Computations with greater Quantum depth are strictly more powerful (relative to an oracle)

Coudron, Matthew; Menda, Sanketh

doi:10.1145/3357713.3384269

Cited by 25 publications

(44 citation statements)

References 11 publications

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“…However, recently, Simon's algorithm was upgraded to a recursive version 34 , which was used to provide an example of an exponential separation between the computational power of quantum circuits (with access to a black box) of different depths. Another example of such a separation of the depth hierarchy was given in 35 . Interestingly, these results can be interpreted (with a little bit of translation work) into two other examples of exponential separations between coherent and incoherent QUALMs, albeit for tasks, which are quite contrived from a physics perspective.…”

Section: Discussionmentioning

confidence: 99%

Quantum algorithmic measurement

Aharonov

Cotler

2022

Nat Commun

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There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system’s Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.

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Section: Discussionmentioning

confidence: 99%

Quantum algorithmic measurement

Aharonov

Cotler

2022

Nat Commun

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“…[42] consider a problem on learning two spatially separated quantum states using local quantum learning algorithms and give an exponential separation between having a quantum or a classical communication channel between the local quantum learning algorithms. In [43,44], an exponential separation between two bounded-depth quantum learning algorithms are given for learning about an exponential-time quantum process.…”

Section: C6 Related Workmentioning

confidence: 99%

Quantum advantage in learning from experiments

Huang,

Broughton,

Cotler

et al. 2021

Preprint

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Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature.

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“…This inspires a line of studies [51,56,62,29,52] on parallel quantum query algorithms and complexity bounds. The low-depth (parallel) quantum circuit classes are also studied (see e.g., [54,81,53,95,47,61,17,94,44,34,63]), amongst which one surprising result is a quantum advantage established by constant-depth quantum circuits over their classical counterparts [25,96,70,26].…”

Section: Introductionmentioning

confidence: 99%

Parallel Quantum Algorithm for Hamiltonian Simulation

Zhang¹,

Wang

Ying

2021

Preprint

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We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including various Hamiltonians of practical interest like local Hamiltonians and Pauli sums. Given the oracle access to the target sparse Hamiltonian, in both query and gate complexity, the running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence polylog log(1/ǫ) on the simulation precision ǫ. This presents an exponential improvement over the dependence polylog(1/ǫ) of previous optimal sparse Hamiltonian simulation algorithm without parallelism. To obtain this result, we introduce a novel notion of parallel quantum walk, based on Childs' quantum walk. The target evolution unitary is approximated by a truncated Taylor series, which is obtained by combining these quantum walks in a parallel way. A lower bound Ω(log log(1/ǫ)) is established, showing that the ǫ-dependence of the gate depth achieved in this work cannot be significantly improved.Our algorithm is applied to simulating three physical models: the Heisenberg model, the Sachdev-Ye-Kitaev model and a quantum chemistry model in second quantization. By explicitly calculating the gate complexity for implementing the oracles, we show that on all these models, the total gate depth of our algorithm has a polylog log(1/ǫ) dependence in the parallel setting.

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Computations with greater Quantum depth are strictly more powerful (relative to an oracle)

Cited by 25 publications

References 11 publications

Quantum algorithmic measurement

Quantum algorithmic measurement

Quantum advantage in learning from experiments

Parallel Quantum Algorithm for Hamiltonian Simulation

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