Philipp and Clivaz, Fabien and Huber, Marcus}, journal = {Phys. Rev. Appl.}, volume = {14}, pages = {054005}, year = {2020}, doi = {10.1103/PhysRevApplied.14.054005}, archiveprefix = {arXiv}, eprint = {2004.00323}, } -
Memory Effects in Quantum ProcessesPhilip TarantoInt. J. Quantum Inf., 2020Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics that define a stochastic process lies at the heart of any proper treatment of memory effects. This is well understood in classical theory, where a hierarchy of joint probability distributions completely characterizes the process at hand. However, attempting to generalize this notion to quantum mechanics is problematic: observing realizations of a quantum process necessarily disturbs the state of the system, breaking an implicit, and crucial, assumption in the classical setting. This issue can be overcome by separating the experimental interventions from the underlying process, enabling an unambiguous description of the process itself and accounting for all possible multi-time correlations for any choice of interrogating instruments. In this paper, using a novel framework for the characterization of quantum stochastic processes, we first solve the long standing question of unambiguously describing the memory length of a quantum processes. This is achieved by constructing a quantum Markov order condition, which naturally generalizes its classical counterpart for the quantification of finite-length memory effects. As measurements are inherently invasive in quantum mechanics, one has no choice but to define Markov order with respect to the interrogating instruments that are used to probe the process at hand: different memory effects are exhibited depending on how one addresses the system, in contrast to the standard classical setting. We then fully characterize the structural constraints imposed on quantum processes with finite Markov order, shedding light on a variety of memory effects that can arise through various examples. Finally, we introduce an instrument-specific notion of memory strength that allows for a meaningful quantification of the temporal correlations between the history and the future of a process for a given choice of experimental intervention. These findings are directly relevant to both characterizing and exploiting memory effects that persist for a finite duration. In particular, immediate applications range from developing efficient compression and recovery schemes for the description of quantum processes with memory to designing coherent control protocols that efficiently perform information-theoretic tasks, amongst a plethora of others.
@article{ijqi.S0219749919410028, title = {{Memory Effects in Quantum Processes}}, author = {Taranto, Philip}, journal = {Int. J. Quantum Inf.}, doi = {10.1142/S0219749919410028}, volume = {18}, pages = {1941002}, year = {2020}, archiveprefix = {arXiv}, eprint = {1909.05245}, }
2019
- Quantum Markov OrderPhilip Taranto, Felix A. Pollock, Simon Milz, Marco Tomamichel, and Kavan ModiPhys. Rev. Lett., 2019
We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical property in the appropriate limit: when the stochastic process is classical and the instruments are noninvasive, i.e., restricted to orthogonal, projective measurements. We then prove that there do not exist non-Markovian quantum processes that have finite Markov order with respect to all possible instruments; the same process exhibits distinct memory effects when probed by different instruments. This naturally leads to a relaxed definition of quantum Markov order with respect to specified instrument sequences. The memory effects captured by different choices of instruments vary dramatically, providing a rich landscape for future exploration.
@article{PhysRevLett.122.140401, title = {{Quantum Markov Order}}, author = {Taranto, Philip and Pollock, Felix A. and Milz, Simon and Tomamichel, Marco and Modi, Kavan}, journal = {Phys. Rev. Lett.}, volume = {122}, pages = {140401}, year = {2019}, doi = {10.1103/PhysRevLett.122.140401}, archiveprefix = {arXiv}, eprint = {1805.11341}, } - Structure of Quantum Stochastic Processes with finite Markov orderPhilip Taranto, Simon Milz, Felix A. Pollock, and Kavan ModiPhys. Rev. A, 2019
Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics. This instrument-specific notion of quantum Markov order displays stark differences to its classical counterpart. Here, we explore the structure of quantum stochastic processes with finite memory length in detail. We begin by examining a generalized collision model with memory, before framing this instance within the general theory. We detail the constraints that are placed on the underlying system-environment dynamics for a process to exhibit finite Markov order with respect to natural classes of probing instruments, including deterministic (unitary) operations and sequences of generalized quantum measurements with informationally complete repreparations. Lastly, we show how processes with vanishing quantum conditional mutual information form a special case of the theory. Throughout, we provide a number of representative, pedagogical examples to display the salient features of memory effects in quantum processes.
@article{PhysRevA.99.042108, title = {{Structure of Quantum Stochastic Processes with finite Markov order}}, author = {Taranto, Philip and Milz, Simon and Pollock, Felix A. and Modi, Kavan}, journal = {Phys. Rev. A}, volume = {99}, pages = {042108}, year = {2019}, doi = {10.1103/PhysRevA.99.042108}, archiveprefix = {arXiv}, eprint = {1810.10809}, }
2018
- Emergence of a Fluctuation Relation for Heat in Nonequilibrium Landauer ProcessesPhilip Taranto, Kavan Modi, and Felix A. PollockPhys. Rev. E, 2018
In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for nonequilibrium processes, heat fluctuations away from its average value are suppressed independently of the underlying dynamics exponentially quickly in the dimension of the larger subsystem and linearly in the inverse temperature. We achieve these results by generalizing a concentration of measure relation for subsystem states to the case where the global state is mixed.
@article{PhysRevE.97.052111, title = {{Emergence of a Fluctuation Relation for Heat in Nonequilibrium Landauer Processes}}, author = {Taranto, Philip and Modi, Kavan and Pollock, Felix A.}, journal = {Phys. Rev. E}, volume = {97}, pages = {052111}, year = {2018}, doi = {10.1103/PhysRevE.97.052111}, url = {https://link.aps.org/doi/10.1103/PhysRevE.97.052111}, archiveprefix = {arXiv}, eprint = {1510.08219}, }