Two-Unitary Decomposition Algorithm and Open Quantum System Simulation

• URL: http://arxiv.org/abs/2207.10007v2
• Date: Sun, 7 May 2023 04:20:50 GMT
• Title: Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
• Authors: Nishchay Suri, Joseph Barreto, Stuart Hadfield, Nathan Wiebe, Filip Wudarski, Jeffrey Marshall
• Abstract summary: We propose a quantum two-unitary decomposition (TUD) algorithm to decompose a $d$-dimensional operator $A$ with non-zero singular values. The two unitaries can be deterministically implemented, thus requiring only a single call to the state preparation oracle for each. Since the TUD method can be used to implement non-unitary operators as only two unitaries, it also has potential applications in linear algebra and quantum machine learning.
• Score: 0.17126708168238122
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating general quantum processes that describe realistic interactions of quantum systems following a non-unitary evolution is challenging for conventional quantum computers that directly implement unitary gates. We analyze complexities for promising methods such as the Sz.-Nagy dilation and linear combination of unitaries that can simulate open systems by the probabilistic realization of non-unitary operators, requiring multiple calls to both the encoding and state preparation oracles. We propose a quantum two-unitary decomposition (TUD) algorithm to decompose a $d$-dimensional operator $A$ with non-zero singular values as $A=(U_1+U_2)/2$ using the quantum singular value transformation algorithm, avoiding classically expensive singular value decomposition (SVD) with an $O(d^3)$ overhead in time. The two unitaries can be deterministically implemented, thus requiring only a single call to the state preparation oracle for each. The calls to the encoding oracle can also be reduced significantly at the expense of an acceptable error in measurements. Since the TUD method can be used to implement non-unitary operators as only two unitaries, it also has potential applications in linear algebra and quantum machine learning.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Efficient application of the factorized form of the unitary coupled-cluster ansatz for the variational quantum eigensolver algorithm by using linear combination of unitaries [0.0]
  The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons.
  arXiv  Detail & Related papers  (2023-02-17T04:03:06Z)
• Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators [0.0]
  We present a dilation based algorithm to simulate non-unitary operations on unitary quantum devices. We use this algorithm to prepare random sub-normalized two-level states on a quantum device with high fidelity. We also present the accurate non-unitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude damping channel computed on a quantum device.
  arXiv  Detail & Related papers  (2022-05-05T17:56:41Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• K-sparse Pure State Tomography with Phase Estimation [1.2183405753834557]
  Quantum state tomography (QST) for reconstructing pure states requires exponentially increasing resources and measurements with the number of qubits. QST reconstruction for any pure state composed of the superposition of $K$ different computational basis states of $n$bits in a specific measurement set-up is presented.
  arXiv  Detail & Related papers  (2021-11-08T09:43:12Z)
• Halving the cost of quantum multiplexed rotations [0.0]
  We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls. Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
  arXiv  Detail & Related papers  (2021-10-26T06:49:44Z)
• Quantum Causal Unravelling [44.356294905844834]
  We develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography.
  arXiv  Detail & Related papers  (2021-09-27T16:28:06Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators [0.0]
  We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. The results are in agreement with classical calculations, showing promise in non-unitary operations on intermediate-term and future quantum devices.
  arXiv  Detail & Related papers  (2021-06-23T18:00:02Z)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.