Quantum-JEPA: Quantum Born Priors for Latent-Action JEPA World Models

Zhiyuan Liu; Sicheng Liu; Haiyu Wu

cs.AIOct 20, 2026

Quantum-JEPA: Quantum Born Priors for Latent-Action JEPA World Models

Authors: Zhiyuan Liu, Sicheng Liu, Haiyu Wu

Organizations: Qinous Technology Co., Ltd., Beijing, China · Tsinghua University, Beijing, China · University of Notre Dame, Notre Dame, IN, USA

Abstract

A single observation can admit several plausible futures, making uncertainty an essential part of world modelling. However, quantum generative models remain underexplored for this task. We introduce Quantum-JEPA, a latent-action JEPA framework that learns distributions of future representations using a conditional quantum Born prior. Circuit measurements generate binary latent actions, which a shared predictor maps to alternative future representations. We train the quantum prior through the quality and diversity of these predictions using a sampled energy objective. Our model learns distinct continuations on constructed multimodal tasks and captures latent-action correlations that support coordinated multi-agent futures. On D3IL, a benchmark of diverse human demonstrations, our trained models generate multiple obstacle-crossing routes from a common starting point without observed motion. On the controlled tasks, our classical and quantum prior implementations improve prediction validity and distributional fidelity over the evaluated variational baselines. Our quantum priors combine competitive predictive quality with a parameter-efficient sampling structure: they avoid an exponentially sized categorical output layer while supporting correlated latent actions. We further validate finite-shot parameter-shift training, including training with readout noise. Unlike most prior work, which focuses on simulation, we also verify the feasibility of inference with trained priors on a real QPU. These results establish a trainable quantum component for JEPA future prediction and a basis for exploring quantum-enhanced world models at larger scales.

Figures & tables

Figure 1: Conditional quantum Born prior for latent-action generation. The circuit samples binary actions conditioned on an observation; a shared predictor maps these inputs to alternative future representations. The solid trace depicts the observation, and colour-matched dashed branches illustrate possible continuations.

Figure 2: Quantum-JEPA architecture. Filled blocks denote modules and outlined tokens denote data. The observation representation

h

conditions both the Born prior and the shared predictor. Measured bits

z

select a predicted future representation

\widehat{t}

, which is scored against the encoded target

t

. This score trains the predictor and prior; feature regularization stabilizes the shared encoder and is omitted for clarity. The circuit is schematic;

M_{\varphi}

denotes the measurement stage.

Prior	Parameters	Generation work
Softmax-Categorical	$O(dH_{p}+H_{p}2^{n})$	$O(dH_{p}+H_{p}2^{n}+Kn)$
Independent-Bernoulli	$O(dH_{p}+H_{p}n)$	$O(dH_{p}+H_{p}n+Kn)$
Mixture- $R$	$O(dH_{p}+H_{p}Rn)$	$O(dH_{p}+H_{p}Rn+R+Kn)$
AR-GRU	$O(dH_{p}+H_{p}^{2})$	$O(dH_{p}+KnH_{p}^{2})$
Conditional QCBM	$O(dH_{p}+H_{p}nL)$	$O(dH_{p}+H_{p}nL)$ classical $O(KnL)$ quantum gates

Table 1: Leading prior costs for one observation and

K

sampled

n

-bit codes. Parameter counts are asymptotic; constants, biases, and normalization parameters are omitted. Classical costs allow cached context projections and alias-table categorical sampling. Quantum gate counts assume compatible connectivity. Every method also stores

O(Kn)

measured or sampled bits.

