Pub Date : 2023-01-12DOI: 10.1103/prxquantum.4.030317
Jong Yeon Lee, Chao-Ming Jian, Cenke Xu
Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCP) in a nontrivial way. As was pointed out in recent literature on $(1+1)d$ conformal field theory (CFT), the effect of weak measurement can be mathematically mapped to the problem of boundary CFT. In this work, we focus on the $(2+1)d$ QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently. We focus on decoherence caused by weak measurements with and without post-selecting the measurement outcomes. Our main results are: (1) for an O(N) Wilson-Fisher QCP under weak measurement with post-selection, an observer would in general observe two different types of boundary/defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic"extraordinary-log"correlation. (2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy. We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model. (3) When there is no post-selection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the"disorder operator"would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement.
{"title":"Quantum Criticality Under Decoherence or Weak Measurement","authors":"Jong Yeon Lee, Chao-Ming Jian, Cenke Xu","doi":"10.1103/prxquantum.4.030317","DOIUrl":"https://doi.org/10.1103/prxquantum.4.030317","url":null,"abstract":"Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCP) in a nontrivial way. As was pointed out in recent literature on $(1+1)d$ conformal field theory (CFT), the effect of weak measurement can be mathematically mapped to the problem of boundary CFT. In this work, we focus on the $(2+1)d$ QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently. We focus on decoherence caused by weak measurements with and without post-selecting the measurement outcomes. Our main results are: (1) for an O(N) Wilson-Fisher QCP under weak measurement with post-selection, an observer would in general observe two different types of boundary/defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic\"extraordinary-log\"correlation. (2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy. We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model. (3) When there is no post-selection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the\"disorder operator\"would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46353472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-11DOI: 10.1103/PRXQuantum.4.030330
D. Haag, F. Baccari, Georgios Styliaris
The complexity of quantum many-body systems is manifested in the vast diversity of their correlations, making it challenging to distinguish the generic from the atypical features. This can be addressed by analyzing correlations through ensembles of random states, chosen to faithfully embody the relevant physical properties. Here, we focus on spins with local interactions, whose correlations are extremely well captured by tensor network states. Adopting an operational perspective, we define ensembles of random tensor network states in one and two spatial dimensions that admit a sequential generation. As such, they directly correspond to outputs of quantum circuits with a sequential architecture and random gates. In one spatial dimension, the ensemble explores the entire family of matrix product states, while in two spatial dimensions, it corresponds to random isometric tensor network states. We extract the scaling behavior of the average correlations between two subsystems as a function of their distance. Using elementary concentration results, we then deduce the typical case for measures of correlation such as the von Neumann mutual information and a measure arising from the Hilbert-Schmidt norm. We find for all considered cases that the typical behavior is an exponential decay (for both one and two spatial dimensions). We observe the consistent emergence of a correlation length that depends only on the underlying spatial dimension and not the considered measure. Remarkably, increasing the bond dimension leads to a higher correlation length in one spatial dimension but has the opposite effect in two spatial dimensions.
{"title":"Typical Correlation Length of Sequentially Generated Tensor Network States","authors":"D. Haag, F. Baccari, Georgios Styliaris","doi":"10.1103/PRXQuantum.4.030330","DOIUrl":"https://doi.org/10.1103/PRXQuantum.4.030330","url":null,"abstract":"The complexity of quantum many-body systems is manifested in the vast diversity of their correlations, making it challenging to distinguish the generic from the atypical features. This can be addressed by analyzing correlations through ensembles of random states, chosen to faithfully embody the relevant physical properties. Here, we focus on spins with local interactions, whose correlations are extremely well captured by tensor network states. Adopting an operational perspective, we define ensembles of random tensor network states in one and two spatial dimensions that admit a sequential generation. As such, they directly correspond to outputs of quantum circuits with a sequential architecture and random gates. In one spatial dimension, the ensemble explores the entire family of matrix product states, while in two spatial dimensions, it corresponds to random isometric tensor network states. We extract the scaling behavior of the average correlations between two subsystems as a function of their distance. Using elementary concentration results, we then deduce the typical case for measures of correlation such as the von Neumann mutual information and a measure arising from the Hilbert-Schmidt norm. We find for all considered cases that the typical behavior is an exponential decay (for both one and two spatial dimensions). We observe the consistent emergence of a correlation length that depends only on the underlying spatial dimension and not the considered measure. Remarkably, increasing the bond dimension leads to a higher correlation length in one spatial dimension but has the opposite effect in two spatial dimensions.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48590720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-09DOI: 10.1103/PRXQuantum.4.020330
F. Surace, P. Fromholz, N. Oppong, M. Dalmonte, M. Aidelsburger
We introduce a method for quantum simulation of U$(1)$ lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices. The proposal enables the study of both gauge and fermionic-matter fields without integrating out one of them in one and two dimensions. We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species. Starting from an $ab,initio$ modelling of the experimental setting, we systematically carry out a derivation of the target U$(1)$ gauge theory. This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that - while pivotal for a successful implementation - have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions, and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics. We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope $^{173}$Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one- and two-dimensional settings.
