The Programme Committee of TQC 2024 selected 92 out of 460 submissions for a contributed talk (20% acceptance rate).
You may find the contributed talks here.
The list of accepted posters will be published on the 2nd of May, after the poster notification date. The conference schedule will be published in July.
Note on the list: The talks are listed in alphabetical order of title. Later they will be listed by day of presentation. The topic tags were self-selected by the authors upon submission, given the options provided by the PC chairs.
1.
Jun Takahashi, Chaithanya Rayudu, Cunlu Zhou, Robbie King, Kevin Thompson, Ojas Parekh
An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum complexity theory, Simulation of quantum systems
@Talk{T24_437,
title = {An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut},
author = {Jun Takahashi and Chaithanya Rayudu and Cunlu Zhou and Robbie King and Kevin Thompson and Ojas Parekh},
year = {2024},
date = {2024-01-01},
abstract = {Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in particular the ``Quantum Max Cut'' (QMaxCut) problem, which is closely related to the antiferromagnetic Heisenberg model. In this work, we introduce a family of semidefinite programming (SDP) relaxations based on the Navascues-Pironio-Acin (NPA) hierarchy which is tailored for QMaxCut by taking into account its SU(2) symmetry. We show that the hierarchy converges to the optimal QMaxCut value at a finite level, which is based on a characterization of the algebra of SWAP operators. We give several analytic proofs and computational results showing exactness/inexactness of our hierarchy at the lowest level on several important families of graphs. We also discuss relationships between SDP approaches for QMaxCut and frustration-freeness in condensed matter physics and numerically demonstrate that the SDP-solvability practically becomes an efficiently-computable generalization of frustration-freeness. Furthermore, by numerical demonstration we show the potential of SDP algorithms to perform as an approximate method to compute physical quantities and capture physical features of some Heisenberg-type statistical mechanics models even away from the frustration-free regions.},
keywords = {Intersection of quantum information and condensed-matter theory, Quantum complexity theory, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in particular the ``Quantum Max Cut'' (QMaxCut) problem, which is closely related to the antiferromagnetic Heisenberg model. In this work, we introduce a family of semidefinite programming (SDP) relaxations based on the Navascues-Pironio-Acin (NPA) hierarchy which is tailored for QMaxCut by taking into account its SU(2) symmetry. We show that the hierarchy converges to the optimal QMaxCut value at a finite level, which is based on a characterization of the algebra of SWAP operators. We give several analytic proofs and computational results showing exactness/inexactness of our hierarchy at the lowest level on several important families of graphs. We also discuss relationships between SDP approaches for QMaxCut and frustration-freeness in condensed matter physics and numerically demonstrate that the SDP-solvability practically becomes an efficiently-computable generalization of frustration-freeness. Furthermore, by numerical demonstration we show the potential of SDP algorithms to perform as an approximate method to compute physical quantities and capture physical features of some Heisenberg-type statistical mechanics models even away from the frustration-free regions.
2.
Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang, Ke Wang
Efficient Optimal Control of Open Quantum Systems Talk
2024.
Abstract | Tags: Proceedings, Quantum algorithms, Quantum information theory, Simulation of quantum systems
@Talk{T24_423,
title = {Efficient Optimal Control of Open Quantum Systems},
author = {Wenhao He and Tongyang Li and Xiantao Li and Zecheng Li and Chunhao Wang and Ke Wang},
year = {2024},
date = {2024-01-01},
abstract = {The optimal control problem for open quantum systems can be formulated as a time- dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables. At the technical level, we provide the first (to the best of our knowledge) simulation al- gorithm for time-dependent Lindbladians with an ℓ1-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest},
keywords = {Proceedings, Quantum algorithms, Quantum information theory, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
The optimal control problem for open quantum systems can be formulated as a time- dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables. At the technical level, we provide the first (to the best of our knowledge) simulation al- gorithm for time-dependent Lindbladians with an ℓ1-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest
3.
Joshua Cudby, Sergii Strelchuk
Gaussian decomposition of magic states for matchgate computations Talk
2024.
