Pub Date : 2024-09-05DOI: 10.1103/prxquantum.5.030345
Tao Zhang, Zhihao Chi, Jiazhong Hu
We propose an efficient yet simple protocol to generate arbitrary symmetric entangled states with only global single-qubit rotations in a torn Hilbert space. The system is based on spin-1/2 qubits in a resonator such as atoms in an optical cavity or superconducting qubits coupled to a main bus. By sending light or microwave into the resonator, it induces ac Stark shifts on particular angular-momentum eigenstates (Dicke states) of qubits. Then we are able to generate barriers that hinder transitions between adjacent Dicke states and tear the original Hilbert space into pieces. Therefore, a simple global single-qubit rotation becomes highly nontrivial, and thus generates entanglement among the many-body system. By optimal control of energy shifts on Dicke states, we are able to generate arbitrary symmetric entangled states. We also exemplify that we can create varieties of useful states with near-unity fidelities in only one or very few steps, including W states, spin-squeezed states (SSSs), and Greenberger-Horne-Zeilinger states. Particularly, the SSS can be created by only one step with a squeezing parameter approaching the Heisenberg limit. Our finding establishes a way for universal entanglement generations with only single-qubit drivings where all the multiple-qubit controls are integrated into simply switching on or off microwave. It has direct applications in the variational quantum optimizer, which is available with existing technology.
我们提出了一种高效而简单的协议，只需在撕裂的希尔伯特空间中进行全局单量子比特旋转，就能生成任意对称的纠缠态。该系统基于共振器中的自旋-1/2 量子位，例如光腔中的原子或耦合到主总线上的超导量子位。通过向谐振器发送光或微波，可在量子比特的特定角动量特征态（迪克态）上诱发交流斯塔克偏移。然后，我们就能产生障碍，阻碍相邻 Dicke 状态之间的转换，并将原始的希尔伯特空间撕成碎片。因此，简单的全局单量子比特旋转变得非常不简单，从而在多体系统之间产生纠缠。通过对 Dicke 状态能量移动的优化控制，我们能够生成任意对称的纠缠状态。我们还举例说明，只需一步或极少几步，我们就能产生各种有用的、保真度接近统一的状态，包括 W 状态、自旋挤压状态（SSS）和格林伯格-霍恩-蔡林格状态。特别是，SSS 只需一步就能产生，其挤压参数ξR2∼1/N0.843 接近海森堡极限。我们的发现确立了一种只用单量子比特驱动就能产生普遍纠缠的方法，在这种方法中，所有多量子比特控制都被集成到了简单的微波开关中。它可直接应用于现有技术的可变量子优化器。
{"title":"Entanglement Generation via Single-Qubit Rotations in a Torn Hilbert Space","authors":"Tao Zhang, Zhihao Chi, Jiazhong Hu","doi":"10.1103/prxquantum.5.030345","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030345","url":null,"abstract":"We propose an efficient yet simple protocol to generate arbitrary symmetric entangled states with only global single-qubit rotations in a torn Hilbert space. The system is based on spin-1/2 qubits in a resonator such as atoms in an optical cavity or superconducting qubits coupled to a main bus. By sending light or microwave into the resonator, it induces ac Stark shifts on particular angular-momentum eigenstates (Dicke states) of qubits. Then we are able to generate barriers that hinder transitions between adjacent Dicke states and tear the original Hilbert space into pieces. Therefore, a simple global single-qubit rotation becomes highly nontrivial, and thus generates entanglement among the many-body system. By optimal control of energy shifts on Dicke states, we are able to generate arbitrary symmetric entangled states. We also exemplify that we can create varieties of useful states with near-unity fidelities in only one or very few steps, including W states, spin-squeezed states (SSSs), and Greenberger-Horne-Zeilinger states. Particularly, the SSS can be created by only one step with a squeezing parameter <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>ξ</mi><mi>R</mi><mn>2</mn></msubsup><mo>∼</mo><mn>1</mn><mo>/</mo><msup><mi>N</mi><mrow><mn>0.843</mn></mrow></msup></math> approaching the Heisenberg limit. Our finding establishes a way for universal entanglement generations with only single-qubit drivings where all the multiple-qubit controls are integrated into simply switching on or off microwave. It has direct applications in the variational quantum optimizer, which is available with existing technology.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223470","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 : 2024-09-04DOI: 10.1103/prxquantum.5.030344
Kevin C. Smith, Abid Khan, Bryan K. Clark, S.M. Girvin, Tzu-Chieh Wei
Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith et al., PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states.