Method / prior	Cov. $\uparrow$	Valid $\uparrow$	TV $\downarrow$	minADE $\downarrow$	ES $\downarrow$
Variational JEPA	$63.3\,\pm\,8.1$	$31.0\,\pm\,2.3$	$0.730\,\pm\,0.009$	$2.43\,\pm\,0.30$	$11.55\,\pm\,0.66$
Latent-CVAE	$\mathbf{98.6}\,\pm\,1.0$	$53.5\,\pm\,2.3$	$0.470\,\pm\,0.023$	$\mathbf{0.70}\,\pm\,0.03$	$9.96\,\pm\,0.05$
Deterministic JEPA	$0.0\,\pm\,0.0$	$0.0\,\pm\,0.0$	$1.000\,\pm\,0.000$	$8.04\,\pm\,0.01$	$15.04\,\pm\,0.01$
Uniform-Bernoulli	$\underline{94.4}\,\pm\,1.6$	$\mathbf{96.5}\,\pm\,1.2$	$0.168\,\pm\,0.018$	$0.81\,\pm\,0.08$	$\underline{9.60}\,\pm\,0.02$
Softmax-Categorical	$93.6\,\pm\,0.5$	$95.8\,\pm\,0.5$	$\mathbf{0.145}\,\pm\,0.002$	$\underline{0.79}\,\pm\,0.04$	$\mathbf{9.58}\,\pm\,0.02$
AR-GRU	$90.5\,\pm\,4.1$	$96.0\,\pm\,1.1$	$0.180\,\pm\,0.015$	$0.97\,\pm\,0.18$	$9.65\,\pm\,0.06$

Table 2: MovingMNIST (80 observations, 128 draws each). Mean

\pm

sample s.d. over three trainings; coverage/validity in percent, minADE/ES in pixels. The first two rows are external methods. Trained QCBMs use parameter shift with 0.5% readout flips. Shading marks trained QCBMs; bold/underline mark best/second-best displayed means, including ties.

Figure 3: Latent-action interventions using the ideal-gradient reference checkpoint. (a) One observation, all eight codes. (b) Code 000, different digits. Grey shows the observation; cyan, purple and orange show future frames 1–3. Red labels mark invalid endpoints. Quantitative evaluation uses prior sampling; direction frequencies appear in Appendix H ( Figure 7 ).

Method / prior	Cov. $\uparrow$	Valid $\uparrow$	TV $\downarrow$	minADE $\downarrow$	ES $\downarrow$
Variational JEPA	$0.00\,\pm\,0.00$	$0.00\,\pm\,0.00$	$1.000\,\pm\,0.000$	$5.68\,\pm\,0.51$	$44.78\,\pm\,1.59$
Latent-CVAE	$59.82\,\pm\,4.73$	$14.64\,\pm\,1.65$	$0.854\,\pm\,0.016$	$0.60\,\pm\,0.09$	$34.54\,\pm\,0.07$
Deterministic JEPA	$2.68\,\pm\,2.78$	$48.18\,\pm\,50.10$	$0.973\,\pm\,0.028$	$15.19\,\pm\,0.16$	$64.58\,\pm\,0.68$
Uniform-Bernoulli	$29.41\,\pm\,1.53$	$6.53\,\pm\,0.15$	$0.935\,\pm\,0.001$	$1.40\,\pm\,0.07$	$40.86\,\pm\,0.02$
Softmax-Categorical	$\mathbf{99.97}\,\pm\,0.03$	$\mathbf{98.00}\,\pm\,0.42$	$\mathbf{0.157}\,\pm\,0.005$	$\underline{0.20}\,\pm\,0.03$	$\underline{34.34}\,\pm\,0.05$
Independent-Bernoulli	$41.32\,\pm\,4.56$	$25.66\,\pm\,2.49$	$0.764\,\pm\,0.020$	$4.37\,\pm\,0.67$	$42.63\,\pm\,0.65$

Table 3: HEP18 (128 observations, 128 draws each). Mean

\pm

sample s.d. over three trainings; coverage/validity in percent, minADE/ES in metres. The first two rows are external methods. Training and highlighting follow Table 2 .

Method / prior	Routes $\uparrow$	Coverage $\uparrow$	TV $\downarrow$
Deterministic JEPA	$0.33\,\pm\,0.33$	$1.39\,\pm\,1.39$	–
Latent-CVAE	$14.31\,\pm\,0.71$	$59.63\,\pm\,2.96$	$0.542\,\pm\,0.008$
Softmax-Categorical	$18.08\,\pm\,0.89$	$75.33\,\pm\,3.71$	$0.401\,\pm\,0.028$
AR-GRU	$17.65\,\pm\,0.69$	$73.54\,\pm\,2.87$	$0.412\,\pm\,0.018$
Mixture-4	$17.77\,\pm\,0.18$	$74.05\,\pm\,0.75$	$0.419\,\pm\,0.014$
Frozen-QCBM	$17.37\,\pm\,0.68$	$72.36\,\pm\,2.82$	$0.430\,\pm\,0.011$