Abstract | Tags: Simulation of quantum systems
@Talk{T24_33,
title = {Gaussian decomposition of magic states for matchgate computations},
author = {Joshua Cudby and Sergii Strelchuk},
year = {2024},
date = {2024-01-01},
abstract = {Magic states, pivotal for universal quantum computation via classically simulable Clifford gates, often undergo decomposition into resourceless stabilizer states, facilitating simulation through classical means. This approach yields three operationally significant metrics: stabilizer rank, fidelity, and extent. We extend these methods to encompass Matchgate circuits (MGCs). We begin with an investigation into the algebraic constraints defining Gaussian states, marking the first explicit characterisation of these states. The explicit description of Gaussian states is pivotal to our methods for tackling all the simulation tasks. Central to our inquiry is the concept of Gaussian rank – a pivotal metric defining the minimum terms required for decomposing a quantum state into Gaussian constituents. This metric holds paramount significance in determining the runtime of rank-based simulations for matchgate circuits featuring magic state inputs. The absence of low-rank decompositions presents a formidable computational hurdle, thereby prompting a deeper examination of fermionic magic states. We find that the Gaussian rank of 2 instances of our canonical magic state is 4 under symmetry-restricted decompositions. Additionally, our numerical analysis suggests the absence of low-rank decompositions for 2 or 3 copies of this magic state. Further, we explore the Gaussian extent, a convex metric offering an upper bound on the rank. We prove the Gaussian extent's multiplicative behaviour on 4-qubit systems, along with initial strides towards proving its sub-multiplicative nature in general settings. One important result in that direction we present is an upper bound on the Gaussian fidelity of generic states.},
keywords = {Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
Magic states, pivotal for universal quantum computation via classically simulable Clifford gates, often undergo decomposition into resourceless stabilizer states, facilitating simulation through classical means. This approach yields three operationally significant metrics: stabilizer rank, fidelity, and extent. We extend these methods to encompass Matchgate circuits (MGCs). We begin with an investigation into the algebraic constraints defining Gaussian states, marking the first explicit characterisation of these states. The explicit description of Gaussian states is pivotal to our methods for tackling all the simulation tasks. Central to our inquiry is the concept of Gaussian rank – a pivotal metric defining the minimum terms required for decomposing a quantum state into Gaussian constituents. This metric holds paramount significance in determining the runtime of rank-based simulations for matchgate circuits featuring magic state inputs. The absence of low-rank decompositions presents a formidable computational hurdle, thereby prompting a deeper examination of fermionic magic states. We find that the Gaussian rank of 2 instances of our canonical magic state is 4 under symmetry-restricted decompositions. Additionally, our numerical analysis suggests the absence of low-rank decompositions for 2 or 3 copies of this magic state. Further, we explore the Gaussian extent, a convex metric offering an upper bound on the rank. We prove the Gaussian extent's multiplicative behaviour on 4-qubit systems, along with initial strides towards proving its sub-multiplicative nature in general settings. One important result in that direction we present is an upper bound on the Gaussian fidelity of generic states.
4.
Sergey Bravyi, Natalie Parham, Minh Tran
Identity check problem for shallow quantum circuits Talk
2024.
