Recycling qubits in near-term quantum computers
TL;DR: This paper proposes a protocol that can unitarily reset qubits when the circuit has a common convolutional form, thus dramatically reducing the spatial cost for implementing the contraction algorithm on general near-term quantum computers.
Abstract: The authors propose a protocol that can unitarily reset or recycle qubits when the circuit has a common convolutional form. This protocol could potentially dramatically reduce the spatial cost for implementing the contraction algorithm on general near-term quantum computers.
Citations
More filters
••
TL;DR: Algorithms for computing the trace of the n-th power of the density operator of a quantum system, Tr(ρn), are developed that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices.
Abstract: One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n-th power of the density operator of a quantum system, $Tr(\rho^n)$, (related to the Renyi entropy of order n) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n, are variants of previous algorithms with width proportional to n, an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating $Tr(\rho^n)$ for larger n than possible with previous algorithms.
21 citations
Cites background from "Recycling qubits in near-term quant..."
...The TCT is a special case of convolutional circuits recently studied by [4]....
[...]
••
TL;DR: In this article , a reduced version of Shor's algorithm is proposed to increase the range of numbers that can be factorized on noisy quantum devices, and the implementation presented in this work is general and does not use any assumptions on the number to factor.
Abstract: Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor’s algorithm, this peculiar problem can be solved in polynomial time. However, both the number of qubits and applied gates detrimentally affect the ability to run a particular quantum circuit on the near term Quantum hardware. In this work, we help addressing both these problems by introducing a reduced version of Shor’s algorithm that proposes a step forward in increasing the range of numbers that can be factorized on noisy Quantum devices. More specifically, the structure of the Shor’s circuit has been modified to reduce the number of gates in the modular arithmetic and the Quantum Fourier Transform. The implementation presented in this work is general and does not use any assumptions on the number to factor. In particular, we have found noteworthy results in most cases, often being able to factor the given number with only one iteration of the proposed algorithm. Finally, comparing the original quantum algorithm with our version on simulator, the outcomes are identical for some of the numbers considered.
2 citations
••
02 Sep 2021TL;DR: In this paper, the trace of the n-th power of the density operator of a quantum system, related to the Renyi entropy of order n, was computed using fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise.
Abstract: One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n-th power of the density operator of a quantum system, $Tr(\rho^n)$, (related to the Renyi entropy of order n) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n, are variants of previous algorithms with width proportional to n, an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating $Tr(\rho^n)$ for larger n than possible with previous algorithms.
2 citations
•
TL;DR: In this paper, the ground state of the critical Ising model has been numerically and experimentally studied using quantum channels constructed from MERA circuits with renormalization group fixed points.
Abstract: Noisy intermediate-scale quantum (NISQ) hardware is typically limited to low-depth quantum circuits to limit the number of opportunities for introduction of error by unreliable quantum gates. A less-explored alternative approach is to repeatedly apply a quantum channel with a desired quantum state as a stable fixed point. Increased circuit depth can in this case be beneficial rather than harmful due to dissipative self-correction. The quantum channels constructed from MERA circuits can be interpreted in terms of the renormalization group(RG), and their fixed points are RG fixed points, i.e. scale-invariant systems such as conformal field theories. Here, building upon the theoretical proposal of Kim and Swingle, we numerically and experimentally study the robust preparation of the ground state of the critical Ising model using circuits adapted from the work of Evenbly and White. The experimental implementation exhibits self-correction through renormalization seen in the convergence and stability of local observables, and makes essential use of the ability to measure and reset individual qubits afforded by the "quantum CCD" architecture of the Honeywell ion-trap. We also numerically test error mitigation by zero-noise extrapolation schemes specially adapted for renormalization circuits, which are able to outperform typical extrapolation schemes using lower gate overhead.
1 citations
References
More filters
••
[...]
01 Jan 2012
139,059 citations
"Recycling qubits in near-term quant..." refers background in this paper
...One promising approach is to pursue variational quantum algorithms [4, 5]....
[...]
••
[...]
40,330 citations
"Recycling qubits in near-term quant..." refers background or methods in this paper
...Second, one may be able to concatenate our method with the well-known algorithmic cooling method to further improve the purity of the ancilla qubits [22, 23]....
[...]
...Alternatively, one could resort to algorithmic cooling [22, 23]....
[...]
••
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.
Abstract: A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.
7,427 citations
••
TL;DR: In this paper, an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature, is presented.
Abstract: This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at this https URL. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.
4,873 citations
••
TL;DR: The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future.
Abstract: Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansatze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry--calculating the ground-state molecular energy for He-H(+). The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future.
3,114 citations