Pub Date : 2025-02-04DOI: 10.22331/q-2025-02-04-1621
Denis A. Kopylov, Torsten Meier, Polina R. Sharapova
A unified theoretical approach to describe the properties of multimode squeezed light generated in a lossy medium is presented. This approach is valid for Markovian environments and includes both a model of discrete losses based on the beamsplitter approach and a generalized continuous loss model based on the spatial Langevin equation. For an important class of Gaussian states, we derive master equations for the second-order correlation functions and illustrate their solution for both frequency-independent and frequency-dependent losses. Studying the mode structure, we demonstrate that in a lossy environment no broadband basis without quadrature correlations between the different broadband modes exists. Therefore, various techniques and strategies to introduce broadband modes can be considered. We show that the Mercer expansion and the Williamson-Euler decomposition do not provide modes in which the maximal squeezing contained in the system can be measured. In turn, we find a new broadband basis that maximizes squeezing in the lossy system and present an algorithm to construct it.
{"title":"Theory of Multimode Squeezed Light Generation in Lossy Media","authors":"Denis A. Kopylov, Torsten Meier, Polina R. Sharapova","doi":"10.22331/q-2025-02-04-1621","DOIUrl":"https://doi.org/10.22331/q-2025-02-04-1621","url":null,"abstract":"A unified theoretical approach to describe the properties of multimode squeezed light generated in a lossy medium is presented. This approach is valid for Markovian environments and includes both a model of discrete losses based on the beamsplitter approach and a generalized continuous loss model based on the spatial Langevin equation. For an important class of Gaussian states, we derive master equations for the second-order correlation functions and illustrate their solution for both frequency-independent and frequency-dependent losses. Studying the mode structure, we demonstrate that in a lossy environment no broadband basis without quadrature correlations between the different broadband modes exists. Therefore, various techniques and strategies to introduce broadband modes can be considered. We show that the Mercer expansion and the Williamson-Euler decomposition do not provide modes in which the maximal squeezing contained in the system can be measured. In turn, we find a new broadband basis that maximizes squeezing in the lossy system and present an algorithm to construct it.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"37 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143124651","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 : 2025-02-04DOI: 10.22331/q-2025-02-04-1619
Jasper Kranias, Guillaume Thekkadath, Khabat Heshami, Aaron Z. Goldberg
The quantum Fisher information (QFI) bounds the sensitivity of a quantum measurement, heralding the conditions for quantum advantages when compared with classical strategies. Here, we calculate analytical expressions for the QFI of nonlinear interferometers under lossy conditions and with coherent-state seeding. We normalize the results based on the number of photons going through the sample that induces a phase shift on the incident quantum state, which eliminates some of the previously declared metrological advantages. We analyze the performance of nonlinear interferometers in a variety of geometries and robustness of the quantum advantage with respect to internal and external loss through direct comparison with a linear interferometer. We find the threshold on the internal loss at which the quantum advantage vanishes, specify when and how much coherent-state seeding optimally counters internal loss, and show that a sufficient amount of squeezing confers to the quantum advantages robustness against external loss and inefficient detection.
{"title":"Metrological Advantages in Seeded and Lossy Nonlinear Interferometers","authors":"Jasper Kranias, Guillaume Thekkadath, Khabat Heshami, Aaron Z. Goldberg","doi":"10.22331/q-2025-02-04-1619","DOIUrl":"https://doi.org/10.22331/q-2025-02-04-1619","url":null,"abstract":"The quantum Fisher information (QFI) bounds the sensitivity of a quantum measurement, heralding the conditions for quantum advantages when compared with classical strategies. Here, we calculate analytical expressions for the QFI of nonlinear interferometers under lossy conditions and with coherent-state seeding. We normalize the results based on the number of photons going through the sample that induces a phase shift on the incident quantum state, which eliminates some of the previously declared metrological advantages. We analyze the performance of nonlinear interferometers in a variety of geometries and robustness of the quantum advantage with respect to internal and external loss through direct comparison with a linear interferometer. We find the threshold on the internal loss at which the quantum advantage vanishes, specify when and how much coherent-state seeding optimally counters internal loss, and show that a sufficient amount of squeezing confers to the quantum advantages robustness against external loss and inefficient detection.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"8 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143124646","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 : 2025-02-04DOI: 10.22331/q-2025-02-04-1622
Nathaniel Johnston, Vincent Russo, Jamie Sikora
A set of pure quantum states is said to be antidistinguishable if upon sampling one at random, there exists a measurement to perfectly determine some state that was not sampled. We show that antidistinguishability of a set of $n$ pure states is equivalent to a property of its Gram matrix called $(n-1)$-incoherence, thus establishing a connection with quantum resource theories that lets us apply a wide variety of new tools to antidistinguishability. As a particular application of our result, we present an explicit formula (not involving any semidefinite programming) that determines whether or not a set with a circulant Gram matrix is antidistinguishable. We also show that if all inner products are smaller than $sqrt{(n-2)/(2n-2)}$ then the set must be antidistinguishable, and we show that this bound is tight when $n leq 4$. We also give a simpler proof that if all the inner products are strictly larger than $(n-2)/(n-1)$, then the set cannot be antidistinguishable, and we show that this bound is tight for all $n$.