Abstract | Tags: Other, Quantum information theory, Simulation of quantum systems
@Talk{T24_233,
title = {Identity check problem for shallow quantum circuits},
author = {Sergey Bravyi and Natalie Parham and Minh Tran},
year = {2024},
date = {2024-01-01},
abstract = {Checking whether two quantum circuits are approximately equivalent is a common task in quantum computing. We consider a closely related identity check problem: given a quantum circuit $U$, one has to estimate the diamond-norm distance between $U$ and the identity channel. We present a classical algorithm approximating the distance to the identity within a factor $alpha=D+1$ for shallow geometrically local $D$-dimensional circuits provided that the circuit is sufficiently close to the identity. The runtime of the algorithm scales linearly with the number of qubits for any constant circuit depth and spatial dimension. We also show that the operator-norm distance to the identity $|U-I|$ can be efficiently approximated within a factor $alpha=5$ for shallow 1D circuits and, under a certain technical condition, within a factor $alpha=2D+3$ for shallow $D$-dimensional circuits. A numerical implementation of the identity check algorithm is reported for 1D Trotter circuits with up to 100 qubits.},
keywords = {Other, Quantum information theory, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
Checking whether two quantum circuits are approximately equivalent is a common task in quantum computing. We consider a closely related identity check problem: given a quantum circuit $U$, one has to estimate the diamond-norm distance between $U$ and the identity channel. We present a classical algorithm approximating the distance to the identity within a factor $alpha=D+1$ for shallow geometrically local $D$-dimensional circuits provided that the circuit is sufficiently close to the identity. The runtime of the algorithm scales linearly with the number of qubits for any constant circuit depth and spatial dimension. We also show that the operator-norm distance to the identity $|U-I|$ can be efficiently approximated within a factor $alpha=5$ for shallow 1D circuits and, under a certain technical condition, within a factor $alpha=2D+3$ for shallow $D$-dimensional circuits. A numerical implementation of the identity check algorithm is reported for 1D Trotter circuits with up to 100 qubits.
5.
Daniel Stilck França, Cambyse Rouze, Álvaro Alhambra
Making both ends meet: from efficient simulation to universal quantum computing with quantum Gibbs sampling Talk
2024.
Abstract | Tags: Models of quantum computation, Quantum algorithms, Quantum information theory, Simulation of quantum systems
@Talk{T24_359,
title = {Making both ends meet: from efficient simulation to universal quantum computing with quantum Gibbs sampling},
author = {Daniel Stilck França and Cambyse Rouze and Álvaro Alhambra},
year = {2024},
date = {2024-01-01},
abstract = {The preparation of thermal states of matter is a crucial task in quantum simulation. In this work, we prove that an efficiently implementable dissipative evolution recently introduced by Chen et al. thermalizes into its equilibrium Gibbs state in time scaling polynomially with system size at high enough temperatures for any Hamiltonian that satisfies a Lieb-Robinson bound, such as local Hamiltonians on a lattice. Furthermore, we show the efficient adiabatic preparation of the associated purifications or ``thermofield double" states. To the best of our knowledge, these are the first results rigorously establishing the efficient preparation of high temperature Gibbs states and their purifications. In the low-temperature regime, we show that implementing this family of Lindbladians for inverse temperatures logarithmic in the system's size is polynomially equivalent to standard quantum computation. On a technical level, for high temperatures, our proof makes use of the mapping of the generator of the evolution into a Hamiltonian and the analysis of the stability of its gap. For low temperature, we instead perform a perturbation at zero temperature of the Laplace transform of the energy observable at fixed runtime, and resort to circuit-to-Hamiltonian mappings akin to the proof of universality of quantum adiabatic computing. Taken together, our results show that the family of Lindbladians of Chen et al. efficiently prepares a large class of quantum many-body states of interest, and have the potential to mirror the success of classical Monte Carlo methods for quantum many-body systems.},
keywords = {Models of quantum computation, Quantum algorithms, Quantum information theory, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
The preparation of thermal states of matter is a crucial task in quantum simulation. In this work, we prove that an efficiently implementable dissipative evolution recently introduced by Chen et al. thermalizes into its equilibrium Gibbs state in time scaling polynomially with system size at high enough temperatures for any Hamiltonian that satisfies a Lieb-Robinson bound, such as local Hamiltonians on a lattice. Furthermore, we show the efficient adiabatic preparation of the associated purifications or ``thermofield double" states. To the best of our knowledge, these are the first results rigorously establishing the efficient preparation of high temperature Gibbs states and their purifications. In the low-temperature regime, we show that implementing this family of Lindbladians for inverse temperatures logarithmic in the system's size is polynomially equivalent to standard quantum computation. On a technical level, for high temperatures, our proof makes use of the mapping of the generator of the evolution into a Hamiltonian and the analysis of the stability of its gap. For low temperature, we instead perform a perturbation at zero temperature of the Laplace transform of the energy observable at fixed runtime, and resort to circuit-to-Hamiltonian mappings akin to the proof of universality of quantum adiabatic computing. Taken together, our results show that the family of Lindbladians of Chen et al. efficiently prepares a large class of quantum many-body states of interest, and have the potential to mirror the success of classical Monte Carlo methods for quantum many-body systems.