Table 4: D3IL from one direction-free starting point, evaluated with all three folds and three training seeds per method. Each checkpoint supplies 384 raw rollouts. We compute exact expected route statistics for a uniformly selected subset of 60 geometrically accepted paths. Entries are mean

\pm

sample s.d. over three seed-level means, each averaging three folds; coverage is a percentage of 24 routes. Six deterministic checkpoints have no accepted paths, giving zero coverage and undefined TV. Quantum models use finite-shot parameter-shift training and 0.5% readout flips. Metrics describe accepted-path diversity, not raw generation success.

Figure 4: D3IL continuations from one direction-free starting point (black dot). The reference panel contains all 96 recorded demonstrations. Each prediction panel shows 64 accepted paths from the first training seed and first fold, selected from 384 draws without route balancing. Table 4 instead aggregates all nine models per method at a common 60-accepted-path budget. All panels use common axes; grey discs mark obstacles and pale rings the scoring margin. Geometric acceptance does not ensure smooth motion, and residual bends are retained. Appendix B.5 shows all eight methods.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	MovingMNIST	HEP18
Latent dimension $d$ / predictor width	64 / 96	64 / 64
Prior width $H_{p}$	48	48
Bits $n$ / body layers $L$	3 / 2	12 / 4
Terminal $R_{Y}$ angles	3	12
World-model iterations	4,000	6,000
Batch size / prior samples	64 / 32	32 / 32

Appendix

Table 5: Reference training configuration for Tables 2 and 3 . Readout training is a separate stage with all JEPA parameters frozen. These trained QCBMs use finite-shot parameter shift and a 0.5% independent readout-flip probability per bit.

Method / prior	Prior	JEPA training	Readout	Deployment
Deterministic JEPA	0	211,266	35,088	246,354
Latent-CVAE	4,296	169,248	35,088	184,728
Softmax-Categorical	15,792	227,058	35,088	262,146
AR-GRU	10,641	221,907	35,088	256,995
Mixture-4	5,012	216,278	35,088	251,366
Frozen-QCBM	0	211,266	35,088	251,146

Appendix

Table 6: D3IL model resources. The first three numeric columns count trainable parameters in their respective stages; deployment includes fixed prior weights but excludes the CVAE posterior. Frozen-QCBM stores 4,792 fixed prior values in addition to its trainable neural modules. Quantum counts include 64 inactive coordinates retained for checkpoint compatibility. AR-GRU uses the same width-48 recurrent prior as MovingMNIST and HEP18.

Figure 5: D3IL from one common point, with no observed direction. The reference shows all demonstrations; stochastic panels show 64 accepted paths per method. The single deterministic prediction is red because it collides. All panels share the starting point (black dot), axes and obstacle geometry. Paths are not balanced across routes or smoothed. Trainable QCBMs use noisy parameter-shift training and 0.5% readout flips at evaluation.

Task / prior	Encoder	Predictor	Prior	Active	Readout
Digits / Deterministic JEPA	439,600	50,112	0	0	12,966
Digits / Uniform-Bernoulli	439,600	50,112	0	0	12,966
Digits / Frozen-QCBM	439,600	50,112	3,435	3,423	12,966
Digits / Softmax-Categorical	439,600	50,112	3,640	3,640	12,966
Digits / AR-GRU	439,600	50,112	10,641	10,641	12,966
Digits / Mixture-2	439,600	50,112	3,640	3,640	12,966

Appendix

Table 7: Parameter counts for MovingMNIST (Digits, 3-bit) and HEP18 (Traffic, 12-bit). The Prior column counts all allocated prior parameters; Active counts only those used in the forward computation. Frozen-QCBM has the same architecture as Entangled-QCBM but receives no prior updates. Product-QCBM has the same active rotation count, although only their sum on each qubit affects its output probability.

