Quantum phase estimation with optimal confidence interval using three control qubits

• URL: http://arxiv.org/abs/2601.16474v1
• Date: Fri, 23 Jan 2026 06:05:11 GMT
• Title: Quantum phase estimation with optimal confidence interval using three control qubits
• Authors: Kaur Kristjuhan, Dominic W. Berry,
• Abstract summary: We show how to prepare the corresponding state in a far more efficient way than prior work.<n>When the dimension is a power of 2, the phase estimation can be performed with only three qubits for the control register.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum phase estimation is an important routine in many quantum algorithms, particularly for estimating the ground state energy in quantum chemistry simulations. This estimation involves applying powers of a unitary to the ground state, controlled by an auxiliary state prepared on a control register. In many applications the goal is to provide a confidence interval for the phase estimate, and optimal performance is provided by a discrete prolate spheroidal sequence. We show how to prepare the corresponding state in a far more efficient way than prior work. We find that a matrix product state representation with a bond dimension of 4 is sufficient to give a highly accurate approximation for all dimensions tested, up to $2^{24}$. This matrix product state can be efficiently prepared using a sequence of simple three-qubit operations. When the dimension is a power of 2, the phase estimation can be performed with only three qubits for the control register, making it suitable for early-generation fault-tolerant quantum computers with a limited number of logical qubits.

Related papers

• Estimating ground-state properties in quantum simulators with global control [35.3616472951301]
  Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation.<n>We present a protocol for estimating the ground-state energy using only global time evolution under a target Hamiltonian.
  arXiv  Detail & Related papers  (2025-11-06T15:08:00Z)
• Efficient state estimation on quantum processors [0.0]
  We present two scalable and entanglement-free methods for estimating the collective state of an n-qubit quantum computer.<n>The first method consists of a fixed set of five quantum circuits-regardless of the number of qubits-that avoid the use of entanglement as a measurement resource.<n>The second method requires only 2n+1 circuits, each of which applies a single local gate to one of the n qubits during the measurement stage.
  arXiv  Detail & Related papers  (2025-10-17T18:03:21Z)
• Ptychographic estimation of pure multiqubit states in a quantum device [8.74712236516413]
  Quantum ptychography is a method for estimating an unknown pure quantum state by subjecting it to overlapping projections.<n>We present a study of this method applied for estimating $n$-qubit states in a circuit-based quantum computer.
  arXiv  Detail & Related papers  (2024-12-03T03:18:23Z)
• Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers [37.69303106863453]
  We propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers. Our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28% and 57% on average.
  arXiv  Detail & Related papers  (2024-06-17T14:10:10Z)
• Quantum state preparation for multivariate functions [2.344936782036958]
  We develop protocols for preparing quantum states whose amplitudes encode multivariate functions.<n>We analyze requirements both pragmatically and in terms of near/medium-term resources.<n>We use 24 qubits and up to 237 two-qubit gates on the Quantinuum H2-1 trapped-ion quantum processor.
  arXiv  Detail & Related papers  (2024-05-31T17:49:27Z)
• Quantum State Tomography for Matrix Product Density Operators [28.799576051288888]
  Reconstruction of quantum states from experimental measurements is crucial for the verification and benchmarking of quantum devices. Many physical quantum states, such as states generated by noisy, intermediate-scale quantum computers, are usually structured. We establish theoretical guarantees for the stable recovery of MPOs using tools from compressive sensing and the theory of empirical processes.
  arXiv  Detail & Related papers  (2023-06-15T18:23:55Z)
• Optimum phase estimation with two control qubits [0.0]
  We show how to measure a phase with a minimum mean-square error using only two control qubits. Our method corresponds to preparing the optimal control state one qubit at a time, while it is simultaneously consumed by the measurement procedure.
  arXiv  Detail & Related papers  (2023-03-22T12:18:33Z)
• Pulse-controlled qubit in semiconductor double quantum dots [57.916342809977785]
  We present a numerically-optimized multipulse framework for the quantum control of a single-electron charge qubit. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation.
  arXiv  Detail & Related papers  (2023-03-08T19:00:02Z)
• On low-depth algorithms for quantum phase estimation [11.678822620192438]
  For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to use a minimal number of ancilla qubits. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. We propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.
  arXiv  Detail & Related papers  (2023-02-05T18:40:49Z)
• Iterative Qubit Coupled Cluster using only Clifford circuits [36.136619420474766]
  An ideal state preparation protocol can be characterized by being easily generated classically. We propose a method that meets these requirements by introducing a variant of the iterative qubit coupled cluster (iQCC) We demonstrate the algorithm's correctness in ground-state simulations and extend our study to complex systems like the titanium-based compound Ti(C5H5)(CH3)3 with a (20, 20) active space.
  arXiv  Detail & Related papers  (2022-11-18T20:31:10Z)
• Determining ground-state phase diagrams on quantum computers via a generalized application of adiabatic state preparation [61.49303789929307]
  We use a local adiabatic ramp for state preparation to allow us to directly compute ground-state phase diagrams on a quantum computer via time evolution. We are able to calculate an accurate phase diagram on both two and three site systems using IBM quantum machines.
  arXiv  Detail & Related papers  (2021-12-08T23:59:33Z)
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences [41.42601188771239]
  We create non-classical states of light in three-dimensional microwave cavities. These states are useful for quantum computation. We show that this way of creating non-classical states is robust to fluctuations of the system parameters.
  arXiv  Detail & Related papers  (2021-11-15T18:20:38Z)
• 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)

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.