{"title":"Tight bounds for antidistinguishability and circulant sets of pure quantum states","authors":"Nathaniel Johnston, Vincent Russo, Jamie Sikora","doi":"10.22331/q-2025-02-04-1622","DOIUrl":"https://doi.org/10.22331/q-2025-02-04-1622","url":null,"abstract":"A set of pure quantum states is said to be antidistinguishable if upon sampling one at random, there exists a measurement to perfectly determine some state that was not sampled. We show that antidistinguishability of a set of $n$ pure states is equivalent to a property of its Gram matrix called $(n-1)$-incoherence, thus establishing a connection with quantum resource theories that lets us apply a wide variety of new tools to antidistinguishability. As a particular application of our result, we present an explicit formula (not involving any semidefinite programming) that determines whether or not a set with a circulant Gram matrix is antidistinguishable. We also show that if all inner products are smaller than $sqrt{(n-2)/(2n-2)}$ then the set must be antidistinguishable, and we show that this bound is tight when $n leq 4$. We also give a simpler proof that if all the inner products are strictly larger than $(n-2)/(n-1)$, then the set cannot be antidistinguishable, and we show that this bound is tight for all $n$.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"123 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143124647","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 : 2025-02-04DOI: 10.22331/q-2025-02-04-1620
Sara Santos, Xinyu Song, Vincenzo Savona
The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dynamical properties, thanks to hybrid quantum-classical variational algorithms to approximate the dynamics of the density matrix describing the quantum state in terms of an ensemble average. Here, a variational quantum algorithm is developed to simulate the real-time evolution of the density matrix governed by the Lindblad master equation, under the assumption that the quantum state has a bounded entropy along the dynamics, entailing a low-rank representation of its density matrix. The algorithm encodes each pure state of the statistical mixture as a parametrized quantum circuit, and the associated probabilities as additional variational parameters stored classically, thereby requiring a significantly lower number of qubits than algorithms where the full density matrix is encoded in the quantum memory. Two variational ansatze are proposed, and their effectiveness is assessed in the simulation of the dynamics of a 2D dissipative transverse field Ising model. The results underscore the algorithm's efficiency in simulating the dynamics of open quantum systems in the low-rank regime with limited quantum resources on a near-term quantum device.
