Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators

• URL: http://arxiv.org/abs/2205.02826v1
• Date: Thu, 5 May 2022 17:56:41 GMT
• Title: Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators
• Authors: Anthony W. Schlimgen, Kade Head-Marsden, LeeAnn M. Sager-Smith, Prineha Narang, and David A. Mazziotti
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based algorithm to simulate non-unitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal non-unitary operator, which we show can be implemented by a diagonal unitary operator in a 1-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random sub-normalized two-level states on a quantum device with high fidelity. Furthermore, we 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. The algorithm presented will be most useful for implementing general non-unitary operations when the SVD can be readily computed, which is the case with most operators in the noisy intermediate-scale quantum computing era.

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