6.
Antonio Anna Mele, Armando Angrisani, Soumik Ghosh, Sumeet Khatri, Jens Eisert, Daniel Stilck Franca, Yihui Quek
Noise-induced shallow circuits and absence of barren plateaus Talk
2024.
Abstract | Tags: Intersection of quantum information and machine learning, Other, Quantum complexity theory, Simulation of quantum systems
@Talk{T24_409,
title = {Noise-induced shallow circuits and absence of barren plateaus},
author = {Antonio Anna Mele and Armando Angrisani and Soumik Ghosh and Sumeet Khatri and Jens Eisert and Daniel Stilck Franca and Yihui Quek},
year = {2024},
date = {2024-01-01},
abstract = {We study the impact of non-unital noise on random quantum circuits, generalizing many previous results about the impact of noise on near-term computation that assumed that noise was unital or even specifically depolarizing. Non-unital noise (a class that includes amplitude damping noise and other loss processes) is a more natural noise model for certain physical platforms than unital noise. Yet it is analytically more challenging and has in the past led to starkly different conclusions about computational tasks, like error correction and random circuit sampling. Our main result is that non-unital noise ``truncates" deep random quantum circuits to effectively have logarithmic depth, in the task of computing Pauli expectation values. By way of proving this, we contribute a contraction result for quantum circuits under non-unital noise, which significantly strengthens all previous results in this setting. As an application, we show that circuits used for variational quantum algorithms, under non-unital noise, avoid the problem of barren plateaus for cost functions made of local observables. This is not necessarily good news, however, as their effective shallowness also makes such circuits vulnerable to classical simulators. Accordingly, we also provide an algorithm to estimate local expectation values in the presence of non-unital noise, that succeeds with high probability over the ensemble. The runtime of our algorithm is independent of both the number of qubits and circuit depth, and depends polynomially on the accuracy for one-dimensional architectures and quasi-polynomially for two-dimensional ones. While the hardness of sampling from random circuits under non–unital noise is yet unresolved, our results indicate that for the vast majority of quantum circuits under non-unital noise, we are unlikely to glean quantum advantage for algorithms that output expectation values.},
keywords = {Intersection of quantum information and machine learning, Other, Quantum complexity theory, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
We study the impact of non-unital noise on random quantum circuits, generalizing many previous results about the impact of noise on near-term computation that assumed that noise was unital or even specifically depolarizing. Non-unital noise (a class that includes amplitude damping noise and other loss processes) is a more natural noise model for certain physical platforms than unital noise. Yet it is analytically more challenging and has in the past led to starkly different conclusions about computational tasks, like error correction and random circuit sampling. Our main result is that non-unital noise ``truncates" deep random quantum circuits to effectively have logarithmic depth, in the task of computing Pauli expectation values. By way of proving this, we contribute a contraction result for quantum circuits under non-unital noise, which significantly strengthens all previous results in this setting. As an application, we show that circuits used for variational quantum algorithms, under non-unital noise, avoid the problem of barren plateaus for cost functions made of local observables. This is not necessarily good news, however, as their effective shallowness also makes such circuits vulnerable to classical simulators. Accordingly, we also provide an algorithm to estimate local expectation values in the presence of non-unital noise, that succeeds with high probability over the ensemble. The runtime of our algorithm is independent of both the number of qubits and circuit depth, and depends polynomially on the accuracy for one-dimensional architectures and quasi-polynomially for two-dimensional ones. While the hardness of sampling from random circuits under non–unital noise is yet unresolved, our results indicate that for the vast majority of quantum circuits under non-unital noise, we are unlikely to glean quantum advantage for algorithms that output expectation values.