{"title":"Constant-Depth Preparation of Matrix Product States with Adaptive Quantum Circuits","authors":"Kevin C. Smith, Abid Khan, Bryan K. Clark, S.M. Girvin, Tzu-Chieh Wei","doi":"10.1103/prxquantum.5.030344","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030344","url":null,"abstract":"Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith <i>et al.</i>, PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"54 71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176517","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 : 2024-09-03DOI: 10.1103/prxquantum.5.030343
Michael Zurel, Cihan Okay, Robert Raussendorf
A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number of magic states, the number of bits that describe the quantum system at any given time is .
最近推出的一种经典模拟方法是通过对概率函数的重复采样来实现具有神奇状态的通用量子计算[M. Zurel 等人，PRL 260404 (2020)]。这种方法与基于维格纳函数的采样算法密切相关，但有一个重要区别，即维格纳函数的负值会阻碍采样。事实上，维格纳函数的负值被认为是量子提速的先决条件。然而，在目前的经典模拟方法中，准概率函数的负值从未出现过。这个模型对所有量子计算都保持了概率性。本文分析了模拟程序必须跟踪的经典数据量。我们发现，这个数量很小。具体来说，对于任意数量的 n 个神奇状态，在任何给定时间内描述量子系统的比特数为 2n2+O(n)。
{"title":"Simulating Quantum Computation: How Many “Bits” for “It”?","authors":"Michael Zurel, Cihan Okay, Robert Raussendorf","doi":"10.1103/prxquantum.5.030343","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030343","url":null,"abstract":"A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel <i>et al.</i> PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>n</mi></math> of magic states, the number of bits that describe the quantum system at any given time is <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>O</mi><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math>.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176545","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 : 2024-08-28DOI: 10.1103/prxquantum.5.030342
Jie-Yu Zhang, Meng-Yuan Li, Peng Ye
In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications, such as secret-sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., linelike subsystems in the two-dimensional cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is mixed-subsystem SPT that has either fractal and linelike subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is chaotic-subsystem SPT in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in a square lattice can be locally simulated by an HOCA-generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call multi point strange correlators. We propose a universal procedure to design the spatial configuration of the multi point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long-range behavior in a short-range entangled state. Our HOCA approaches and multi point strange correlators pave the way for a unified paradigm to design, classify, and detect phases of matter with symmetries supported on a great variety of subsystems, and also provide potential useful perspective in surpassing the computational irreducibility of HOCA in a quantum mechanical way.
{"title":"Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi Point Strange Correlators","authors":"Jie-Yu Zhang, Meng-Yuan Li, Peng Ye","doi":"10.1103/prxquantum.5.030342","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030342","url":null,"abstract":"In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications, such as secret-sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., linelike subsystems in the two-dimensional cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is <i>mixed-subsystem SPT</i> that has either fractal and linelike subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is <i>chaotic-subsystem SPT</i> in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in a square lattice can be locally simulated by an HOCA-generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call <i>multi point strange correlators</i>. We propose a universal procedure to design the spatial configuration of the multi point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long-range behavior in a short-range entangled state. Our HOCA approaches and multi point strange correlators pave the way for a unified paradigm to design, classify, and detect phases of matter with symmetries supported on a great variety of subsystems, and also provide potential useful perspective in surpassing the computational irreducibility of HOCA in a quantum mechanical way.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176518","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 : 2024-08-27DOI: 10.1103/prxquantum.5.030341
Mallika T. Randeria, Thomas M. Hazard, Agustin Di Paolo, Kate Azar, Max Hays, Leon Ding, Junyoung An, Michael Gingras, Bethany M. Niedzielski, Hannah Stickler, Jeffrey A. Grover, Jonilyn L. Yoder, Mollie E. Schwartz, William D. Oliver, Kyle Serniak
Phase slips occur across all Josephson junctions (JJs) at a rate that increases with the impedance of the junction. In superconducting qubits composed of JJ-array superinductors—such as fluxonium—phase slips in the array can lead to decoherence. In particular, phase-slip processes at the individual array junctions can coherently interfere, each with an Aharonov-Casher phase that depends on the offset charges of the array islands. These coherent quantum phase slips (CQPS) perturbatively modify the qubit frequency, and therefore charge noise on the array islands will lead to dephasing. By varying the impedance of the array junctions, we design a set of fluxonium qubits in which the expected phase-slip rate within the JJ array changes by several orders of magnitude. We characterize the coherence times of these qubits and demonstrate that the scaling of CQPS-induced dephasing rates agrees with our theoretical model. Furthermore, we perform noise spectroscopy of two qubits in regimes dominated by either CQPS or flux noise. We find that the noise power spectrum associated with CQPS dephasing appears to be featureless at low frequencies and not . Numerical simulations indicate that this behavior is consistent with charge noise generated by charge-parity fluctuations within the array. Our findings broadly inform JJ-array-design trade-offs, relevant for the numerous superconducting-qubit designs employing JJ-array superinductors.