{"title":"Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems","authors":"Sara Santos, Xinyu Song, Vincenzo Savona","doi":"10.22331/q-2025-02-04-1620","DOIUrl":"https://doi.org/10.22331/q-2025-02-04-1620","url":null,"abstract":"The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dynamical properties, thanks to hybrid quantum-classical variational algorithms to approximate the dynamics of the density matrix describing the quantum state in terms of an ensemble average. Here, a variational quantum algorithm is developed to simulate the real-time evolution of the density matrix governed by the Lindblad master equation, under the assumption that the quantum state has a bounded entropy along the dynamics, entailing a low-rank representation of its density matrix. The algorithm encodes each pure state of the statistical mixture as a parametrized quantum circuit, and the associated probabilities as additional variational parameters stored classically, thereby requiring a significantly lower number of qubits than algorithms where the full density matrix is encoded in the quantum memory. Two variational ansatze are proposed, and their effectiveness is assessed in the simulation of the dynamics of a 2D dissipative transverse field Ising model. The results underscore the algorithm's efficiency in simulating the dynamics of open quantum systems in the low-rank regime with limited quantum resources on a near-term quantum device.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"38 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143124857","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 : 2025-01-30DOI: 10.22331/q-2025-01-30-1616
Ladina Hausmann, Alexander Schmidhuber, Esteban Castro-Ruiz
The Page-Wootters formalism is a proposal for reconciling the background-dependent, quantum-mechanical notion of time with the background independence of general relativity. However, the physical meaning of this framework remains debated. In this work, we compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements with respect to a temporal quantum reference frame. The so-called "twirled observable" approach implements measurements as operators that are invariant with respect to the Hamiltonian constraint. The "purified measurement" approach instead models measurements dynamically by modifying the constraint itself. While both approaches agree in the limit of ideal clocks, a natural generalization of the purified measurement approach to the case of non-ideal, finite-resource clocks yields a radically different picture. We discuss the physical origin of this discrepancy and argue that these approaches describe operationally distinct situations. Moreover, we show that, for non-ideal clocks, the purified measurement approach yields a time non-local evolution equation, which can lead to non-unitary evolution. Moreover, it implies a fundamental limitation to the operational definition of the temporal order of events. Nevertheless, unitarity and definite temporal order can be restored if we assume that time is discrete.
{"title":"Measurement events relative to temporal quantum reference frames","authors":"Ladina Hausmann, Alexander Schmidhuber, Esteban Castro-Ruiz","doi":"10.22331/q-2025-01-30-1616","DOIUrl":"https://doi.org/10.22331/q-2025-01-30-1616","url":null,"abstract":"The Page-Wootters formalism is a proposal for reconciling the background-dependent, quantum-mechanical notion of time with the background independence of general relativity. However, the physical meaning of this framework remains debated. In this work, we compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements with respect to a temporal quantum reference frame. The so-called \"twirled observable\" approach implements measurements as operators that are invariant with respect to the Hamiltonian constraint. The \"purified measurement\" approach instead models measurements dynamically by modifying the constraint itself. While both approaches agree in the limit of ideal clocks, a natural generalization of the purified measurement approach to the case of non-ideal, finite-resource clocks yields a radically different picture. We discuss the physical origin of this discrepancy and argue that these approaches describe operationally distinct situations. Moreover, we show that, for non-ideal clocks, the purified measurement approach yields a time non-local evolution equation, which can lead to non-unitary evolution. Moreover, it implies a fundamental limitation to the operational definition of the temporal order of events. Nevertheless, unitarity and definite temporal order can be restored if we assume that time is discrete.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"23 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143056221","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 : 2025-01-30DOI: 10.22331/q-2025-01-30-1615
Tom Holden-Dye, Lluis Masanes, Arijeet Pal
Dual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. Consisting of a 1+1D lattice of 2-qudit gates arranged in a 'brickwork' pattern, these models are defined by the constraint that each gate must remain unitary under swapping the roles of space and time. This dual-unitarity restricts the dynamics of local operators in these circuits: the support of any such operator must grow at the effective speed of light of the system, along one or both of the edges of a causal light cone set by the geometry of the circuit. Using this property, it is shown here that for 1+1D dual-unitary circuits the set of width-$w$ conserved densities (constructed from operators supported over $w$ consecutive sites) is in one-to-one correspondence with the set of width-$w$ solitons – operators which, up to a multiplicative phase, are simply spatially translated at the effective speed of light by the dual-unitary dynamics. A number of ways to construct these many-body solitons (explicitly in the case where the local Hilbert space dimension $d=2$) are then demonstrated: firstly, via a simple construction involving products of smaller, constituent solitons; and secondly, via a construction which cannot be understood as simply in terms of products of smaller solitons, but which does have a neat interpretation in terms of products of fermions under a Jordan-Wigner transformation. This provides partial progress towards a characterisation of the microscopic structure of complex many-body solitons (in dual-unitary circuits on qubits), whilst also establishing a link between fermionic models and dual-unitary circuits, advancing our understanding of what kinds of physics can be explored in this framework.