Product-QCBM
Training	Cov. $\uparrow$	Valid $\uparrow$	TV $\downarrow$	minADE $\downarrow$	ES $\downarrow$	Dice $\uparrow$
Ideal gradient	$90.9\,\pm\,5.1$	$95.6\,\pm\,1.9$	$0.179\,\pm\,0.023$	$0.92\,\pm\,0.14$	$9.64\,\pm\,0.03$	$0.591\,\pm\,0.014$
Parameter shift	$94.2\,\pm\,2.7$	$96.4\,\pm\,1.6$	$0.168\,\pm\,0.018$	$0.80\,\pm\,0.07$	$9.60\,\pm\,0.02$	$0.601\,\pm\,0.005$
Shift + noise	$94.3\,\pm\,2.4$	$96.2\,\pm\,1.6$	$0.167\,\pm\,0.019$	$0.80\,\pm\,0.08$	$9.60\,\pm\,0.02$	$0.602\,\pm\,0.007$
Entangled-QCBM
Ideal gradient	$93.1\,\pm\,2.3$	$96.6\,\pm\,0.9$	$0.159\,\pm\,0.016$	$0.85\,\pm\,0.11$	$9.60\,\pm\,0.03$	$0.597\,\pm\,0.013$

Appendix

Table 8: MovingMNIST: quantum-training comparison. Mean

\pm

sample standard deviation of three matched trainings. Coverage and validity are percentages; ADE and ES are in pixels. Noise denotes 0.5% independent bit flips at training and evaluation. All settings use 128 evaluation samples per observation.

Product-QCBM
Training	Cov. $\uparrow$	Valid $\uparrow$	TV $\downarrow$	minADE $\downarrow$	ES $\downarrow$
Ideal gradient	$39.45\,\pm\,10.31$	$25.56\,\pm\,4.21$	$0.765\,\pm\,0.037$	$4.155\,\pm\,0.530$	$42.53\,\pm\,0.63$
Parameter shift	$41.17\,\pm\,5.07$	$25.80\,\pm\,4.46$	$0.763\,\pm\,0.037$	$4.332\,\pm\,0.482$	$42.58\,\pm\,0.52$
Shift + noise	$38.77\,\pm\,5.13$	$24.50\,\pm\,4.11$	$0.777\,\pm\,0.033$	$4.230\,\pm\,0.490$	$42.45\,\pm\,0.53$
Entangled-QCBM
Ideal gradient	$99.83\,\pm\,0.17$	$98.55\,\pm\,0.40$	$0.164\,\pm\,0.013$	$0.189\,\pm\,0.019$	$34.31\,\pm\,0.01$

Appendix

Table 9: HEP18: quantum-training comparison. Mean

\pm

sample standard deviation of three matched trainings. Coverage and validity are percentages; ADE and ES are in metres. Noise denotes 0.5% independent bit flips at training and evaluation. All settings use 128 evaluation samples per observation.

Task	Method	Trainable parameters
MovingMNIST	Variational JEPA	464,496
MovingMNIST	Latent-CVAE	472,208
HEP18	Variational JEPA	22,288
HEP18	Latent-CVAE	28,848

Appendix

Table 10: Trainable world-model parameters in the two external-method adaptations, reported separately for each dataset. Counts include the encoder and the networks that predict future representations or their distributions. They exclude the non-trainable EMA encoder in Variational JEPA and the separately fitted readout in both methods.

Figure 6: Diverse continuation examples in HEP18, using ideal-gradient reference checkpoints. Each group shows four examples for the same test observation, with targets in (a) and sampled predictions in (b–d). We select distinct combinations of local behaviours from the 18 targets or each model’s 128 prior draws, favouring visibly different trajectories. All groups use the first test observation and first training run. Selection is independent across groups, so examples in corresponding positions are not paired. The display illustrates different continuations; their counts do not estimate how often the model samples them. Invalid predictions are labelled, and all groups share agent colours and spatial limits. Increasing marker sizes indicate 3, 6 and 9 s; squares mark the observed positions. The numerical tables use all prior draws, without this selection for display.