{"title":"Ab Initio\u0000 Derivation of Lattice-Gauge-Theory Dynamics for Cold Gases in Optical Lattices","authors":"F. Surace, P. Fromholz, N. Oppong, M. Dalmonte, M. Aidelsburger","doi":"10.1103/PRXQuantum.4.020330","DOIUrl":"https://doi.org/10.1103/PRXQuantum.4.020330","url":null,"abstract":"We introduce a method for quantum simulation of U$(1)$ lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices. The proposal enables the study of both gauge and fermionic-matter fields without integrating out one of them in one and two dimensions. We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species. Starting from an $ab,initio$ modelling of the experimental setting, we systematically carry out a derivation of the target U$(1)$ gauge theory. This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that - while pivotal for a successful implementation - have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions, and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics. We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope $^{173}$Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one- and two-dimensional settings.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46260299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-05DOI: 10.1103/PRXQuantum.4.020352
Aw Clive Cenxin, Kelvin Onggadinata, D. Kaszlikowski, V. Scarani
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed in the language of Hilbert spaces. In this paper, we derive the expression of the Petz recovery map within any quasiprobability representation, with explicit formulas for the two canonical choices of normal quasiprobability representations (which include Discrete Wigner representations) and of representations based on symmetric, informationally complete positive operator-valued measures (SIC-POVMs). By using the same mathematical syntax of (quasi-)stochastic matrices acting on (quasi-)stochastic vectors, the core difference in logical inference between classical and quantum theory is found in the manipulation of the reference prior rather than in the representation of the channel.
{"title":"Quantum Bayesian Inference in Quasiprobability Representations","authors":"Aw Clive Cenxin, Kelvin Onggadinata, D. Kaszlikowski, V. Scarani","doi":"10.1103/PRXQuantum.4.020352","DOIUrl":"https://doi.org/10.1103/PRXQuantum.4.020352","url":null,"abstract":"Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed in the language of Hilbert spaces. In this paper, we derive the expression of the Petz recovery map within any quasiprobability representation, with explicit formulas for the two canonical choices of normal quasiprobability representations (which include Discrete Wigner representations) and of representations based on symmetric, informationally complete positive operator-valued measures (SIC-POVMs). By using the same mathematical syntax of (quasi-)stochastic matrices acting on (quasi-)stochastic vectors, the core difference in logical inference between classical and quantum theory is found in the manipulation of the reference prior rather than in the representation of the channel.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49659557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-30DOI: 10.1103/prxquantum.4.030329
E. Poem, S. Gupta, I. Morris, K. Klink, L. Singh, T. Zhong, S. Nicley, J. Becker, O. Firstenberg
We present general guidelines for finding solid-state systems that could serve as coherent electron spin-photon interfaces even at relatively high temperatures, where phonons are abundant but cooling is easier, and show that transition metal ions in various crystals could comply with these guidelines. As an illustrative example, we focus on divalent nickel ions in magnesium oxide. We perform electron spin resonance spectroscopy and polarization-sensitive magneto-optical fluorescence spectroscopy of a dense ensemble of these ions and find that (i) the ground-state electron spin stays coherent at liquid-helium temperatures for several microseconds, and (ii) there exists energetically well-isolated excited states which can couple to two ground state spin sub-levels via optical transitions of orthogonal polarizations. The latter implies that fast, coherent optical control over the electron spin is possible. We then propose schemes for optical initialization and control of the ground-state electron spin using polarized optical pulses, as well as two schemes for implementing a noise-free, broadband quantum-optical memory at near-telecom wavelengths in this material system.