{"title":"Fundamental charges for dual-unitary circuits","authors":"Tom Holden-Dye, Lluis Masanes, Arijeet Pal","doi":"10.22331/q-2025-01-30-1615","DOIUrl":"https://doi.org/10.22331/q-2025-01-30-1615","url":null,"abstract":"Dual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. Consisting of a 1+1D lattice of 2-qudit gates arranged in a 'brickwork' pattern, these models are defined by the constraint that each gate must remain unitary under swapping the roles of space and time. This dual-unitarity restricts the dynamics of local operators in these circuits: the support of any such operator must grow at the effective speed of light of the system, along one or both of the edges of a causal light cone set by the geometry of the circuit. Using this property, it is shown here that for 1+1D dual-unitary circuits the set of width-$w$ conserved densities (constructed from operators supported over $w$ consecutive sites) is in one-to-one correspondence with the set of width-$w$ solitons – operators which, up to a multiplicative phase, are simply spatially translated at the effective speed of light by the dual-unitary dynamics. A number of ways to construct these many-body solitons (explicitly in the case where the local Hilbert space dimension $d=2$) are then demonstrated: firstly, via a simple construction involving products of smaller, constituent solitons; and secondly, via a construction which cannot be understood as simply in terms of products of smaller solitons, but which does have a neat interpretation in terms of products of fermions under a Jordan-Wigner transformation. This provides partial progress towards a characterisation of the microscopic structure of complex many-body solitons (in dual-unitary circuits on qubits), whilst also establishing a link between fermionic models and dual-unitary circuits, advancing our understanding of what kinds of physics can be explored in this framework.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"20 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143056964","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 : 2025-01-30DOI: 10.22331/q-2025-01-30-1617
Phattharaporn Singkanipa, Daniel A. Lidar
Variational quantum algorithms (VQAs) hold much promise but face the challenge of exponentially small gradients. Unmitigated, this barren plateau (BP) phenomenon leads to an exponential training overhead for VQAs. Perhaps the most pernicious are noise-induced barren plateaus (NIBPs), a type of unavoidable BP arising from open system effects, which have so far been shown to exist for unital noise maps. Here, we generalize the study of NIBPs to more general completely positive, trace-preserving maps, investigating the existence of NIBPs in the unital case and a class of non-unital maps we call Hilbert-Schmidt (HS)-contractive. The latter includes amplitude damping. We identify the associated phenomenon of noise-induced limit sets (NILS) of the VQA cost function and prove its existence for both unital and HS-contractive non-unital noise maps. Along the way, we extend the parameter shift rule of VQAs to the noisy setting. We provide rigorous bounds in terms of the relevant variables that give rise to NIBPs and NILSs, along with numerical simulations of the depolarizing and amplitude-damping maps that illustrate our analytical results.
{"title":"Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets","authors":"Phattharaporn Singkanipa, Daniel A. Lidar","doi":"10.22331/q-2025-01-30-1617","DOIUrl":"https://doi.org/10.22331/q-2025-01-30-1617","url":null,"abstract":"Variational quantum algorithms (VQAs) hold much promise but face the challenge of exponentially small gradients. Unmitigated, this barren plateau (BP) phenomenon leads to an exponential training overhead for VQAs. Perhaps the most pernicious are noise-induced barren plateaus (NIBPs), a type of unavoidable BP arising from open system effects, which have so far been shown to exist for unital noise maps. Here, we generalize the study of NIBPs to more general completely positive, trace-preserving maps, investigating the existence of NIBPs in the unital case and a class of non-unital maps we call Hilbert-Schmidt (HS)-contractive. The latter includes amplitude damping. We identify the associated phenomenon of noise-induced limit sets (NILS) of the VQA cost function and prove its existence for both unital and HS-contractive non-unital noise maps. Along the way, we extend the parameter shift rule of VQAs to the noisy setting. We provide rigorous bounds in terms of the relevant variables that give rise to NIBPs and NILSs, along with numerical simulations of the depolarizing and amplitude-damping maps that illustrate our analytical results.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"37 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143072033","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 : 2025-01-30DOI: 10.22331/q-2025-01-30-1618
Argyris Giannisis Manes, Jahan Claes
Unlike the surface code, quantum low-density parity-check (QLDPC) codes can have a finite encoding rate, potentially lowering the error correction overhead. However, finite-rate QLDPC codes have nonlocal stabilizers, making it difficult to design stabilizer measurement circuits that are low-depth and do not decrease the effective distance. Here, we demonstrate that a popular family of finite-rate QLDPC codes, hypergraph product codes, has the convenient property of distance-robustness: any stabilizer measurement circuit preserves the effective distance. In particular, we prove the depth-optimal circuit in [Tremblay et al, PRL 129, 050504 (2022)] is also optimal in terms of effective distance.
