Pub Date : 2024-05-20DOI: 10.1103/prxquantum.5.020338
Ken Xuan Wei, Isaac Lauer, Emily Pritchett, William Shanks, David C. McKay, Ali Javadi-Abhari
Fixed-frequency superconducting qubits demonstrate remarkable success as platforms for stable and scalable quantum computing. Cross-resonance gates have been the workhorse of fixed-coupling, fixed-frequency superconducting processors, leveraging the entanglement generated by driving one qubit resonantly with a neighbor’s frequency to achieve high-fidelity, universal controlled-not (cnot) gates. Here, we use on-resonant and off-resonant microwave drives to go beyond cross-resonance, realizing natively interesting two-qubit gates that are not equivalent to cnot gates. In particular, we implement and benchmark native swap, swap, , and swap gates; in fact, any unitary can be achieved using these techniques. Furthermore, we apply these techniques for an efficient construction of the gate: a perfect entangler from which any two-qubit gate can be reached in only two applications. We show that these native two-qubit gates are better than their counterparts compiled from cross-resonance gates. We elucidate the resonance conditions required to drive each two-qubit gate and provide a novel frame tracking technique to implement them in Qiskit.
{"title":"Native Two-Qubit Gates in Fixed-Coupling, Fixed-Frequency Transmons Beyond Cross-Resonance Interaction","authors":"Ken Xuan Wei, Isaac Lauer, Emily Pritchett, William Shanks, David C. McKay, Ali Javadi-Abhari","doi":"10.1103/prxquantum.5.020338","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020338","url":null,"abstract":"Fixed-frequency superconducting qubits demonstrate remarkable success as platforms for stable and scalable quantum computing. Cross-resonance gates have been the workhorse of fixed-coupling, fixed-frequency superconducting processors, leveraging the entanglement generated by driving one qubit resonantly with a neighbor’s frequency to achieve high-fidelity, universal controlled-<span>not</span> (<span>cnot</span>) gates. Here, we use on-resonant and off-resonant microwave drives to go beyond cross-resonance, realizing natively interesting two-qubit gates that are not equivalent to <span>cnot</span> gates. In particular, we implement and benchmark native <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>i</mi></math><span>swap</span>, <span>swap</span>, <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mi>i</mi><mrow><mstyle mathsize=\"0.85em\"><mi>SWAP</mi></mstyle></mrow></msqrt></math>, and <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>b</mi></math><span>swap</span> gates; in fact, any <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>SU</mi><mo stretchy=\"false\">(</mo><mn>4</mn><mo stretchy=\"false\">)</mo></math> unitary can be achieved using these techniques. Furthermore, we apply these techniques for an efficient construction of the <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>B</mi></math> gate: a perfect entangler from which any two-qubit gate can be reached in only two applications. We show that these native two-qubit gates are better than their counterparts compiled from cross-resonance gates. We elucidate the resonance conditions required to drive each two-qubit gate and provide a novel frame tracking technique to implement them in Qiskit.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148287","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 : 2024-05-17DOI: 10.1103/prxquantum.5.020337
Cameron Calcluth, Nicolas Reichel, Alessandro Ferraro, Giulia Ferrini
Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained elusive. We address this gap by focusing on promoting circuits that are otherwise simulatable to computational universality. The class of simulatable, albeit non-Gaussian, circuits that we consider is composed of Gottesman-Kitaev-Preskill (GKP) states, Gaussian operations, and homodyne measurements. Based on these circuits, we first introduce a general framework for mapping a continuous-variable state into a qubit state. Subsequently, we cast existing maps into this framework, including the modular and stabilizer subsystem decompositions. By combining these findings with established results for discrete-variable systems, we formulate a sufficient condition for achieving universal quantum computation. Leveraging this, we evaluate the computational resourcefulness of a variety of states, including Gaussian states, finite-squeezing GKP states, and cat states. Furthermore, our framework reveals that both the stabilizer subsystem decomposition and the modular subsystem decomposition (of position-symmetric states) can be constructed in terms of simulatable operations. This establishes a robust resource-theoretical foundation for employing these techniques to evaluate the logical content of a generic continuous-variable state, which can be of independent interest.