{"title":"Dephasing in Fluxonium Qubits from Coherent Quantum Phase Slips","authors":"Mallika T. Randeria, Thomas M. Hazard, Agustin Di Paolo, Kate Azar, Max Hays, Leon Ding, Junyoung An, Michael Gingras, Bethany M. Niedzielski, Hannah Stickler, Jeffrey A. Grover, Jonilyn L. Yoder, Mollie E. Schwartz, William D. Oliver, Kyle Serniak","doi":"10.1103/prxquantum.5.030341","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030341","url":null,"abstract":"Phase slips occur across all Josephson junctions (JJs) at a rate that increases with the impedance of the junction. In superconducting qubits composed of JJ-array superinductors—such as fluxonium—phase slips in the array can lead to decoherence. In particular, phase-slip processes at the individual array junctions can coherently interfere, each with an Aharonov-Casher phase that depends on the offset charges of the array islands. These coherent quantum phase slips (CQPS) perturbatively modify the qubit frequency, and therefore charge noise on the array islands will lead to dephasing. By varying the impedance of the array junctions, we design a set of fluxonium qubits in which the expected phase-slip rate within the JJ array changes by several orders of magnitude. We characterize the coherence times of these qubits and demonstrate that the scaling of CQPS-induced dephasing rates agrees with our theoretical model. Furthermore, we perform noise spectroscopy of two qubits in regimes dominated by either CQPS or flux noise. We find that the noise power spectrum associated with CQPS dephasing appears to be featureless at low frequencies and not <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>/</mo><mi>f</mi></math>. Numerical simulations indicate that this behavior is consistent with charge noise generated by charge-parity fluctuations within the array. Our findings broadly inform JJ-array-design trade-offs, relevant for the numerous superconducting-qubit designs employing JJ-array superinductors.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"132 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176566","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 : 2024-08-26DOI: 10.1103/prxquantum.5.030340
Jesús Cobos, David F. Locher, Alejandro Bermudez, Markus Müller, Enrique Rico
We propose a novel variational ansatz for the ground-state preparation of the lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve precision in energy in both the confined and deconfined phase of the LGT. We benchmark our proposal against the unitary Hamiltonian variational ansatz showing a reduction in the required number of variational layers to achieve a target precision. After performing a finite-size scaling analysis, we show that our dissipative variational ansatz can predict accurate critical exponents without requiring a number of layers that scales with the system size, which is the standard situation for unitary ansätze. Furthermore, we investigate the performance of this variational eigensolver subject to circuit-level noise, determining variational error thresholds that fix the error rate below which it would be beneficial to increase the number of layers. In light of these quantities and for typical gate errors in current quantum processors, we provide a detailed assessment of the prospects of our scheme to explore the LGT on near-term devices.