7.
Joel Rajakumar, James Watson, Yi-Kai Liu
Polynomial-Time Classical Simulation of Noisy IQP Circuits after Constant Depth Talk
2024.
Abstract | Tags: Models of quantum computation, Quantum complexity theory, Simulation of quantum systems
@Talk{T24_82,
title = {Polynomial-Time Classical Simulation of Noisy IQP Circuits after Constant Depth},
author = {Joel Rajakumar and James Watson and Yi-Kai Liu},
year = {2024},
date = {2024-01-01},
abstract = {Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has become a leading candidate for testing the capabilities of quantum devices. Here we demonstrate that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, the output distribution can be efficiently sampled by a classical computer after a critical $O(1)$ depth. Unlike other simulation algorithms for quantum supremacy tasks, we do not require assumptions on the circuit's architecture, on anti-concentration properties, nor do we require $Ømega(łog(n))$ circuit depth. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit. Our results suggest that quantum supremacy experiments based on IQP circuits may be more susceptible to classical simulation than previously thought.},
keywords = {Models of quantum computation, Quantum complexity theory, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has become a leading candidate for testing the capabilities of quantum devices. Here we demonstrate that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, the output distribution can be efficiently sampled by a classical computer after a critical $O(1)$ depth. Unlike other simulation algorithms for quantum supremacy tasks, we do not require assumptions on the circuit's architecture, on anti-concentration properties, nor do we require $Ømega(łog(n))$ circuit depth. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit. Our results suggest that quantum supremacy experiments based on IQP circuits may be more susceptible to classical simulation than previously thought.
8.
Nicholas Rubin, Dominic Berry, Alina Kononov, Fionn Malone, Tanuj Khattar, Alec White, Joonho Lee, Hartmut Neven, Ryan Babbush, Andrew Baczewski
Quantum computation of stopping power for inertial fusion target design Talk
2024.
Abstract | Tags: Quantum algorithms, Simulation of quantum systems
@Talk{T24_124,
title = {Quantum computation of stopping power for inertial fusion target design},
author = {Nicholas Rubin and Dominic Berry and Alina Kononov and Fionn Malone and Tanuj Khattar and Alec White and Joonho Lee and Hartmut Neven and Ryan Babbush and Andrew Baczewski},
year = {2024},
date = {2024-01-01},
abstract = {Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it – one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quantum 2, 040332 2021], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with a novel implementation of a high-order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450.},
keywords = {Quantum algorithms, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it – one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quantum 2, 040332 2021], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with a novel implementation of a high-order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450.
9.
Yiyi Cai, Yu Tong, John Preskill
Stochastic error cancellation in analog quantum simulation Talk
2024.
Abstract | Tags: Proceedings, Simulation of quantum systems
@Talk{T24_58,
title = {Stochastic error cancellation in analog quantum simulation},
author = {Yiyi Cai and Yu Tong and John Preskill},
year = {2024},
date = {2024-01-01},
abstract = {Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian we want to simulate by small local perturbations, which are assumed to be random and unbiased. We analyze the error accumulated in observables in this setting and show that, due to stochastic error cancellation, with high probability the error scales as the square root of the number of qubits instead of linearly. We explore the concentration phenomenon of this error as well as its implications for local observables in the thermodynamic limit. Moreover, we show that stochastic error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise. This indicates that, to reach a certain fidelity, more noise can be tolerated than implied by the worst-case bound if the noise comes from many statistically independent sources.},
keywords = {Proceedings, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian we want to simulate by small local perturbations, which are assumed to be random and unbiased. We analyze the error accumulated in observables in this setting and show that, due to stochastic error cancellation, with high probability the error scales as the square root of the number of qubits instead of linearly. We explore the concentration phenomenon of this error as well as its implications for local observables in the thermodynamic limit. Moreover, we show that stochastic error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise. This indicates that, to reach a certain fidelity, more noise can be tolerated than implied by the worst-case bound if the noise comes from many statistically independent sources.