{"title":"Sufficient Condition for Universal Quantum Computation Using Bosonic Circuits","authors":"Cameron Calcluth, Nicolas Reichel, Alessandro Ferraro, Giulia Ferrini","doi":"10.1103/prxquantum.5.020337","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020337","url":null,"abstract":"Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained elusive. We address this gap by focusing on promoting circuits that are otherwise simulatable to computational universality. The class of simulatable, albeit non-Gaussian, circuits that we consider is composed of Gottesman-Kitaev-Preskill (GKP) states, Gaussian operations, and homodyne measurements. Based on these circuits, we first introduce a general framework for mapping a continuous-variable state into a qubit state. Subsequently, we cast existing maps into this framework, including the modular and stabilizer subsystem decompositions. By combining these findings with established results for discrete-variable systems, we formulate a sufficient condition for achieving universal quantum computation. Leveraging this, we evaluate the computational resourcefulness of a variety of states, including Gaussian states, finite-squeezing GKP states, and cat states. Furthermore, our framework reveals that both the stabilizer subsystem decomposition and the modular subsystem decomposition (of position-symmetric states) can be constructed in terms of simulatable operations. This establishes a robust resource-theoretical foundation for employing these techniques to evaluate the logical content of a generic continuous-variable state, which can be of independent interest.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060489","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 : 2024-05-16DOI: 10.1103/prxquantum.5.020336
Balint Pato, Theerapat Tansuwannont, Shilin Huang, Kenneth R. Brown
Lookup-table decoding is fast and distance preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup-table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup-table construction, the meet-in-the-middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separate - and -counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in an increase of more than an order of magnitude in the pseudothreshold for the hexagonal color code of distance 9, from to .
查找表解码速度快且能保持距离，因此对采用小距离量子纠错码的近期量子计算机体系结构很有吸引力。在这项工作中，我们开发了几种优化工具，它们有可能减少在 Calderbank-Shor-Steane （CSS）代码上使用查找表解码的旗帜容错量子纠错（FTQEC）所需的空间和时间开销。我们的技术包括紧凑型查找表结构、中间相遇技术、用于旗帜 FTQEC 的自适应时间解码、旗帜信息的经典处理技术以及单独的 X 和 Z 计数技术。我们通过对距离为 3、5、7 和 9 的六边形色码进行数值模拟，评估了这些工具在电路级噪声下的性能。综合所有工具，距离为 9 的六边形色码的伪阈值提高了一个数量级以上，从 (1.34±0.01)×10-4 提高到 (1.43±0.07)×10-3。
{"title":"Optimization Tools for Distance-Preserving Flag Fault-Tolerant Error Correction","authors":"Balint Pato, Theerapat Tansuwannont, Shilin Huang, Kenneth R. Brown","doi":"10.1103/prxquantum.5.020336","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020336","url":null,"abstract":"Lookup-table decoding is fast and distance preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup-table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup-table construction, the meet-in-the-middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separate <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>X</mi></math>- and <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Z</mi></math>-counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in an increase of more than an order of magnitude in the pseudothreshold for the hexagonal color code of distance 9, from <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><mn>1.34</mn><mo>±</mo><mn>0.01</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> to <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><mn>1.43</mn><mo>±</mo><mn>0.07</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060457","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 : 2024-05-15DOI: 10.1103/prxquantum.5.020335
Patryk Lipka-Bartosik, Christopher T. Chubb, Joseph M. Renes, Marco Tomamichel, Kamil Korzekwa
We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel mapping into with an error (measured by trace distance) and into exactly, for a large number . We derive second-order asymptotic expressions for the optimal transformation rate in the small-, moderate-, and large-deviation error regimes, as well as the zero-error regime, for an arbitrary pair of initial states and a commuting pair of final states. We also prove that for and given by thermal Gibbs states, the derived optimal transformation rates in the first three regimes can be attained by thermal operations. This allows us, for the first time, to study the second-order asymptotics of thermodynamic state interconversion with fully general initial states that may have coherence between different energy eigenspaces. Thus, we discuss the optimal performance of thermodynamic protocols with coherent inputs and describe three novel resonance phenomena allowing one to significantly reduce transformation errors induced by fin
{"title":"Quantum Dichotomies and Coherent Thermodynamics beyond First-Order Asymptotics","authors":"Patryk Lipka-Bartosik, Christopher T. Chubb, Joseph M. Renes, Marco Tomamichel, Kamil Korzekwa","doi":"10.1103/prxquantum.5.020335","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020335","url":null,"abstract":"We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mi mathvariant=\"script\">E</mi></mrow></mrow></math> mapping <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>ρ</mi><mn>1</mn><mrow><mo>⊗</mo><mi>n</mi></mrow></msubsup></math> into <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>ρ</mi><mn>2</mn><mrow><mo>⊗</mo><msub><mi>R</mi><mi>n</mi></msub><mi>n</mi></mrow></msubsup></math> with an error <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>ϵ</mi><mi>n</mi></msub></math> (measured by trace distance) and <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>σ</mi><mn>1</mn><mrow><mo>⊗</mo><mi>n</mi></mrow></msubsup></math> into <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>σ</mi><mn>2</mn><mrow><mo>⊗</mo><msub><mi>R</mi><mi>n</mi></msub><mi>n</mi></mrow></msubsup></math> exactly, for a large number <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>n</mi></math>. We derive second-order asymptotic expressions for the optimal transformation rate <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>R</mi><mi>n</mi></msub></math> in the small-, moderate-, and large-deviation error regimes, as well as the zero-error regime, for an arbitrary pair <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><msub><mi>ρ</mi><mn>1</mn></msub><mo>,</mo><msub><mi>σ</mi><mn>1</mn></msub><mo stretchy=\"false\">)</mo></math> of initial states and a commuting pair <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><msub><mi>ρ</mi><mn>2</mn></msub><mo>,</mo><msub><mi>σ</mi><mn>2</mn></msub><mo stretchy=\"false\">)</mo></math> of final states. We also prove that for <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>σ</mi><mn>1</mn></msub></math> and <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>σ</mi><mn>2</mn></msub></math> given by thermal Gibbs states, the derived optimal transformation rates in the first three regimes can be attained by thermal operations. This allows us, for the first time, to study the second-order asymptotics of thermodynamic state interconversion with fully general initial states that may have coherence between different energy eigenspaces. Thus, we discuss the optimal performance of thermodynamic protocols with coherent inputs and describe three novel resonance phenomena allowing one to significantly reduce transformation errors induced by fin","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060460","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 : 2024-05-14DOI: 10.1103/prxquantum.5.020334
R.M. Goldblatt, A.M. Martin, A.A. Wood
The unpolarized spin environment surrounding a central spin qubit is typically considered as an incoherent source of dephasing, however, precise characterization and control of the spin bath can yield a resource for storing and sensing with quantum states. In this work, we use nitrogen-vacancy (NV) centers in diamond to measure the coherence of optically dark paramagnetic nitrogen defects (P1 centers) and detect coherent interactions between the P1 centers and a local bath of nuclear spins. The dipolar coupling between the P1 centers and nuclear spins is identified by signature periodic collapses and revivals in the P1 spin coherence signal. We then demonstrate, using a range of dynamical decoupling protocols, that the probing NV centers and the P1 spins are coupled to independent ensembles of nuclear spins. Our work illustrates how the optically dark P1 spins can be used to extract information from their local environment and offers new insight into the interactions within a many-body system.
{"title":"Sensing Coherent Nuclear Spin Dynamics with an Ensemble of Paramagnetic Nitrogen Spins","authors":"R.M. Goldblatt, A.M. Martin, A.A. Wood","doi":"10.1103/prxquantum.5.020334","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020334","url":null,"abstract":"The unpolarized spin environment surrounding a central spin qubit is typically considered as an incoherent source of dephasing, however, precise characterization and control of the spin bath can yield a resource for storing and sensing with quantum states. In this work, we use nitrogen-vacancy (NV) centers in diamond to measure the coherence of optically dark paramagnetic nitrogen defects (P1 centers) and detect coherent interactions between the P1 centers and a local bath of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi></mi><mn>13</mn></msup><mrow><mi mathvariant=\"normal\">C</mi></mrow></math> nuclear spins. The dipolar coupling between the P1 centers and <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi></mi><mn>13</mn></msup><mrow><mi mathvariant=\"normal\">C</mi></mrow></math> nuclear spins is identified by signature periodic collapses and revivals in the P1 spin coherence signal. We then demonstrate, using a range of dynamical decoupling protocols, that the probing NV centers and the P1 spins are coupled to independent ensembles of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi></mi><mn>13</mn></msup><mrow><mi mathvariant=\"normal\">C</mi></mrow></math> nuclear spins. Our work illustrates how the optically dark P1 spins can be used to extract information from their local environment and offers new insight into the interactions within a many-body system.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140928993","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 : 2024-05-13DOI: 10.1103/prxquantum.5.020333
Daniel K. Ruttley, Alexander Guttridge, Tom R. Hepworth, Simon L. Cornish
Control over the quantum states of individual molecules is crucial in the quest to harness their rich internal structure and dipolar interactions for applications in quantum science. In this paper, we develop a toolbox of techniques for the control and readout of individually trapped polar molecules in an array of optical tweezers. Starting with arrays of up to eight Rb and eight Cs atoms, we assemble arrays of RbCs molecules in their rovibrational and hyperfine ground state with an overall efficiency of 48(2)%. We demonstrate global microwave control of multiple rotational states of the molecules and use an auxiliary tweezer array to implement site-resolved addressing and state control. We show how the rotational state of the molecule can be mapped onto the position of Rb atoms and use this capability to readout multiple rotational states in a single experimental run. Further, using a scheme for the midsequence detection of molecule formation errors, we perform rearrangement of assembled molecules to prepare small defect-free arrays. Finally, we discuss a feasible route to scaling to larger arrays of molecules.