{"title":"Noise-Aware Variational Eigensolvers: A Dissipative Route for Lattice Gauge Theories","authors":"Jesús Cobos, David F. Locher, Alejandro Bermudez, Markus Müller, Enrique Rico","doi":"10.1103/prxquantum.5.030340","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030340","url":null,"abstract":"We propose a novel variational ansatz for the ground-state preparation of the <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"double-struck\">Z</mi></mrow><mn>2</mn></msub></math> lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>></mo><mn>99</mn><mi mathvariant=\"normal\">%</mi></math> precision in energy in both the confined and deconfined phase of the <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"double-struck\">Z</mi></mrow><mn>2</mn></msub></math> LGT. We benchmark our proposal against the unitary Hamiltonian variational ansatz showing a reduction in the required number of variational layers to achieve a target precision. After performing a finite-size scaling analysis, we show that our dissipative variational ansatz can predict accurate critical exponents without requiring a number of layers that scales with the system size, which is the standard situation for unitary ansätze. Furthermore, we investigate the performance of this variational eigensolver subject to circuit-level noise, determining variational error thresholds that fix the error rate below which it would be beneficial to increase the number of layers. In light of these quantities and for typical gate errors <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math> in current quantum processors, we provide a detailed assessment of the prospects of our scheme to explore the <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi mathvariant=\"double-struck\">Z</mi></mrow><mn>2</mn></msub></math> LGT on near-term devices.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176563","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 : 2024-08-22DOI: 10.1103/prxquantum.5.030339
Elisa Bäumer, Vinay Tripathi, Derek S. Wang, Patrick Rall, Edward H. Chen, Swarnadeep Majumder, Alireza Seif, Zlatko K. Minev
Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by nonunitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: controlled-not gate teleportation between up to 101 qubits by feeding forward 99 midcircuit measurement outcomes, and the preparation of Greenberger–Horne–Zeilinger states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices.
{"title":"Efficient Long-Range Entanglement Using Dynamic Circuits","authors":"Elisa Bäumer, Vinay Tripathi, Derek S. Wang, Patrick Rall, Edward H. Chen, Swarnadeep Majumder, Alireza Seif, Zlatko K. Minev","doi":"10.1103/prxquantum.5.030339","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030339","url":null,"abstract":"Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by nonunitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: controlled-<span>not</span> gate teleportation between up to 101 qubits by feeding forward 99 midcircuit measurement outcomes, and the preparation of Greenberger–Horne–Zeilinger states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223471","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 : 2024-08-21DOI: 10.1103/prxquantum.5.030338
Vittorio Vitale, Aniket Rath, Petar Jurcevic, Andreas Elben, Cyril Branciard, Benoît Vermersch
We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that converge to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust regarding drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement. Then we prepare the ground state of the transverse-field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by our increasing the circuit depth.
{"title":"Robust Estimation of the Quantum Fisher Information on a Quantum Processor","authors":"Vittorio Vitale, Aniket Rath, Petar Jurcevic, Andreas Elben, Cyril Branciard, Benoît Vermersch","doi":"10.1103/prxquantum.5.030338","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030338","url":null,"abstract":"We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that <i>converge</i> to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust regarding drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement. Then we prepare the ground state of the transverse-field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by our increasing the circuit depth.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"385 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176564","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 : 2024-08-20DOI: 10.1103/prxquantum.5.030337
M. Hinderling, S.C. ten Kate, D.Z. Haxell, M. Coraiola, S. Paredes, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, D. Sabonis, F. Nichele
The properties of superconducting devices depend sensitively on the parity (even or odd) of the quasiparticles that they contain. Encoding quantum information in the parity degree of freedom is central in several emerging solid-state qubit architectures, including in hybrid superconductor-semiconductor devices. In the latter case, accurate, nondestructive, and time-resolved parity measurements are a challenging issue. Here, we report on control and real-time parity measurement in a superconducting island embedded in a superconducting loop and realized in a hybrid two-dimensional heterostructure using a microwave resonator. To avoid microwave losses impeding time-resolved measurements, the device and readout resonator are located on separate chips, connected via flip-chip bonding, and couple inductively through vacuum. The superconducting resonator detects the parity-dependent circuit inductance, allowing for fast parity readout. We have resolved even- and odd-parity states with a signal-to-noise ratio of for an integration time of and a detection fidelity exceeding . The real-time parity measurement shows a state lifetime extending into the millisecond range. Our approach will lead to a better understanding of coherence-limiting mechanisms in superconducting quantum hardware and help to advance inductive-readout schemes for hybrid qubits.