{"title":"Transition Metal Ion Ensembles in Crystals as Solid-State Coherent Spin-Photon Interfaces: The Case of Nickel in Magnesium Oxide","authors":"E. Poem, S. Gupta, I. Morris, K. Klink, L. Singh, T. Zhong, S. Nicley, J. Becker, O. Firstenberg","doi":"10.1103/prxquantum.4.030329","DOIUrl":"https://doi.org/10.1103/prxquantum.4.030329","url":null,"abstract":"We present general guidelines for finding solid-state systems that could serve as coherent electron spin-photon interfaces even at relatively high temperatures, where phonons are abundant but cooling is easier, and show that transition metal ions in various crystals could comply with these guidelines. As an illustrative example, we focus on divalent nickel ions in magnesium oxide. We perform electron spin resonance spectroscopy and polarization-sensitive magneto-optical fluorescence spectroscopy of a dense ensemble of these ions and find that (i) the ground-state electron spin stays coherent at liquid-helium temperatures for several microseconds, and (ii) there exists energetically well-isolated excited states which can couple to two ground state spin sub-levels via optical transitions of orthogonal polarizations. The latter implies that fast, coherent optical control over the electron spin is possible. We then propose schemes for optical initialization and control of the ground-state electron spin using polarized optical pulses, as well as two schemes for implementing a noise-free, broadband quantum-optical memory at near-telecom wavelengths in this material system.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48611627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-23DOI: 10.1103/prxquantum.3.040334
Jens Nettersheim, Sabrina Burgardt, Q. Bouton, Daniel Adam, E. Lutz, A. Widera
{"title":"Power of a Quasispin Quantum Otto Engine at Negative Effective Spin Temperature","authors":"Jens Nettersheim, Sabrina Burgardt, Q. Bouton, Daniel Adam, E. Lutz, A. Widera","doi":"10.1103/prxquantum.3.040334","DOIUrl":"https://doi.org/10.1103/prxquantum.3.040334","url":null,"abstract":"","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45466110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-21DOI: 10.1103/prxquantum.4.020354
T. Tsunoda, James D. Teoh, W. D. Kalfus, Stijn J. de Graaf, Benjamin J. Chapman, Jacob C. Curtis, Neel Thakur, S. Girvin, R. Schoelkopf
Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings. From a new geometric framework based on a"Bloch sphere"of bosonic operators, we construct $ZZ_L(theta)$ and $text{eSWAP}(theta)$ gates for the binomial, 4-legged cat, dual-rail and several other bosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beamsplitter between two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be realized in circuit QED hardware with ancilla transmons and microwave cavities. The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively generate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates. We show that this allows one to reach error-detected gate fidelities at the $10^{-4}$ level with today's hardware, limited only by second-order hardware errors.
{"title":"Error-Detectable Bosonic Entangling Gates with a Noisy Ancilla","authors":"T. Tsunoda, James D. Teoh, W. D. Kalfus, Stijn J. de Graaf, Benjamin J. Chapman, Jacob C. Curtis, Neel Thakur, S. Girvin, R. Schoelkopf","doi":"10.1103/prxquantum.4.020354","DOIUrl":"https://doi.org/10.1103/prxquantum.4.020354","url":null,"abstract":"Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings. From a new geometric framework based on a\"Bloch sphere\"of bosonic operators, we construct $ZZ_L(theta)$ and $text{eSWAP}(theta)$ gates for the binomial, 4-legged cat, dual-rail and several other bosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beamsplitter between two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be realized in circuit QED hardware with ancilla transmons and microwave cavities. The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively generate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates. We show that this allows one to reach error-detected gate fidelities at the $10^{-4}$ level with today's hardware, limited only by second-order hardware errors.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45926467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-19DOI: 10.1103/PRXQuantum.4.030314
A. Miller, Zolt'an Zimbor'as, S. Knecht, S. Maniscalco, Guillermo Garc'ia-P'erez
Fermion-to-qubit mappings are used to represent fermionic modes on quantum computers, an essential first step in many quantum algorithms for electronic structure calculations. In this work, we present a formalism to design flexible fermion-to-qubit mappings from ternary trees. We discuss in an intuitive manner the connection between the generating trees' structure and certain properties of the resulting mapping, such as Pauli weight and the delocalisation of mode occupation. Moreover, we introduce a recipe that guarantees Fock basis states are mapped to computational basis states in qubit space, a desirable property for many applications in quantum computing. Based on this formalism, we introduce the Bonsai algorithm, which takes as input the potentially limited topology of the qubit connectivity of a quantum device and returns a tailored fermion-to-qubit mapping that reduces the SWAP overhead with respect to other paradigmatic mappings. We illustrate the algorithm by producing mappings for the heavy-hexagon topology widely used in IBM quantum computers. The resulting mappings have a favourable Pauli weight scaling $mathcal{O}(sqrt{N})$ on this connectivity, while ensuring that no SWAP gates are necessary for single excitation operations.