{"title":"Enhanced Quantum Control of Individual Ultracold Molecules Using Optical Tweezer Arrays","authors":"Daniel K. Ruttley, Alexander Guttridge, Tom R. Hepworth, Simon L. Cornish","doi":"10.1103/prxquantum.5.020333","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020333","url":null,"abstract":"Control over the quantum states of individual molecules is crucial in the quest to harness their rich internal structure and dipolar interactions for applications in quantum science. In this paper, we develop a toolbox of techniques for the control and readout of individually trapped polar molecules in an array of optical tweezers. Starting with arrays of up to eight Rb and eight Cs atoms, we assemble arrays of RbCs molecules in their rovibrational and hyperfine ground state with an overall efficiency of 48(2)%. We demonstrate global microwave control of multiple rotational states of the molecules and use an auxiliary tweezer array to implement site-resolved addressing and state control. We show how the rotational state of the molecule can be mapped onto the position of Rb atoms and use this capability to readout multiple rotational states in a single experimental run. Further, using a scheme for the midsequence detection of molecule formation errors, we perform rearrangement of assembled molecules to prepare small defect-free arrays. Finally, we discuss a feasible route to scaling to larger arrays of molecules.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140928659","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 : 2024-05-10DOI: 10.1103/prxquantum.5.020332
Zhiyan Ding, Xiantao Li, Lin Lin
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order.
{"title":"Simulating Open Quantum Systems Using Hamiltonian Simulations","authors":"Zhiyan Ding, Xiantao Li, Lin Lin","doi":"10.1103/prxquantum.5.020332","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020332","url":null,"abstract":"We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140928729","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 : 2024-05-09DOI: 10.1103/prxquantum.5.020331
Isaac Layton, Jonathan Oppenheim
The standard notion of a classical limit, represented schematically by , provides a method for approximating a quantum system by a classical one. In this work, we explain why the standard classical limit fails when applied to subsystems, and show how one may resolve this by explicitly modeling the decoherence of a subsystem by its environment. Denoting the decoherence time by , we demonstrate that a double scaling limit in which and such that the ratio remains fixed leads to an irreversible open-system evolution with well-defined classical and quantum subsystems. The main technical result is showing that, for arbitrary Hamiltonians, the generators of partial versions of the Wigner, Husimi, and Glauber-Sudarshan quasiprobability distributions may all be mapped in the above-mentioned double scaling limit to the same completely positive classical-quantum generator. This provides a regime in which one can study effective and consistent classical-quantum dynamics.
{"title":"The Classical-Quantum Limit","authors":"Isaac Layton, Jonathan Oppenheim","doi":"10.1103/prxquantum.5.020331","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020331","url":null,"abstract":"The standard notion of a classical limit, represented schematically by <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ℏ</mi><mo stretchy=\"false\">→</mo><mn>0</mn></math>, provides a method for approximating a quantum system by a classical one. In this work, we explain why the standard classical limit fails when applied to subsystems, and show how one may resolve this by explicitly modeling the decoherence of a subsystem by its environment. Denoting the decoherence time by <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>τ</mi></math>, we demonstrate that a double scaling limit in which <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ℏ</mi><mo stretchy=\"false\">→</mo><mn>0</mn></math> and <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>τ</mi><mo stretchy=\"false\">→</mo><mn>0</mn></math> such that the ratio <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>E</mi><mi>f</mi></msub><mo>=</mo><mi>ℏ</mi><mo>/</mo><mi>τ</mi></math> remains fixed leads to an irreversible open-system evolution with well-defined classical and quantum subsystems. The main technical result is showing that, for arbitrary Hamiltonians, the generators of partial versions of the Wigner, Husimi, and Glauber-Sudarshan quasiprobability distributions may all be mapped in the above-mentioned double scaling limit to the same completely positive classical-quantum generator. This provides a regime in which one can study effective and consistent classical-quantum dynamics.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140928813","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}
Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work, we present qSWIFT, a high-order randomized algorithm for Hamiltonian simulation. In qSWIFT, the required number of gates for a given precision is independent of the number of terms in the Hamiltonian, while the systematic error is exponentially reduced with regard to the order parameter. In this respect, our qSWIFT is a higher-order counterpart of the previously proposed quantum stochastic drift protocol (qDRIFT), the number of gates in which scales linearly with the inverse of the precision required. We construct the qSWIFT channel and establish a rigorous bound for the systematic error quantified by the diamond norm. qSWIFT provides an algorithm to estimate given physical quantities by using a system with one ancilla qubit, which is as simple as other product-formula-based approaches such as regular Trotter-Suzuki decompositions and qDRIFT. Our numerical experiment reveals that the required number of gates in qSWIFT is significantly reduced compared to qDRIFT. In particular, the advantage is significant for problems where high precision is required; e.g., to achieve a systematic relative propagation error of , the required number of gates in third-order qSWIFT is 1000 times smaller than that of qDRIFT.