Prior	$R(t-h)$	Cov. $\uparrow$	Valid $\uparrow$	TV $\downarrow$
Entangled-QCBM	Yes	$99.88\,\pm\,0.05$	$98.62\,\pm\,0.37$	$0.166\,\pm\,0.012$
Entangled-QCBM	No	$70.72\,\pm\,50.34$	$67.47\,\pm\,52.74$	$0.417\,\pm\,0.451$
Mixture-4	Yes	$99.80\,\pm\,0.05$	$97.86\,\pm\,1.69$	$0.157\,\pm\,0.004$
Mixture-4	No	$90.65\,\pm\,16.11$	$91.91\,\pm\,10.37$	$0.228\,\pm\,0.121$

Appendix

Table 11: Effect of change regularization on 64 HEP18 validation observations. Values are means

\pm

sample standard deviations across three matched initializations, with 128 prior draws per observation. All rows use joint predictive energy and coefficient

2/3

on each of

R(h)

and

R(t)

. The retained configuration also includes

\frac{2}{3}R(t-h)

. Coverage and validity are percentages, and every run is retained, including unsuccessful training outcomes.

Prior	Setting	Coverage (%)	Validity (%)	TV
Entangled-QCBM	$K=32$	82.60	98.59	0.31
Entangled-QCBM	$K=64$	96.88	98.53	0.22
Entangled-QCBM	$K=128$	99.83	98.55	0.16
Entangled-QCBM	1 m / 0.5 m/s	91.42	82.84	0.28
Entangled-QCBM	3 m / 1.5 m/s	99.83	98.70	0.16
Product-QCBM	$K=32$	25.77	25.44	0.80

Appendix

Table 12: Ideal-gradient reference: sampling-budget and tolerance checks on 128 HEP18 test observations. Values are means over three independent training runs. The sample-budget rows use the first

K

draws from the same 128-draw set, with position/speed tolerances of 2 m/1 m/s. The tolerance rows retain all 128 draws and change only the matching thresholds.

Figure 7: MovingMNIST direction frequencies from the ideal-gradient reference models. We average sampled frequencies over all test observations and three independently trained models, retaining the invalid category. Printed values give the actual percentages in every cell. Colour intensity is capped at 25%, so concentrated rows do not obscure differences among the more evenly distributed rows.

Prior	Prior input	TV $\downarrow$	Coverage $\uparrow$	Valid $\uparrow$
Product-QCBM	Original observation	$0.199\,\pm\,0.009$	$83.02\,\pm\,1.42$	$94.67\,\pm\,0.48$
	Other image, same digit	$0.210\,\pm\,0.007$	$83.02\,\pm\,1.42$	$94.72\,\pm\,0.58$
	Other digit	$0.219\,\pm\,0.019$	$83.02\,\pm\,1.42$	$94.63\,\pm\,0.58$
	Training-input mixture	$0.207\,\pm\,0.012$	$83.02\,\pm\,1.42$	$94.55\,\pm\,0.68$
Entangled-QCBM	Original observation	$0.170\,\pm\,0.014$	$87.34\,\pm\,0.78$	$95.02\,\pm\,1.93$
	Other image, same digit	$0.197\,\pm\,0.018$	$87.34\,\pm\,0.78$	$94.29\,\pm\,2.29$

Appendix

Table 13: Digit-dependent MovingMNIST: mean

\pm

sample s.d. over three training runs. Only the prior input changes between conditions; the predictor and readout keep the original observation. Each test observation has 384 sampled futures. TV includes invalid predictions; coverage and validity are percentages. Training uses finite-shot parameter shift and 0.5% readout flips for both priors.

Prior	Sampling	Cov. $\uparrow$	Valid $\uparrow$	TV $\downarrow$	minADE $\downarrow$	ES $\downarrow$	Dice $\uparrow$
Product-QCBM	GPU / ideal	89.06	98.44	0.1678	1.059	9.633	0.567
Product-QCBM	QPU	89.06	98.73	0.1674	1.059	9.670	0.567
Entangled-QCBM	GPU / ideal	96.88	96.48	0.1482	0.680	9.565	0.607
Entangled-QCBM	QPU	96.88	97.17	0.1520	0.680	9.548	0.607

Appendix

Table 14: Real-QPU inference on the first eight MovingMNIST test observations, using the first trained model of each circuit family. GPU and QPU rows both use 128 actual draws per observation; each circuit-family pair shares its frozen neural networks. Coverage and validity are percentages; ADE and ES are in pixels. These are single-model deployment results, not means across independent trainings.