{"title":"Flip-Chip-Based Fast Inductive Parity Readout of a Planar Superconducting Island","authors":"M. Hinderling, S.C. ten Kate, D.Z. Haxell, M. Coraiola, S. Paredes, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, D. Sabonis, F. Nichele","doi":"10.1103/prxquantum.5.030337","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030337","url":null,"abstract":"The properties of superconducting devices depend sensitively on the parity (even or odd) of the quasiparticles that they contain. Encoding quantum information in the parity degree of freedom is central in several emerging solid-state qubit architectures, including in hybrid superconductor-semiconductor devices. In the latter case, accurate, nondestructive, and time-resolved parity measurements are a challenging issue. Here, we report on control and real-time parity measurement in a superconducting island embedded in a superconducting loop and realized in a hybrid two-dimensional heterostructure using a microwave resonator. To avoid microwave losses impeding time-resolved measurements, the device and readout resonator are located on separate chips, connected via flip-chip bonding, and couple inductively through vacuum. The superconducting resonator detects the parity-dependent circuit inductance, allowing for fast parity readout. We have resolved even- and odd-parity states with a signal-to-noise ratio of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>SNR</mi><mo>≈</mo><mn>3</mn></math> for an integration time of <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>20</mn><mspace width=\"0.2em\"></mspace><mtext fontfamily=\"times\">μ</mtext><mrow><mi mathvariant=\"normal\">s</mi></mrow></math> and a detection fidelity exceeding <math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>98</mn><mi mathvariant=\"normal\">%</mi></math>. The real-time parity measurement shows a state lifetime extending into the millisecond range. Our approach will lead to a better understanding of coherence-limiting mechanisms in superconducting quantum hardware and help to advance inductive-readout schemes for hybrid qubits.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176565","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}
We use a bulk acoustic wave resonator to demonstrate coherent control of the excited orbital states in a diamond nitrogen-vacancy () center at cryogenic temperature. Coherent quantum control is an essential tool for understanding and mitigating decoherence. Moreover, characterizing and controlling orbital states is a central challenge for quantum networking, where optical coherence is tied to orbital coherence. We study resonant multiphonon orbital Rabi oscillations in both the frequency and time domain, extracting the strength of the orbital-phonon interactions and the coherence of the acoustically driven orbital states. We reach the strong-driving limit, where the physics is dominated by the coupling induced by the acoustic waves. We find agreement between our measurements, quantum master-equation simulations, and a Landau-Zener transition model in the strong-driving limit. Using perturbation theory, we derive an expression for the orbital Rabi frequency versus the acoustic drive strength that is nonperturbative in the drive strength and agrees well with our measurements for all acoustic powers. Motivated by continuous-wave spin-resonance-based decoherence protection schemes, we model the orbital decoherence and find good agreement between our model and our measured few-to-several-nanoseconds orbital decoherence times. We discuss the outlook for orbital decoherence protection.
{"title":"Coherent Acoustic Control of Defect Orbital States in the Strong-Driving Limit","authors":"B.A. McCullian, V. Sharma, H.Y. Chen, J.C. Crossman, E.J. Mueller, G.D. Fuchs","doi":"10.1103/prxquantum.5.030336","DOIUrl":"https://doi.org/10.1103/prxquantum.5.030336","url":null,"abstract":"We use a bulk acoustic wave resonator to demonstrate coherent control of the excited orbital states in a diamond nitrogen-vacancy (<math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>N</mtext></math><math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">V</mi></mrow></math>) center at cryogenic temperature. Coherent quantum control is an essential tool for understanding and mitigating decoherence. Moreover, characterizing and controlling orbital states is a central challenge for quantum networking, where optical coherence is tied to orbital coherence. We study resonant multiphonon orbital Rabi oscillations in both the frequency and time domain, extracting the strength of the orbital-phonon interactions and the coherence of the acoustically driven orbital states. We reach the strong-driving limit, where the physics is dominated by the coupling induced by the acoustic waves. We find agreement between our measurements, quantum master-equation simulations, and a Landau-Zener transition model in the strong-driving limit. Using perturbation theory, we derive an expression for the orbital Rabi frequency versus the acoustic drive strength that is nonperturbative in the drive strength and agrees well with our measurements for all acoustic powers. Motivated by continuous-wave spin-resonance-based decoherence protection schemes, we model the orbital decoherence and find good agreement between our model and our measured few-to-several-nanoseconds orbital decoherence times. We discuss the outlook for orbital decoherence protection.","PeriodicalId":501296,"journal":{"name":"PRX Quantum","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176567","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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