Abstract:We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In this paper, we show that our hybrid algorithm can reduce a circuit depth from the original HHL algorithm by means of a classical information feed-forward after the quantum phase estimation algorithm, and the results of the hybrid algorithm are identical to those of the HHL algorithm. In addition, it is experimentally examined with four qubits in the IBM Quantum Experience setups… Show more
“…Simulating the m = 3 circuit we find that real symmetric matrices up to dimension 10 can be inverted with algorithm errors less than 5%, as shown in Fig. 7, a considerable increase in problem size over the existing gate-based realizations [22][23][24][25][26] .…”
Section: Matrix Inversionmentioning
confidence: 87%
“…Simulating the circuit we find that real symmetric matrices up to dimension 10 can be inverted with algorithm errors less than 5%, as shown in Fig. 7 , a considerable increase in problem size over the existing gate-based realizations 22 – 26 . Figure 7 Matrix inversion algorithm error for , averaged over random real symmetric matrices A (with eigenvalues ).…”
There is a tremendous interest in developing practical applications for noisy intermediate-scale quantum processors without the overhead required by full error correction. Near-term quantum information processing is especially challenging within the standard gate model, as algorithms quickly lose fidelity as the problem size and circuit depth grow. This has lead to a number of non-gate-model approaches such as analog quantum simulation and quantum annealing. These come with specific hardware requirements that are different than that of a universal gate-based quantum computer. We have previously proposed an approach called the single-excitation subspace (SES) method, which uses a complete graph of superconducting qubits with tunable coupling. Without error correction the SES method is not scalable, but it offers several algorithmic components with constant depth, which is highly desirable for near-term use. The challenge of the SES method is that it requires a physical qubit for every basis state in the computer’s Hilbert space. This imposes exponentially large resource costs for algorithms using registers of ancillary qubits, as each ancilla would double the required graph size. Here we show how to circumvent this doubling by leaving the SES and fusing it with a multi-ancilla Hilbert space. Specifically, we implement the tensor product of an SES register holding “data” with one or more ancilla qubits, which are able to independently control arbitrary $$n\!\times \!n$$
n
×
n
unitary operations on the data in a constant number of steps. This enables a hybrid form of quantum computation where fast SES operations are performed on the data, traditional logic gates and measurements are performed on the ancillas, and controlled-unitaries act between. As example applications, we give ancilla-assisted SES implementations of quantum phase estimation and the quantum linear system solver of Harrow, Hassidim, and Lloyd.
“…Simulating the m = 3 circuit we find that real symmetric matrices up to dimension 10 can be inverted with algorithm errors less than 5%, as shown in Fig. 7, a considerable increase in problem size over the existing gate-based realizations [22][23][24][25][26] .…”
Section: Matrix Inversionmentioning
confidence: 87%
“…Simulating the circuit we find that real symmetric matrices up to dimension 10 can be inverted with algorithm errors less than 5%, as shown in Fig. 7 , a considerable increase in problem size over the existing gate-based realizations 22 – 26 . Figure 7 Matrix inversion algorithm error for , averaged over random real symmetric matrices A (with eigenvalues ).…”
There is a tremendous interest in developing practical applications for noisy intermediate-scale quantum processors without the overhead required by full error correction. Near-term quantum information processing is especially challenging within the standard gate model, as algorithms quickly lose fidelity as the problem size and circuit depth grow. This has lead to a number of non-gate-model approaches such as analog quantum simulation and quantum annealing. These come with specific hardware requirements that are different than that of a universal gate-based quantum computer. We have previously proposed an approach called the single-excitation subspace (SES) method, which uses a complete graph of superconducting qubits with tunable coupling. Without error correction the SES method is not scalable, but it offers several algorithmic components with constant depth, which is highly desirable for near-term use. The challenge of the SES method is that it requires a physical qubit for every basis state in the computer’s Hilbert space. This imposes exponentially large resource costs for algorithms using registers of ancillary qubits, as each ancilla would double the required graph size. Here we show how to circumvent this doubling by leaving the SES and fusing it with a multi-ancilla Hilbert space. Specifically, we implement the tensor product of an SES register holding “data” with one or more ancilla qubits, which are able to independently control arbitrary $$n\!\times \!n$$
n
×
n
unitary operations on the data in a constant number of steps. This enables a hybrid form of quantum computation where fast SES operations are performed on the data, traditional logic gates and measurements are performed on the ancillas, and controlled-unitaries act between. As example applications, we give ancilla-assisted SES implementations of quantum phase estimation and the quantum linear system solver of Harrow, Hassidim, and Lloyd.
“…Faulttolerant implementations can take advantage of quantum arithmetic methods to implement efficient algorithms for the required arcsin computation. An alternative approach for the near term is a hybrid version of HHL [212], which the developers of NISQ-HHL extended. This approach utilizes QPE to first estimate the required eigenvalues to perform the rotations for.…”
Section: Portfolio Optimization On a Trapped-ion Devicementioning
Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.
“…This is challenging for current technology. Recently, there has been great interest in quantum computing in the Noisy Intermediate Scaled Quantum (NISQ) regime, for finding energy spectra of a many-body Hamiltonian [12][13][14][15][16][17][18][19][20][21][22][23], simulating real and imaginary time dynamics of many-body systems [24][25][26][27][28][29], applications with machine learning [30][31][32][33][34][35][36][37], circuit learning [38][39][40][41][42], and others [43,44]. These algorithms are generally hybrid in a sense that they only solve the core problem with a shallow quantum circuit and leave the higher level calculation to be performed with a classical computer.…”
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