{"title":"Distance-preserving stabilizer measurements in hypergraph product codes","authors":"Argyris Giannisis Manes, Jahan Claes","doi":"10.22331/q-2025-01-30-1618","DOIUrl":"https://doi.org/10.22331/q-2025-01-30-1618","url":null,"abstract":"Unlike the surface code, quantum low-density parity-check (QLDPC) codes can have a finite encoding rate, potentially lowering the error correction overhead. However, finite-rate QLDPC codes have nonlocal stabilizers, making it difficult to design stabilizer measurement circuits that are low-depth and do not decrease the effective distance. Here, we demonstrate that a popular family of finite-rate QLDPC codes, hypergraph product codes, has the convenient property of distance-robustness: any stabilizer measurement circuit preserves the effective distance. In particular, we prove the depth-optimal circuit in [Tremblay et al, PRL 129, 050504 (2022)] is also optimal in terms of effective distance.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"55 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143072040","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 : 2025-01-28DOI: 10.22331/q-2025-01-28-1612
Jinkang Guo, Oliver Hart, Chi-Fang Chen, Aaron J. Friedman, Andrew Lucas
We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.
{"title":"Designing open quantum systems with known steady states: Davies generators and beyond","authors":"Jinkang Guo, Oliver Hart, Chi-Fang Chen, Aaron J. Friedman, Andrew Lucas","doi":"10.22331/q-2025-01-28-1612","DOIUrl":"https://doi.org/10.22331/q-2025-01-28-1612","url":null,"abstract":"We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"47 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049871","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 : 2025-01-28DOI: 10.22331/q-2025-01-28-1613
Shin Nishio, Nicholas Connolly, Nicolò Lo Piparo, William John Munro, Thomas Rowan Scruby, Kae Nemoto
Connecting multiple processors via quantum interconnect technologies could help overcome scalability issues in single-processor quantum computers. Transmission via these interconnects can be performed more efficiently using quantum multiplexing, where information is encoded in high-dimensional photonic degrees of freedom. We explore the effects of multiplexing on logical error rates in surface codes and hypergraph product codes. We show that, although multiplexing makes loss errors more damaging, assigning qubits to photons in an intelligent manner can minimize these effects, and the ability to encode higher-distance codes in a smaller number of photons can result in overall lower logical error rates. This multiplexing technique can also be adapted to quantum communication and multimode quantum memory with high-dimensional qudit systems.
{"title":"Multiplexed Quantum Communication with Surface and Hypergraph Product Codes","authors":"Shin Nishio, Nicholas Connolly, Nicolò Lo Piparo, William John Munro, Thomas Rowan Scruby, Kae Nemoto","doi":"10.22331/q-2025-01-28-1613","DOIUrl":"https://doi.org/10.22331/q-2025-01-28-1613","url":null,"abstract":"Connecting multiple processors via quantum interconnect technologies could help overcome scalability issues in single-processor quantum computers. Transmission via these interconnects can be performed more efficiently using quantum multiplexing, where information is encoded in high-dimensional photonic degrees of freedom. We explore the effects of multiplexing on logical error rates in surface codes and hypergraph product codes. We show that, although multiplexing makes loss errors more damaging, assigning qubits to photons in an intelligent manner can minimize these effects, and the ability to encode higher-distance codes in a smaller number of photons can result in overall lower logical error rates. This multiplexing technique can also be adapted to quantum communication and multimode quantum memory with high-dimensional qudit systems.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"26 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049902","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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