Sampling / layout	Cov. $\uparrow$	Valid $\uparrow$	TV $\downarrow$	minADE $\downarrow$	ES $\downarrow$
Ideal sampling	99.91	98.41	0.166	0.218	34.38
QPU: original layout	99.05	76.88	0.308	0.238	34.99
QPU: selected layout	98.78	81.53	0.280	0.241	34.86
QPU: reflected layout	99.57	86.69	0.239	0.227	34.66

Appendix

Table 15: HEP18 deployment on AGate-100: one frozen 12-qubit Entangled-QCBM checkpoint and eight observations held out from layout selection. Values average all eight disjoint 128-draw groups per observation (1,024 draws total), including the matched ideal reference. All QPU layouts use the same angles and 29 CZ gates. Coverage and validity are percentages; ADE and ES are in metres.

Prior	Sampling	Routes $\uparrow$	TV $\downarrow$
Product-QCBM	GPU (0% flips)	$9.45\,\pm\,1.82$	$0.606\,\pm\,0.076$
Product-QCBM	GPU (0.5% flips)	$8.45\,\pm\,1.93$	$0.648\,\pm\,0.081$
Product-QCBM	Real QPU	$10.00$	$0.583$
Entangled-QCBM	GPU (0% flips)	$9.30\,\pm\,1.92$	$0.613\,\pm\,0.080$
Entangled-QCBM	GPU (0.5% flips)	$9.40\,\pm\,1.85$	$0.608\,\pm\,0.077$
Entangled-QCBM	Real QPU	$13.00$	$0.458$

Appendix

Table 16: D3IL inference from the common stationary point. Each source uses 40 raw rollouts per prior. GPU rows give mean

\pm

sample s.d. over 20 sampling repetitions of the same checkpoint; each QPU row is one 40-path run. All checkpoints use noisy parameter-shift training. Routes (out of 24) and TV are computed within geometrically valid paths.

Prior	GPU (0%)	GPU (0.5%)	Real QPU
Product-QCBM	$6.42\,\pm\,0.54$	$6.24\,\pm\,0.67$	$6.92$
Entangled-QCBM	$6.47\,\pm\,0.53$	$6.18\,\pm\,0.53$	$7.05$

Appendix

Table 17: D3IL route coverage standardized to eight accepted paths. Entries give the exact expected number of routes in an eight-path subset drawn uniformly without replacement from each saved valid pool. GPU means and sample s.d.s include only pools containing at least eight paths: 19/20 and 18/20 repetitions for Product-QCBM at 0% and 0.5% flips, and 19/20 and 20/20 for Entangled-QCBM. Each hardware entry describes one saved pool.

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May 25, 2026J/K move · Enter open · S save

UWM-JEPA: Predictive World Models That Imagine in Belief Space

Santosh Kumar Radha, Oktay Goktas

AgentField AI, Toronto, Canada

World Model Learning Latent Dynamics Modeling Joint-Embedding Predictive Architecture Action-Conditioned World Models

Open paper AskPDF arXiv

World models for partially observed environments must imagine multiple compatible hidden futures and steer between them under counterfactual actions. Joint Embedding Predictive Architectures (JEPAs) do this in latent space, but a vector-valued latent has no internal structure for carrying the belief over hidden continuations through blind rollout. We introduce the Unitary World Model JEPA (UWM-JEPA), a JEPA world model with a density-matrix latent on a joint system-environment space and a learned unitary predictor. The construction preserves the joint-state spectrum exactly during rollout, so the predictor itself cannot dissipate the represented uncertainty. On a hidden-velocity indicator task requiring five-step forward simulation under a given action sequence with the target observation masked, UWM-JEPA reaches 0.77 accuracy and degrades monotonically as actions are perturbed; a parameter-matched LSTM-JEPA trained under the same counterfactual-target objective and action head collapses to majority-class accuracy (0.53) under every action condition. Under blind rollout, UWM-JEPA loses fewer than ten points of probe R^2 at short horizons while vector-latent baselines lose forty-one and sixty-eight; both nevertheless tie on a held-out context probe, locating the separation in the predictor rather than the encoder. Action sensitivity itself requires training against counterfactual rather than teacher-forced targets, a finding that applies beyond the unitary parameterisation. For JEPA world models to imagine under partial observability, latent geometry and predictor dynamics matter, not frozen context-encoding capacity alone.

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