{"title":"High-Order Randomized Compiler for Hamiltonian Simulation","authors":"Kouhei Nakaji, Mohsen Bagherimehrab, Alán Aspuru-Guzik","doi":"10.1103/prxquantum.5.020330","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020330","url":null,"abstract":"Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work, we present qSWIFT, a high-order randomized algorithm for Hamiltonian simulation. In qSWIFT, the required number of gates for a given precision is independent of the number of terms in the Hamiltonian, while the systematic error is exponentially reduced with regard to the order parameter. In this respect, our qSWIFT is a higher-order counterpart of the previously proposed quantum stochastic drift protocol (qDRIFT), the number of gates in which scales linearly with the inverse of the precision required. We construct the qSWIFT channel and establish a rigorous bound for the systematic error quantified by the diamond norm. qSWIFT provides an algorithm to estimate given physical quantities by using a system with one ancilla qubit, which is as simple as other product-formula-based approaches such as regular Trotter-Suzuki decompositions and qDRIFT. Our numerical experiment reveals that the required number of gates in qSWIFT is significantly reduced compared to qDRIFT. In particular, the advantage is significant for problems where high precision is required; e.g., to achieve a systematic relative propagation error of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, the required number of gates in third-order qSWIFT is 1000 times smaller than that of qDRIFT.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140928816","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 : 2024-05-07DOI: 10.1103/prxquantum.5.020329
Yakov Solomons, Roni Ben-Maimon, Ephraim Shahmoon
We develop a general framework for the analysis of two-sided quantum interfaces, composed of collections of atoms interacting with paraxial light. Accounting for photon-mediated dipole-dipole interactions, our approach is based on the mapping of collective atom-photon interfaces onto a generic one-dimensional model of light scattering, characterized by a reflectivity parameter . This entails two key practical advantages: (i) the efficiency of the quantum interface in performing various quantum tasks, such as quantum memory or entanglement generation, is universally given by and is hence reduced to a measurement or classical calculation of a reflectivity; (ii) the efficiency can be greatly enhanced by a properly designed photon mode that spatially matches a collective-dipole eigenmode of the atoms. We demonstrate our approach for realistic cases of finite-size atomic arrays, partially filled arrays, and circular arrays. This provides a unified approach for treating collective light-matter coupling in various platforms, such as optical lattices and optical tweezers.
{"title":"Universal Approach for Quantum Interfaces with Atomic Arrays","authors":"Yakov Solomons, Roni Ben-Maimon, Ephraim Shahmoon","doi":"10.1103/prxquantum.5.020329","DOIUrl":"https://doi.org/10.1103/prxquantum.5.020329","url":null,"abstract":"We develop a general framework for the analysis of two-sided quantum interfaces, composed of collections of atoms interacting with paraxial light. Accounting for photon-mediated dipole-dipole interactions, our approach is based on the mapping of collective atom-photon interfaces onto a generic one-dimensional model of light scattering, characterized by a reflectivity parameter <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>r</mi><mn>0</mn></msub></math>. This entails two key practical advantages: (i) the efficiency of the quantum interface in performing various quantum tasks, such as quantum memory or entanglement generation, is universally given by <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>r</mi><mn>0</mn></msub></math> and is hence reduced to a measurement or classical calculation of a reflectivity; (ii) the efficiency can be greatly enhanced by a properly designed photon mode that spatially matches a collective-dipole eigenmode of the atoms. We demonstrate our approach for realistic cases of finite-size atomic arrays, partially filled arrays, and circular arrays. This provides a unified approach for treating collective light-matter coupling in various platforms, such as optical lattices and optical tweezers.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885368","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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