{"title":"Bonsai Algorithm: Grow Your Own Fermion-to-Qubit Mappings","authors":"A. Miller, Zolt'an Zimbor'as, S. Knecht, S. Maniscalco, Guillermo Garc'ia-P'erez","doi":"10.1103/PRXQuantum.4.030314","DOIUrl":"https://doi.org/10.1103/PRXQuantum.4.030314","url":null,"abstract":"Fermion-to-qubit mappings are used to represent fermionic modes on quantum computers, an essential first step in many quantum algorithms for electronic structure calculations. In this work, we present a formalism to design flexible fermion-to-qubit mappings from ternary trees. We discuss in an intuitive manner the connection between the generating trees' structure and certain properties of the resulting mapping, such as Pauli weight and the delocalisation of mode occupation. Moreover, we introduce a recipe that guarantees Fock basis states are mapped to computational basis states in qubit space, a desirable property for many applications in quantum computing. Based on this formalism, we introduce the Bonsai algorithm, which takes as input the potentially limited topology of the qubit connectivity of a quantum device and returns a tailored fermion-to-qubit mapping that reduces the SWAP overhead with respect to other paradigmatic mappings. We illustrate the algorithm by producing mappings for the heavy-hexagon topology widely used in IBM quantum computers. The resulting mappings have a favourable Pauli weight scaling $mathcal{O}(sqrt{N})$ on this connectivity, while ensuring that no SWAP gates are necessary for single excitation operations.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41922221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-15DOI: 10.1103/PRXQuantum.4.020334
Arthur J. Parzygnat, J. Fullwood
Bayes' rule $mathbb{P}(B|A)mathbb{P}(A)=mathbb{P}(A|B)mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical inference. Many attempts have been made to extend this rule to quantum systems, the significance of which we are only beginning to understand. In this work, we develop a systematic framework for defining Bayes' rule in the quantum setting, and we show that a vast majority of the proposed quantum Bayes' rules appearing in the literature are all instances of our definition. Moreover, our Bayes' rule is based upon a simple relationship between the notions of state over time and a time-reversal symmetry map, both of which are introduced here.
{"title":"From Time-Reversal Symmetry to Quantum Bayes’ Rules","authors":"Arthur J. Parzygnat, J. Fullwood","doi":"10.1103/PRXQuantum.4.020334","DOIUrl":"https://doi.org/10.1103/PRXQuantum.4.020334","url":null,"abstract":"Bayes' rule $mathbb{P}(B|A)mathbb{P}(A)=mathbb{P}(A|B)mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical inference. Many attempts have been made to extend this rule to quantum systems, the significance of which we are only beginning to understand. In this work, we develop a systematic framework for defining Bayes' rule in the quantum setting, and we show that a vast majority of the proposed quantum Bayes' rules appearing in the literature are all instances of our definition. Moreover, our Bayes' rule is based upon a simple relationship between the notions of state over time and a time-reversal symmetry map, both of which are introduced here.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62088121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-08DOI: 10.1103/PRXQuantum.4.030327
Laurin E. Fischer, A. Chiesa, F. Tacchino, D. Egger, S. Carretta, I. Tavernelli
Gate-based quantum computers typically encode and process information in two-dimensional units called qubits. Using $d$-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction. In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond $99%$ in the $d=4$ case of ququarts with realistic experimental parameters. Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives. As proof-of-concept applications, we numerically demonstrate the synthesis of ${rm SU}(16)$ gates for noisy quantum hardware and an embedded error correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise. We conclude that universal qudit control -- a valuable extension to the operational toolbox of superconducting quantum information processing -- is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.
{"title":"Universal Qudit Gate Synthesis for Transmons","authors":"Laurin E. Fischer, A. Chiesa, F. Tacchino, D. Egger, S. Carretta, I. Tavernelli","doi":"10.1103/PRXQuantum.4.030327","DOIUrl":"https://doi.org/10.1103/PRXQuantum.4.030327","url":null,"abstract":"Gate-based quantum computers typically encode and process information in two-dimensional units called qubits. Using $d$-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction. In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond $99%$ in the $d=4$ case of ququarts with realistic experimental parameters. Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives. As proof-of-concept applications, we numerically demonstrate the synthesis of ${rm SU}(16)$ gates for noisy quantum hardware and an embedded error correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise. We conclude that universal qudit control -- a valuable extension to the operational toolbox of superconducting quantum information processing -- is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42367027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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